TSTP Solution File: SEV158^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV158^5 : 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 16:02:03 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV158^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:42:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.12/0.37 % (23360)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (23355)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)
% 0.12/0.37 % (23354)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (23357)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (23358)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)
% 0.12/0.38 % (23359)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)
% 0.12/0.38 % (23356)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)
% 0.12/0.38 % (23360)Instruction limit reached!
% 0.12/0.38 % (23360)------------------------------
% 0.12/0.38 % (23360)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (23360)Termination reason: Unknown
% 0.12/0.38 % (23360)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (23360)Memory used [KB]: 5628
% 0.12/0.38 % (23360)Time elapsed: 0.009 s
% 0.12/0.38 % (23360)Instructions burned: 21 (million)
% 0.12/0.38 % (23360)------------------------------
% 0.12/0.38 % (23360)------------------------------
% 0.12/0.38 % (23357)Instruction limit reached!
% 0.12/0.38 % (23357)------------------------------
% 0.12/0.38 % (23357)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (23357)Termination reason: Unknown
% 0.12/0.38 % (23357)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (23357)Memory used [KB]: 5500
% 0.12/0.38 % (23357)Time elapsed: 0.004 s
% 0.12/0.38 % (23357)Instructions burned: 2 (million)
% 0.12/0.38 % (23357)------------------------------
% 0.12/0.38 % (23357)------------------------------
% 0.12/0.38 % (23358)Instruction limit reached!
% 0.12/0.38 % (23358)------------------------------
% 0.12/0.38 % (23358)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (23358)Termination reason: Unknown
% 0.12/0.38 % (23358)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (23358)Memory used [KB]: 895
% 0.12/0.38 % (23358)Time elapsed: 0.003 s
% 0.12/0.38 % (23358)Instructions burned: 2 (million)
% 0.12/0.38 % (23358)------------------------------
% 0.12/0.38 % (23358)------------------------------
% 0.12/0.38 % (23355)Instruction limit reached!
% 0.12/0.38 % (23355)------------------------------
% 0.12/0.38 % (23355)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (23355)Termination reason: Unknown
% 0.12/0.38 % (23355)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (23355)Memory used [KB]: 5500
% 0.12/0.38 % (23355)Time elapsed: 0.005 s
% 0.12/0.38 % (23355)Instructions burned: 4 (million)
% 0.12/0.38 % (23355)------------------------------
% 0.12/0.38 % (23355)------------------------------
% 0.12/0.38 % (23356)Refutation not found, incomplete strategy
% 0.12/0.38 % (23356)------------------------------
% 0.12/0.38 % (23356)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (23356)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 % (23356)Memory used [KB]: 5500
% 0.12/0.38 % (23356)Time elapsed: 0.006 s
% 0.12/0.38 % (23356)Instructions burned: 5 (million)
% 0.12/0.38 % (23356)------------------------------
% 0.12/0.38 % (23356)------------------------------
% 0.12/0.38 % (23368)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)
% 0.12/0.39 % (23368)Instruction limit reached!
% 0.12/0.39 % (23368)------------------------------
% 0.12/0.39 % (23368)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (23368)Termination reason: Unknown
% 0.12/0.39 % (23368)Termination phase: Saturation
% 0.12/0.39
% 0.12/0.39 % (23368)Memory used [KB]: 5500
% 0.12/0.39 % (23368)Time elapsed: 0.003 s
% 0.12/0.39 % (23368)Instructions burned: 4 (million)
% 0.12/0.39 % (23368)------------------------------
% 0.12/0.39 % (23368)------------------------------
% 0.12/0.39 % (23370)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)
% 0.12/0.39 % (23371)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)
% 0.12/0.39 % (23372)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)
% 0.12/0.39 % (23359)Refutation not found, incomplete strategy
% 0.12/0.39 % (23359)------------------------------
% 0.12/0.39 % (23359)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (23359)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 % (23359)Memory used [KB]: 5628
% 0.12/0.39 % (23359)Time elapsed: 0.021 s
% 0.12/0.39 % (23359)Instructions burned: 29 (million)
% 0.12/0.39 % (23359)------------------------------
% 0.12/0.39 % (23359)------------------------------
% 0.12/0.39 % (23377)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.12/0.40 % (23374)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.40 % (23372)Instruction limit reached!
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.40 % (23372)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (23372)Termination reason: Unknown
% 0.21/0.40 % (23372)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (23372)Memory used [KB]: 5500
% 0.21/0.40 % (23372)Time elapsed: 0.005 s
% 0.21/0.40 % (23372)Instructions burned: 3 (million)
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.40 % (23372)------------------------------
% 0.21/0.40 % (23377)Instruction limit reached!
% 0.21/0.40 % (23377)------------------------------
% 0.21/0.40 % (23377)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (23377)Termination reason: Unknown
% 0.21/0.40 % (23377)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (23377)Memory used [KB]: 1023
% 0.21/0.40 % (23377)Time elapsed: 0.004 s
% 0.21/0.40 % (23377)Instructions burned: 7 (million)
% 0.21/0.40 % (23377)------------------------------
% 0.21/0.40 % (23377)------------------------------
% 0.21/0.40 % (23371)First to succeed.
% 0.21/0.41 % (23371)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% 0.21/0.41 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $o) > $o).
% 0.21/0.41 thf(func_def_4, type, sP1: (($i > $o) > ($i > $o) > $o) > $o).
% 0.21/0.41 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $o) > $i).
% 0.21/0.41 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 0.21/0.41 thf(func_def_13, type, ph10: !>[X0: $tType]:(X0)).
% 0.21/0.41 thf(f218,plain,(
% 0.21/0.41 $false),
% 0.21/0.41 inference(avatar_sat_refutation,[],[f64,f74,f128,f148,f153,f158,f183,f192,f198,f199,f204,f208,f214])).
% 0.21/0.41 thf(f214,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 0.21/0.41 introduced(theory_tautology_sat_conflict,[])).
% 0.21/0.41 thf(f208,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $false) | ($false != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 0.21/0.41 introduced(theory_tautology_sat_conflict,[])).
% 0.21/0.41 thf(f204,plain,(
% 0.21/0.41 ($false != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $false) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 0.21/0.41 introduced(theory_tautology_sat_conflict,[])).
% 0.21/0.41 thf(f199,plain,(
% 0.21/0.41 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(theory_tautology_sat_conflict,[])).
% 0.21/0.41 thf(f198,plain,(
% 0.21/0.41 spl9_21 | ~spl9_4),
% 0.21/0.41 inference(avatar_split_clause,[],[f168,f61,f194])).
% 0.21/0.41 thf(f194,plain,(
% 0.21/0.41 spl9_21 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_21])])).
% 0.21/0.41 thf(f61,plain,(
% 0.21/0.41 spl9_4 <=> ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_4])])).
% 0.21/0.41 thf(f168,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_4),
% 0.21/0.41 inference(equality_proxy_clausification,[],[f167])).
% 0.21/0.41 thf(f167,plain,(
% 0.21/0.41 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_4),
% 0.21/0.41 inference(beta_eta_normalization,[],[f166])).
% 0.21/0.41 thf(f166,plain,(
% 0.21/0.41 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f165])).
% 0.21/0.41 thf(f165,plain,(
% 0.21/0.41 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_4),
% 0.21/0.41 inference(superposition,[],[f23,f63])).
% 0.21/0.41 thf(f63,plain,(
% 0.21/0.41 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_4),
% 0.21/0.41 inference(avatar_component_clause,[],[f61])).
% 0.21/0.41 thf(f23,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK3 @ X0) @ (sK2 @ X0)) = $true) | ($true != (sP1 @ X0))) )),
% 0.21/0.41 inference(cnf_transformation,[],[f14])).
% 0.21/0.41 thf(f14,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0))) & ((X0 @ (sK3 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)) | ($true != (sP1 @ X0)))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f11,f13,f12])).
% 0.21/0.41 thf(f12,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) => (? [X3] : ((sK3 @ X0 @ X3) != (sK2 @ X0 @ X3)) & ((X0 @ (sK3 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) = $true)))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f13,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3] : ((sK3 @ X0 @ X3) != (sK2 @ X0 @ X3)) => ((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0))))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f11,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) | ($true != (sP1 @ X0)))),
% 0.21/0.41 inference(nnf_transformation,[],[f9])).
% 0.21/0.41 thf(f9,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) | ~($true = (sP1 @ X0)))),
% 0.21/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.41 thf(f192,plain,(
% 0.21/0.41 spl9_19 | spl9_20 | ~spl9_4),
% 0.21/0.41 inference(avatar_split_clause,[],[f174,f61,f189,f185])).
% 0.21/0.41 thf(f185,plain,(
% 0.21/0.41 spl9_19 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_19])])).
% 0.21/0.41 thf(f189,plain,(
% 0.21/0.41 spl9_20 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_20])])).
% 0.21/0.41 thf(f174,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $false) | ~spl9_4),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f172])).
% 0.21/0.41 thf(f172,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_4),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f163])).
% 0.21/0.41 thf(f163,plain,(
% 0.21/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_4),
% 0.21/0.41 inference(superposition,[],[f24,f63])).
% 0.21/0.41 thf(f24,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP1 @ X0)) | ((sK3 @ X0 @ (sK4 @ X0)) != (sK2 @ X0 @ (sK4 @ X0)))) )),
% 0.21/0.41 inference(cnf_transformation,[],[f14])).
% 0.21/0.41 thf(f183,plain,(
% 0.21/0.41 spl9_17 | spl9_18 | ~spl9_4),
% 0.21/0.41 inference(avatar_split_clause,[],[f173,f61,f180,f176])).
% 0.21/0.41 thf(f176,plain,(
% 0.21/0.41 spl9_17 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_17])])).
% 0.21/0.41 thf(f180,plain,(
% 0.21/0.41 spl9_18 <=> ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_18])])).
% 0.21/0.41 thf(f173,plain,(
% 0.21/0.41 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_4),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f172])).
% 0.21/0.41 thf(f158,plain,(
% 0.21/0.41 ~spl9_16 | ~spl9_3),
% 0.21/0.41 inference(avatar_split_clause,[],[f137,f57,f155])).
% 0.21/0.41 thf(f155,plain,(
% 0.21/0.41 spl9_16 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_16])])).
% 0.21/0.41 thf(f57,plain,(
% 0.21/0.41 spl9_3 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_3])])).
% 0.21/0.41 thf(f137,plain,(
% 0.21/0.41 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 0.21/0.41 inference(equality_proxy_clausification,[],[f136])).
% 0.21/0.41 thf(f136,plain,(
% 0.21/0.41 (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_3),
% 0.21/0.41 inference(beta_eta_normalization,[],[f135])).
% 0.21/0.41 thf(f135,plain,(
% 0.21/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_3),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f132])).
% 0.21/0.41 thf(f132,plain,(
% 0.21/0.41 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_3),
% 0.21/0.41 inference(superposition,[],[f25,f59])).
% 0.21/0.41 thf(f59,plain,(
% 0.21/0.41 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 0.21/0.41 inference(avatar_component_clause,[],[f57])).
% 0.21/0.41 thf(f25,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (X0 @ (sK5 @ X0) @ (sK7 @ X0))) | ((sP0 @ X0) != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f18])).
% 0.21/0.41 thf(f18,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK6 @ X0) @ (sK7 @ X0)) = $true) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ($true != (X0 @ (sK5 @ X0) @ (sK7 @ X0)))) | ((sP0 @ X0) != $true))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f16,f17])).
% 0.21/0.41 thf(f17,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X3) != $true)) => (((X0 @ (sK6 @ X0) @ (sK7 @ X0)) = $true) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true) & ($true != (X0 @ (sK5 @ X0) @ (sK7 @ X0)))))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f16,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X2 @ X3) = $true) & ((X0 @ X1 @ X2) = $true) & ((X0 @ X1 @ X3) != $true)) | ((sP0 @ X0) != $true))),
% 0.21/0.41 inference(rectify,[],[f15])).
% 0.21/0.41 thf(f15,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) = $true) & ($true = (X0 @ X6 @ X5)) & ($true != (X0 @ X6 @ X4))) | ((sP0 @ X0) != $true))),
% 0.21/0.41 inference(nnf_transformation,[],[f8])).
% 0.21/0.41 thf(f8,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) = $true) & ($true = (X0 @ X6 @ X5)) & ($true != (X0 @ X6 @ X4))) | ~((sP0 @ X0) = $true))),
% 0.21/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.21/0.41 thf(f153,plain,(
% 0.21/0.41 spl9_15 | ~spl9_3),
% 0.21/0.41 inference(avatar_split_clause,[],[f140,f57,f150])).
% 0.21/0.41 thf(f150,plain,(
% 0.21/0.41 spl9_15 <=> ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_15])])).
% 0.21/0.41 thf(f140,plain,(
% 0.21/0.41 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 0.21/0.41 inference(equality_proxy_clausification,[],[f139])).
% 0.21/0.41 thf(f139,plain,(
% 0.21/0.41 (((sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_3),
% 0.21/0.41 inference(beta_eta_normalization,[],[f138])).
% 0.21/0.41 thf(f138,plain,(
% 0.21/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_3),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f133])).
% 0.21/0.41 thf(f133,plain,(
% 0.21/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl9_3),
% 0.21/0.41 inference(superposition,[],[f27,f59])).
% 0.21/0.41 thf(f27,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK6 @ X0) @ (sK7 @ X0)) = $true) | ((sP0 @ X0) != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f18])).
% 0.21/0.41 thf(f148,plain,(
% 0.21/0.41 spl9_14 | ~spl9_3),
% 0.21/0.41 inference(avatar_split_clause,[],[f143,f57,f145])).
% 0.21/0.41 thf(f145,plain,(
% 0.21/0.41 spl9_14 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_14])])).
% 0.21/0.41 thf(f143,plain,(
% 0.21/0.41 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_3),
% 0.21/0.41 inference(equality_proxy_clausification,[],[f142])).
% 0.21/0.41 thf(f142,plain,(
% 0.21/0.41 (((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_3),
% 0.21/0.41 inference(beta_eta_normalization,[],[f141])).
% 0.21/0.41 thf(f141,plain,(
% 0.21/0.41 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_3),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f134])).
% 0.21/0.41 thf(f134,plain,(
% 0.21/0.41 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true != $true) | ~spl9_3),
% 0.21/0.41 inference(superposition,[],[f26,f59])).
% 0.21/0.41 thf(f26,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP0 @ X0) != $true) | ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f18])).
% 0.21/0.41 thf(f128,plain,(
% 0.21/0.41 spl9_13 | spl9_2),
% 0.21/0.41 inference(avatar_split_clause,[],[f123,f52,f125])).
% 0.21/0.41 thf(f125,plain,(
% 0.21/0.41 spl9_13 <=> ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_13])])).
% 0.21/0.41 thf(f52,plain,(
% 0.21/0.41 spl9_2 <=> ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))),
% 0.21/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_2])])).
% 0.21/0.41 thf(f123,plain,(
% 0.21/0.41 ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | spl9_2),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f122])).
% 0.21/0.41 thf(f122,plain,(
% 0.21/0.41 ($false = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($true != $true) | spl9_2),
% 0.21/0.41 inference(fool_paramodulation,[],[f53])).
% 0.21/0.41 thf(f53,plain,(
% 0.21/0.41 ($true != (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | spl9_2),
% 0.21/0.41 inference(avatar_component_clause,[],[f52])).
% 0.21/0.41 thf(f74,plain,(
% 0.21/0.41 ~spl9_2),
% 0.21/0.41 inference(avatar_contradiction_clause,[],[f73])).
% 0.21/0.41 thf(f73,plain,(
% 0.21/0.41 $false | ~spl9_2),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f72])).
% 0.21/0.41 thf(f72,plain,(
% 0.21/0.41 ($true != $true) | ~spl9_2),
% 0.21/0.41 inference(beta_eta_normalization,[],[f71])).
% 0.21/0.41 thf(f71,plain,(
% 0.21/0.41 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ~spl9_2),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.41 thf(f66,plain,(
% 0.21/0.41 ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))) | ($true != $true) | ~spl9_2),
% 0.21/0.41 inference(superposition,[],[f25,f54])).
% 0.21/0.41 thf(f54,plain,(
% 0.21/0.41 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ~spl9_2),
% 0.21/0.41 inference(avatar_component_clause,[],[f52])).
% 0.21/0.41 thf(f64,plain,(
% 0.21/0.41 spl9_3 | spl9_4),
% 0.21/0.41 inference(avatar_split_clause,[],[f44,f61,f57])).
% 0.21/0.41 thf(f44,plain,(
% 0.21/0.41 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f43])).
% 0.21/0.41 thf(f43,plain,(
% 0.21/0.41 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true != $true)),
% 0.21/0.41 inference(boolean_simplification,[],[f42])).
% 0.21/0.41 thf(f42,plain,(
% 0.21/0.41 ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true != ((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f30])).
% 0.21/0.41 thf(f30,plain,(
% 0.21/0.41 ($true = (sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($true = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 0.21/0.41 inference(primitive_instantiation,[],[f28])).
% 0.21/0.41 thf(f28,plain,(
% 0.21/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ($true = (sP1 @ X0)) | ((sP0 @ X0) = $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f21])).
% 0.21/0.41 thf(f21,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ($true = (sP1 @ X0)) | ((sP0 @ X0) = $true))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20])).
% 0.21/0.41 thf(f20,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f19,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ($true = (sP1 @ X0)) | ((sP0 @ X0) = $true))),
% 0.21/0.41 inference(rectify,[],[f10])).
% 0.21/0.41 thf(f10,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X7 : $i > $o] : ((X0 @ X7 @ X7) != $true) | ($true = (sP1 @ X0)) | ((sP0 @ X0) = $true))),
% 0.21/0.41 inference(definition_folding,[],[f7,f9,f8])).
% 0.21/0.41 thf(f7,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X7 : $i > $o] : ((X0 @ X7 @ X7) != $true) | ? [X1 : $i > $o,X2 : $i > $o] : (? [X3] : ((X1 @ X3) != (X2 @ X3)) & ((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) | ? [X6 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X5 @ X4) = $true) & ($true = (X0 @ X6 @ X5)) & ($true != (X0 @ X6 @ X4))))),
% 0.21/0.41 inference(flattening,[],[f6])).
% 0.21/0.41 thf(f6,plain,(
% 0.21/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (($true != (X0 @ X6 @ X4)) & (($true = (X0 @ X6 @ X5)) & ((X0 @ X5 @ X4) = $true))) | ? [X2 : $i > $o,X1 : $i > $o] : (? [X3] : ((X1 @ X3) != (X2 @ X3)) & (((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true))) | ? [X7 : $i > $o] : ((X0 @ X7 @ X7) != $true))),
% 0.21/0.41 inference(ennf_transformation,[],[f5])).
% 0.21/0.41 thf(f5,plain,(
% 0.21/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X6 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((($true = (X0 @ X6 @ X5)) & ((X0 @ X5 @ X4) = $true)) => ($true = (X0 @ X6 @ X4))) & ! [X2 : $i > $o,X1 : $i > $o] : ((((X0 @ X2 @ X1) = $true) & ((X0 @ X1 @ X2) = $true)) => ! [X3] : ((X1 @ X3) = (X2 @ X3))) & ! [X7 : $i > $o] : ((X0 @ X7 @ X7) = $true))),
% 0.21/0.41 inference(fool_elimination,[],[f4])).
% 0.21/0.41 thf(f4,plain,(
% 0.21/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3] : ((X1 @ X3) = (X2 @ X3))) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X5) & (X0 @ X5 @ X4)) => (X0 @ X6 @ X4)) & ! [X7 : $i > $o] : (X0 @ X7 @ X7))),
% 0.21/0.41 inference(rectify,[],[f2])).
% 0.21/0.41 thf(f2,negated_conjecture,(
% 0.21/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1] : ((X4 @ X1) = (X5 @ X1))) & ! [X3 : $i > $o,X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 0.21/0.41 inference(negated_conjecture,[],[f1])).
% 0.21/0.41 thf(f1,conjecture,(
% 0.21/0.41 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) & (X0 @ X4 @ X5)) => ! [X1] : ((X4 @ X1) = (X5 @ X1))) & ! [X3 : $i > $o,X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)) & ! [X1 : $i > $o] : (X0 @ X1 @ X1))),
% 0.21/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120I_1_pme)).
% 0.21/0.41 % SZS output end Proof for theBenchmark
% 0.21/0.41 % (23371)------------------------------
% 0.21/0.41 % (23371)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.41 % (23371)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (23371)Memory used [KB]: 5756
% 0.21/0.41 % (23371)Time elapsed: 0.014 s
% 0.21/0.41 % (23371)Instructions burned: 10 (million)
% 0.21/0.41 % (23371)------------------------------
% 0.21/0.41 % (23371)------------------------------
% 0.21/0.41 % (23351)Success in time 0.042 s
%------------------------------------------------------------------------------