0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_vampire %s %d THM 0.12/0.33 % Computer : n023.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 : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 02:39:19 EDT 2025 0.12/0.33 % CPUTime : 0.12/0.35 This is a THF_ problem 0.12/0.35 Running higher-order theorem proving 0.12/0.35 Running /export/starexec/sandbox/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.hKZP40va1h/E---3.1_10872.p -m 16384 -t 240 0.12/0.38 % (10982)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 E---3.1_10872 for (2399ds/27Mi) 0.12/0.38 % (10983)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/2Mi) 0.12/0.38 % (10980)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/183Mi) 0.12/0.38 % (10981)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 E---3.1_10872 for (2399ds/4Mi) 0.12/0.38 % (10984)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/2Mi) 0.12/0.38 % (10985)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/275Mi) 0.12/0.38 % (10986)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/18Mi) 0.12/0.38 % (10983)Instruction limit reached! 0.12/0.38 % (10983)------------------------------ 0.12/0.38 % (10983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.38 % (10983)Termination reason: Unknown 0.12/0.38 % (10984)Instruction limit reached! 0.12/0.38 % (10984)------------------------------ 0.12/0.38 % (10984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.38 % (10983)Termination phase: Preprocessing 3 0.12/0.38 0.12/0.38 % (10983)Memory used [KB]: 895 0.12/0.38 % (10983)Time elapsed: 0.003 s 0.12/0.38 % (10983)Instructions burned: 2 (million) 0.12/0.38 % (10983)------------------------------ 0.12/0.38 % (10983)------------------------------ 0.12/0.38 % (10984)Termination reason: Unknown 0.12/0.38 % (10984)Termination phase: Preprocessing 1 0.12/0.38 0.12/0.38 % (10984)Memory used [KB]: 1023 0.12/0.38 % (10984)Time elapsed: 0.003 s 0.12/0.38 % (10984)Instructions burned: 2 (million) 0.12/0.38 % (10984)------------------------------ 0.12/0.38 % (10984)------------------------------ 0.12/0.38 % (10981)Instruction limit reached! 0.12/0.38 % (10981)------------------------------ 0.12/0.38 % (10981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.38 % (10981)Termination reason: Unknown 0.12/0.38 % (10981)Termination phase: Saturation 0.12/0.38 0.12/0.38 % (10981)Memory used [KB]: 5500 0.12/0.38 % (10981)Time elapsed: 0.005 s 0.12/0.38 % (10981)Instructions burned: 5 (million) 0.12/0.38 % (10981)------------------------------ 0.12/0.38 % (10981)------------------------------ 0.12/0.38 % (10982)Refutation not found, incomplete strategy 0.12/0.38 % (10982)------------------------------ 0.12/0.38 % (10982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.38 % (10982)Termination reason: Refutation not found, incomplete strategy 0.12/0.38 0.12/0.38 0.12/0.38 % (10982)Memory used [KB]: 5500 0.12/0.38 % (10982)Time elapsed: 0.007 s 0.12/0.38 % (10982)Instructions burned: 6 (million) 0.12/0.38 % (10982)------------------------------ 0.12/0.38 % (10982)------------------------------ 0.12/0.39 % (10986)Instruction limit reached! 0.12/0.39 % (10986)------------------------------ 0.12/0.39 % (10986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (10986)Termination reason: Unknown 0.12/0.39 % (10986)Termination phase: Saturation 0.12/0.39 0.12/0.39 % (10986)Memory used [KB]: 5628 0.12/0.39 % (10986)Time elapsed: 0.013 s 0.12/0.39 % (10986)Instructions burned: 19 (million) 0.12/0.39 % (10986)------------------------------ 0.12/0.39 % (10986)------------------------------ 0.12/0.39 % (10987)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/3Mi) 0.12/0.39 % (10988)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 E---3.1_10872 for (2399ds/37Mi) 0.12/0.40 % (10987)Instruction limit reached! 0.12/0.40 % (10987)------------------------------ 0.12/0.40 % (10987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (10987)Termination reason: Unknown 0.12/0.40 % (10987)Termination phase: Saturation 0.12/0.40 0.12/0.40 % (10989)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 E---3.1_10872 for (2399ds/15Mi) 0.12/0.40 % (10987)Memory used [KB]: 5500 0.12/0.40 % (10987)Time elapsed: 0.004 s 0.12/0.40 % (10987)Instructions burned: 4 (million) 0.12/0.40 % (10987)------------------------------ 0.12/0.40 % (10987)------------------------------ 0.21/0.40 % (10990)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/3Mi) 0.21/0.40 % (10990)Instruction limit reached! 0.21/0.40 % (10990)------------------------------ 0.21/0.40 % (10990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.40 % (10990)Termination reason: Unknown 0.21/0.40 % (10990)Termination phase: Saturation 0.21/0.40 0.21/0.40 % (10990)Memory used [KB]: 5500 0.21/0.40 % (10990)Time elapsed: 0.004 s 0.21/0.40 % (10990)Instructions burned: 4 (million) 0.21/0.40 % (10990)------------------------------ 0.21/0.40 % (10990)------------------------------ 0.21/0.40 % (10991)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 E---3.1_10872 for (2399ds/1041Mi) 0.21/0.41 % (10989)Instruction limit reached! 0.21/0.41 % (10989)------------------------------ 0.21/0.41 % (10989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.41 % (10989)Termination reason: Unknown 0.21/0.41 % (10989)Termination phase: Saturation 0.21/0.41 0.21/0.41 % (10989)Memory used [KB]: 5628 0.21/0.41 % (10989)Time elapsed: 0.012 s 0.21/0.41 % (10989)Instructions burned: 16 (million) 0.21/0.41 % (10989)------------------------------ 0.21/0.41 % (10989)------------------------------ 0.21/0.41 % (10992)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/7Mi) 0.21/0.41 % (10988)Instruction limit reached! 0.21/0.41 % (10988)------------------------------ 0.21/0.41 % (10988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.41 % (10988)Termination reason: Unknown 0.21/0.41 % (10988)Termination phase: Saturation 0.21/0.41 0.21/0.41 % (10988)Memory used [KB]: 5756 0.21/0.41 % (10988)Time elapsed: 0.022 s 0.21/0.41 % (10988)Instructions burned: 37 (million) 0.21/0.41 % (10988)------------------------------ 0.21/0.41 % (10988)------------------------------ 0.21/0.41 % (10985)First to succeed. 0.21/0.42 % (10992)Instruction limit reached! 0.21/0.42 % (10992)------------------------------ 0.21/0.42 % (10992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.42 % (10992)Termination reason: Unknown 0.21/0.42 % (10992)Termination phase: Saturation 0.21/0.42 0.21/0.42 % (10992)Memory used [KB]: 1023 0.21/0.42 % (10992)Time elapsed: 0.006 s 0.21/0.42 % (10992)Instructions burned: 7 (million) 0.21/0.42 % (10992)------------------------------ 0.21/0.42 % (10992)------------------------------ 0.21/0.42 % (10993)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_10872 for (2399ds/16Mi) 0.21/0.42 % (10985)Refutation found. Thanks to Tanya! 0.21/0.42 % SZS status Theorem for E---3.1_10872 0.21/0.42 % SZS output start Proof for E---3.1_10872 0.21/0.42 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.21/0.42 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.21/0.42 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.21/0.42 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i). 0.21/0.42 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.21/0.42 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i). 0.21/0.42 thf(func_def_11, type, ph7: !>[X0: $tType]:(X0)). 0.21/0.42 thf(func_def_18, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i). 0.21/0.42 thf(func_def_19, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i). 0.21/0.42 thf(f352,plain,( 0.21/0.42 $false), 0.21/0.42 inference(avatar_sat_refutation,[status(thm)],[f53,f79,f351])). 0.21/0.42 thf(f351,plain,( 0.21/0.42 ~spl6_1 | spl6_2), 0.21/0.42 inference(avatar_contradiction_clause,[status(thm)],[f350])). 0.21/0.42 thf(f350,plain,( 0.21/0.42 $false | (~spl6_1 | spl6_2)), 0.21/0.42 inference(subsumption_resolution,[status(thm)],[f336,f294])). 0.21/0.42 thf(f294,plain,( 0.21/0.42 ((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)))))))) | (~spl6_1 | spl6_2)), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f293])). 0.21/0.42 thf(f293,plain,( 0.21/0.42 ((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)))))))) | ($false = $true) | (~spl6_1 | spl6_2)), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f290])). 0.21/0.42 thf(f290,plain,( 0.21/0.42 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0)) | ((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))))))))) ) | (~spl6_1 | spl6_2)), 0.21/0.42 inference(superposition,[status(thm)],[f48,f286])). 0.21/0.42 thf(f286,plain,( 0.21/0.42 ((sK2 @ (^[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)))))))) | spl6_2), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f285])). 0.21/0.42 thf(f285,plain,( 0.21/0.42 ((sK2 @ (^[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)))))))) | ($false = $true) | spl6_2), 0.21/0.42 inference(duplicate_literal_removal,[status(thm)],[f284])). 0.21/0.42 thf(f284,plain,( 0.21/0.42 ($false = $true) | ((sK2 @ (^[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)))))))) | ($false = $true) | spl6_2), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f268])). 0.21/0.42 thf(f268,plain,( 0.21/0.42 ( ! [X8 : $i,X7 : $i] : (($true = ((^[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))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X7)) | ((sK2 @ (^[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)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | spl6_2), 0.21/0.42 inference(primitive_instantiation,[status(thm)],[f156])). 0.21/0.42 thf(f156,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | spl6_2), 0.21/0.42 inference(subsumption_resolution,[status(thm)],[f151,f51])). 0.21/0.42 thf(f51,plain,( 0.21/0.42 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2), 0.21/0.42 inference(avatar_component_clause,[status(thm)],[f50])). 0.21/0.42 thf(f50,definition,( 0.21/0.42 spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))), 0.21/0.42 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])). 0.21/0.42 thf(f151,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f150])). 0.21/0.42 thf(f150,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f149])). 0.21/0.42 thf(f149,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f148])). 0.21/0.42 thf(f148,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true)) )), 0.21/0.42 inference(boolean_simplification,[status(thm)],[f147])). 0.21/0.42 thf(f147,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : ((((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f131])). 0.21/0.42 thf(f131,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8))) )), 0.21/0.42 inference(primitive_instantiation,[status(thm)],[f13])). 0.21/0.42 thf(f13,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X7 : $i] : (($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true)) )), 0.21/0.42 inference(cnf_transformation,[status(thm)],[f12])). 0.21/0.42 thf(f12,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((! [X5 : $i] : (($true = (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5)) | ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5) = $true)) & (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ! [X7 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true))) | ! [X8 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) | (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))), 0.21/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])). 0.21/0.42 thf(f9,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (! [X5 : $i] : (($true = (X0 @ X2 @ X3 @ X5)) | ($true = (X1 @ X2 @ X3 @ X5))) & ? [X6 : $i] : (($true != (X0 @ X2 @ X4 @ X6)) & ($true != (X1 @ X2 @ X4 @ X6))) & ! [X7 : $i] : (((X1 @ X3 @ X4 @ X7) = $true) | ($true = (X0 @ X3 @ X4 @ X7)))) => (! [X5 : $i] : (($true = (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5)) | ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5) = $true)) & ? [X6 : $i] : (($true != (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) & ! [X7 : $i] : (($true = (X1 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X7) = $true))))), 0.21/0.42 introduced(definition,[],[choice_axiom])). 0.21/0.42 thf(f10,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X6 : $i] : (($true != (X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6)) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X6))) => (((X0 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))))), 0.21/0.42 introduced(definition,[],[choice_axiom])). 0.21/0.42 thf(f11,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i > $o,X10 : $i] : (($true != (X0 @ X9 @ X9 @ X10)) & ((X1 @ X9 @ X9 @ X10) != $true)) => (($true != (X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)))))), 0.21/0.42 introduced(definition,[],[choice_axiom])). 0.21/0.42 thf(f8,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : (! [X5 : $i] : (($true = (X0 @ X2 @ X3 @ X5)) | ($true = (X1 @ X2 @ X3 @ X5))) & ? [X6 : $i] : (($true != (X0 @ X2 @ X4 @ X6)) & ($true != (X1 @ X2 @ X4 @ X6))) & ! [X7 : $i] : (((X1 @ X3 @ X4 @ X7) = $true) | ($true = (X0 @ X3 @ X4 @ X7)))) | ! [X8 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) | ? [X9 : $i > $o,X10 : $i] : (($true != (X0 @ X9 @ X9 @ X10)) & ((X1 @ X9 @ X9 @ X10) != $true)))), 0.21/0.42 inference(rectify,[status(thm)],[f7])). 0.21/0.42 thf(f7,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (! [X7 : $i] : (($true = (X0 @ X4 @ X5 @ X7)) | ($true = (X1 @ X4 @ X5 @ X7))) & ? [X9 : $i] : (($true != (X0 @ X4 @ X6 @ X9)) & ($true != (X1 @ X4 @ X6 @ X9))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X6 @ X8)) | ($true = (X0 @ X5 @ X6 @ X8)))) | ! [X10 : $i] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X3 : $i > $o,X2 : $i] : (($true != (X0 @ X3 @ X3 @ X2)) & ($true != (X1 @ X3 @ X3 @ X2))))), 0.21/0.42 inference(flattening,[status(thm)],[f6])). 0.21/0.42 thf(f6,plain,( 0.21/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X2 : $i] : (($true != (X0 @ X3 @ X3 @ X2)) & ($true != (X1 @ X3 @ X3 @ X2))) | ! [X10 : $i] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (? [X9 : $i] : (($true != (X0 @ X4 @ X6 @ X9)) & ($true != (X1 @ X4 @ X6 @ X9))) & (! [X7 : $i] : (($true = (X0 @ X4 @ X5 @ X7)) | ($true = (X1 @ X4 @ X5 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X6 @ X8)) | ($true = (X0 @ X5 @ X6 @ X8))))))), 0.21/0.42 inference(ennf_transformation,[status(thm)],[f5])). 0.21/0.42 thf(f5,plain,( 0.21/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3 : $i > $o,X2 : $i] : (($true = (X0 @ X3 @ X3 @ X2)) | ($true = (X1 @ X3 @ X3 @ X2))) & ~! [X10 : $i] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) & ! [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : ((! [X7 : $i] : (($true = (X0 @ X4 @ X5 @ X7)) | ($true = (X1 @ X4 @ X5 @ X7))) & ! [X8 : $i] : (($true = (X1 @ X5 @ X6 @ X8)) | ($true = (X0 @ X5 @ X6 @ X8)))) => ! [X9 : $i] : (($true = (X0 @ X4 @ X6 @ X9)) | ($true = (X1 @ X4 @ X6 @ X9)))))), 0.21/0.42 inference(fool_elimination,[status(thm)],[f4])). 0.21/0.42 thf(f4,plain,( 0.21/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i,X3 : $i > $o] : ((X0 @ X3 @ X3 @ X2) | (X1 @ X3 @ X3 @ X2)) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((! [X7 : $i] : ((X0 @ X4 @ X5 @ X7) | (X1 @ X4 @ X5 @ X7)) & ! [X8 : $i] : ((X0 @ X5 @ X6 @ X8) | (X1 @ X5 @ X6 @ X8))) => ! [X9 : $i] : ((X1 @ X4 @ X6 @ X9) | (X0 @ X4 @ X6 @ X9))) & ~! [X10 : $i] : ((X1 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X0 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))), 0.21/0.42 inference(rectify,[status(thm)],[f2])). 0.21/0.42 thf(f2,negated_conjecture,( 0.21/0.42 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3 : $i,X2 : $i > $o] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X2 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((! [X3 : $i] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X1 @ X4 @ X5 @ X3) | (X0 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3 : $i] : ((X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))), 0.21/0.42 inference(negated_conjecture,[status(cth)],[f1])). 0.21/0.42 thf(f1,conjecture,( 0.21/0.42 ? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3 : $i,X2 : $i > $o] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)) & ! [X2 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((! [X3 : $i] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3 : $i] : ((X1 @ X4 @ X5 @ X3) | (X0 @ X4 @ X5 @ X3))) => ! [X3 : $i] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3 : $i] : ((X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))), 0.21/0.42 file('/export/starexec/sandbox/tmp/tmp.hKZP40va1h/E---3.1_10872.p',cTHM120D_pme)). 0.21/0.42 thf(f48,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | ~spl6_1), 0.21/0.42 inference(avatar_component_clause,[status(thm)],[f47])). 0.21/0.42 thf(f47,definition,( 0.21/0.42 spl6_1 <=> ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true))), 0.21/0.42 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])). 0.21/0.42 thf(f336,plain,( 0.21/0.42 ((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)))))))) | spl6_2), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f335])). 0.21/0.42 thf(f335,plain,( 0.21/0.42 ($false = $true) | ((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)))))))) | spl6_2), 0.21/0.42 inference(duplicate_literal_removal,[status(thm)],[f334])). 0.21/0.42 thf(f334,plain,( 0.21/0.42 ($false = $true) | ((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)))))))) | ($false = $true) | spl6_2), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f332])). 0.21/0.42 thf(f332,plain,( 0.21/0.42 ( ! [X8 : $i,X5 : $i] : (((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)))))))) | (((^[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))))))) @ X5) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | spl6_2), 0.21/0.42 inference(primitive_instantiation,[status(thm)],[f211])). 0.21/0.42 thf(f211,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (((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) @ X5) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) ) | spl6_2), 0.21/0.42 inference(subsumption_resolution,[status(thm)],[f210,f51])). 0.21/0.42 thf(f210,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((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) @ X5) = $true)) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f209])). 0.21/0.42 thf(f209,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((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) @ X5) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f208])). 0.21/0.42 thf(f208,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((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) @ X5) = $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f207])). 0.21/0.42 thf(f207,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((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) @ X5) = $true)) )), 0.21/0.42 inference(boolean_simplification,[status(thm)],[f206])). 0.21/0.42 thf(f206,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true = ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((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) @ X5) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f186])). 0.21/0.42 thf(f186,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X5) = $true) | ((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) @ X5) = $true)) )), 0.21/0.42 inference(primitive_instantiation,[status(thm)],[f19])). 0.21/0.42 thf(f19,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X5 : $i] : (($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X1 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5) = $true) | ($true = (X0 @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X5)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )), 0.21/0.42 inference(cnf_transformation,[status(thm)],[f12])). 0.21/0.42 thf(f79,plain,( 0.21/0.42 ~spl6_2), 0.21/0.42 inference(avatar_contradiction_clause,[status(thm)],[f78])). 0.21/0.42 thf(f78,plain,( 0.21/0.42 $false | ~spl6_2), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f77])). 0.21/0.42 thf(f77,plain,( 0.21/0.42 ($false = $true) | ~spl6_2), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f76])). 0.21/0.42 thf(f76,plain,( 0.21/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl6_2), 0.21/0.42 inference(argument_congruence,[status(thm)],[f52])). 0.21/0.42 thf(f52,plain,( 0.21/0.42 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2), 0.21/0.42 inference(avatar_component_clause,[status(thm)],[f50])). 0.21/0.42 thf(f53,plain,( 0.21/0.42 spl6_1 | spl6_2), 0.21/0.42 inference(avatar_split_clause,[status(thm)],[f45,f50,f47])). 0.21/0.42 thf(f45,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) != (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f44])). 0.21/0.42 thf(f44,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )), 0.21/0.42 inference(equality_proxy_clausification,[status(thm)],[f43])). 0.21/0.42 thf(f43,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )), 0.21/0.42 inference(trivial_inequality_removal,[status(thm)],[f42])). 0.21/0.42 thf(f42,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )), 0.21/0.42 inference(boolean_simplification,[status(thm)],[f41])). 0.21/0.42 thf(f41,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((sK4 @ (^[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)) @ X8) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )), 0.21/0.42 inference(beta_eta_normalization,[status(thm)],[f21])). 0.21/0.42 thf(f21,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true)) )), 0.21/0.42 inference(primitive_instantiation,[status(thm)],[f15])). 0.21/0.42 thf(f15,plain,( 0.21/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != (X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X8) = $true) | ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) )), 0.21/0.42 inference(cnf_transformation,[status(thm)],[f12])). 0.21/0.42 % SZS output end Proof for E---3.1_10872 0.21/0.42 % (10985)------------------------------ 0.21/0.42 % (10985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.42 % (10985)Termination reason: Refutation 0.21/0.42 0.21/0.42 % (10985)Memory used [KB]: 5884 0.21/0.42 % (10985)Time elapsed: 0.046 s 0.21/0.42 % (10985)Instructions burned: 70 (million) 0.21/0.42 % (10985)------------------------------ 0.21/0.42 % (10985)------------------------------ 0.21/0.42 % (10979)Success in time 0.048 s 0.21/0.42 EOF