0.00/0.10 % Problem : Vampire---4.8_30202 : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.10/0.31 % Computer : n005.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 : 1440 0.10/0.31 % WCLimit : 180 0.10/0.31 % DateTime : Mon Jul 3 12:47:15 EDT 2023 0.10/0.31 % CPUTime : 0.16/0.31 This is a THF_ problem 0.16/0.31 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.ONBg3Qy975/Vampire---4.8_30202 -m 12000 -t 180 0.16/0.33 % (30313)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1800ds/385Mi) 0.16/0.33 % (30311)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1800ds/36Mi) 0.16/0.33 % (30310)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1800ds/96Mi) 0.16/0.33 % (30312)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1800ds/34Mi) 0.16/0.33 % (30314)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1800ds/17Mi) 0.16/0.33 % (30316)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1800ds/4Mi) 0.16/0.33 % (30315)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1800ds/74Mi) 0.16/0.33 % (30317)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1800ds/915Mi) 0.16/0.33 % (30316)Instruction limit reached! 0.16/0.33 % (30316)------------------------------ 0.16/0.33 % (30316)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.33 % (30316)Termination reason: Unknown 0.16/0.33 % (30316)Termination phase: Saturation 0.16/0.33 0.16/0.33 % (30316)Memory used [KB]: 5500 0.16/0.33 % (30316)Time elapsed: 0.004 s 0.16/0.33 % (30316)Instructions burned: 5 (million) 0.16/0.33 % (30316)------------------------------ 0.16/0.33 % (30316)------------------------------ 0.16/0.34 % (30314)Instruction limit reached! 0.16/0.34 % (30314)------------------------------ 0.16/0.34 % (30314)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.34 % (30314)Termination reason: Unknown 0.16/0.34 % (30314)Termination phase: Saturation 0.16/0.34 0.16/0.34 % (30314)Memory used [KB]: 5628 0.16/0.34 % (30314)Time elapsed: 0.010 s 0.16/0.34 % (30314)Instructions burned: 17 (million) 0.16/0.34 % (30314)------------------------------ 0.16/0.34 % (30314)------------------------------ 0.16/0.35 % (30312)Instruction limit reached! 0.16/0.35 % (30312)------------------------------ 0.16/0.35 % (30312)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.35 % (30312)Termination reason: Unknown 0.16/0.35 % (30312)Termination phase: Saturation 0.16/0.35 0.16/0.35 % (30312)Memory used [KB]: 5628 0.16/0.35 % (30312)Time elapsed: 0.017 s 0.16/0.35 % (30312)Instructions burned: 34 (million) 0.16/0.35 % (30312)------------------------------ 0.16/0.35 % (30312)------------------------------ 0.16/0.35 % (30311)Instruction limit reached! 0.16/0.35 % (30311)------------------------------ 0.16/0.35 % (30311)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.35 % (30311)Termination reason: Unknown 0.16/0.35 % (30318)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (1799ds/21Mi) 0.16/0.35 % (30311)Termination phase: Saturation 0.16/0.35 0.16/0.35 % (30311)Memory used [KB]: 5756 0.16/0.35 % (30311)Time elapsed: 0.018 s 0.16/0.35 % (30311)Instructions burned: 36 (million) 0.16/0.35 % (30311)------------------------------ 0.16/0.35 % (30311)------------------------------ 0.16/0.35 % (30319)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.16/0.36 % (30319)Instruction limit reached! 0.16/0.36 % (30319)------------------------------ 0.16/0.36 % (30319)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.36 % (30319)Termination reason: Unknown 0.16/0.36 % (30319)Termination phase: Saturation 0.16/0.36 0.16/0.36 % (30319)Memory used [KB]: 5500 0.16/0.36 % (30319)Time elapsed: 0.005 s 0.16/0.36 % (30319)Instructions burned: 7 (million) 0.16/0.36 % (30319)------------------------------ 0.16/0.36 % (30319)------------------------------ 0.16/0.36 % (30318)Instruction limit reached! 0.16/0.36 % (30318)------------------------------ 0.16/0.36 % (30318)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.36 % (30318)Termination reason: Unknown 0.16/0.36 % (30318)Termination phase: Saturation 0.16/0.36 0.16/0.36 % (30318)Memory used [KB]: 5628 0.16/0.36 % (30318)Time elapsed: 0.012 s 0.16/0.36 % (30318)Instructions burned: 22 (million) 0.16/0.36 % (30318)------------------------------ 0.16/0.36 % (30318)------------------------------ 0.16/0.36 % (30320)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (1799ds/1021Mi) 0.16/0.36 % (30321)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (1799ds/71Mi) 0.16/0.36 % (30315)Instruction limit reached! 0.16/0.36 % (30315)------------------------------ 0.16/0.36 % (30315)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.36 % (30315)Termination reason: Unknown 0.16/0.36 % (30315)Termination phase: Saturation 0.16/0.36 0.16/0.36 % (30315)Memory used [KB]: 5884 0.16/0.36 % (30315)Time elapsed: 0.035 s 0.16/0.36 % (30315)Instructions burned: 75 (million) 0.16/0.36 % (30315)------------------------------ 0.16/0.36 % (30315)------------------------------ 0.16/0.37 % (30322)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on Vampire---4 for (1799ds/9Mi) 0.16/0.37 % (30323)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on Vampire---4 for (1799ds/1044Mi) 0.16/0.37 % (30322)Instruction limit reached! 0.16/0.37 % (30322)------------------------------ 0.16/0.37 % (30322)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.37 % (30322)Termination reason: Unknown 0.16/0.37 % (30322)Termination phase: Saturation 0.16/0.37 0.16/0.37 % (30322)Memory used [KB]: 5500 0.16/0.37 % (30322)Time elapsed: 0.006 s 0.16/0.37 % (30322)Instructions burned: 9 (million) 0.16/0.37 % (30322)------------------------------ 0.16/0.37 % (30322)------------------------------ 0.16/0.37 % (30310)Instruction limit reached! 0.16/0.37 % (30310)------------------------------ 0.16/0.37 % (30310)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.37 % (30310)Termination reason: Unknown 0.16/0.37 % (30310)Termination phase: Saturation 0.16/0.37 0.16/0.37 % (30310)Memory used [KB]: 5884 0.16/0.37 % (30310)Time elapsed: 0.045 s 0.16/0.37 % (30310)Instructions burned: 96 (million) 0.16/0.37 % (30310)------------------------------ 0.16/0.37 % (30310)------------------------------ 0.16/0.38 % (30324)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on Vampire---4 for (1799ds/128Mi) 0.16/0.38 % (30313)First to succeed. 0.16/0.39 % (30313)Refutation found. Thanks to Tanya! 0.16/0.39 % SZS status Theorem for Vampire---4 0.16/0.39 % SZS output start Proof for Vampire---4 0.16/0.39 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.16/0.39 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.16/0.39 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.16/0.39 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i). 0.16/0.39 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o). 0.16/0.39 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i). 0.16/0.39 thf(func_def_12, type, ph7: !>[X0: $tType]:(X0)). 0.16/0.39 thf(func_def_18, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i). 0.16/0.39 thf(func_def_19, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i). 0.16/0.39 thf(f415,plain,( 0.16/0.39 $false), 0.16/0.39 inference(avatar_sat_refutation,[],[f47,f75,f342,f414])). 0.16/0.39 thf(f414,plain,( 0.16/0.39 ~spl6_1), 0.16/0.39 inference(avatar_contradiction_clause,[],[f413])). 0.16/0.39 thf(f413,plain,( 0.16/0.39 $false | ~spl6_1), 0.16/0.39 inference(trivial_inequality_removal,[],[f412])). 0.16/0.39 thf(f412,plain,( 0.16/0.39 ($false = $true) | ~spl6_1), 0.16/0.39 inference(beta_eta_normalization,[],[f411])). 0.16/0.39 thf(f411,plain,( 0.16/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl6_1), 0.16/0.39 inference(argument_congruence,[],[f43])). 0.16/0.39 thf(f43,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_1), 0.16/0.39 inference(avatar_component_clause,[],[f41])). 0.16/0.39 thf(f41,plain,( 0.16/0.39 spl6_1 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))), 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_1])])). 0.16/0.39 thf(f342,plain,( 0.16/0.39 spl6_1 | spl6_4), 0.16/0.39 inference(avatar_contradiction_clause,[],[f341])). 0.16/0.39 thf(f341,plain,( 0.16/0.39 $false | (spl6_1 | spl6_4)), 0.16/0.39 inference(subsumption_resolution,[],[f340,f74])). 0.16/0.39 thf(f74,plain,( 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0)))))))) | spl6_4), 0.16/0.39 inference(avatar_component_clause,[],[f72])). 0.16/0.39 thf(f72,plain,( 0.16/0.39 spl6_4 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0))))))))), 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_4])])). 0.16/0.39 thf(f340,plain,( 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(forward_demodulation,[],[f339,f286])). 0.16/0.39 thf(f286,plain,( 0.16/0.39 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(subsumption_resolution,[],[f279,f42])). 0.16/0.39 thf(f42,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_1), 0.16/0.39 inference(avatar_component_clause,[],[f41])). 0.16/0.39 thf(f279,plain,( 0.16/0.39 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_1), 0.16/0.39 inference(duplicate_literal_removal,[],[f278])). 0.16/0.39 thf(f278,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(equality_proxy_clausification,[],[f277])). 0.16/0.39 thf(f277,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | spl6_1), 0.16/0.39 inference(equality_proxy_clausification,[],[f276])). 0.16/0.39 thf(f276,plain,( 0.16/0.39 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | spl6_1), 0.16/0.39 inference(beta_eta_normalization,[],[f266])). 0.16/0.39 thf(f266,plain,( 0.16/0.39 ( ! [X2 : $i,X8 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0))))))) @ X8) = $true) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_1), 0.16/0.39 inference(primitive_instantiation,[],[f179])). 0.16/0.39 thf(f179,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $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))) ) | spl6_1), 0.16/0.39 inference(subsumption_resolution,[],[f178,f42])). 0.16/0.39 thf(f178,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(equality_proxy_clausification,[],[f177])). 0.16/0.39 thf(f177,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) )), 0.16/0.39 inference(equality_proxy_clausification,[],[f176])). 0.16/0.39 thf(f176,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($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))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(trivial_inequality_removal,[],[f175])). 0.16/0.39 thf(f175,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($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)))) )), 0.16/0.39 inference(boolean_simplification,[],[f174])). 0.16/0.39 thf(f174,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($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))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $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)) )), 0.16/0.39 inference(beta_eta_normalization,[],[f154])). 0.16/0.39 thf(f154,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : ((((^[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)))))) @ (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)) != $true) | ($true = (X0 @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )), 0.16/0.39 inference(primitive_instantiation,[],[f13])). 0.16/0.39 thf(f13,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8))) )), 0.16/0.39 inference(cnf_transformation,[],[f12])). 0.16/0.39 thf(f12,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ((($true != (X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)) & ! [X7] : (($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true)) & ! [X8] : (($true = (X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)))) | (((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))), 0.16/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])). 0.16/0.39 thf(f9,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (? [X6] : (($true != (X1 @ X5 @ X3 @ X6)) & ($true != (X0 @ X5 @ X3 @ X6))) & ! [X7] : (($true = (X0 @ X5 @ X4 @ X7)) | ($true = (X1 @ X5 @ X4 @ X7))) & ! [X8] : (((X0 @ X4 @ X3 @ X8) = $true) | ((X1 @ X4 @ X3 @ X8) = $true))) => (? [X6] : (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) != $true)) & ! [X7] : (($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true)) & ! [X8] : (($true = (X0 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)) | ($true = (X1 @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X8)))))), 0.16/0.39 introduced(choice_axiom,[])). 0.16/0.39 thf(f10,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X6] : (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6)) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ X6) != $true)) => (($true != (X1 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0))) & ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true)))), 0.16/0.39 introduced(choice_axiom,[])). 0.16/0.39 thf(f11,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ($true != (X1 @ X9 @ X9 @ X10))) => (((X0 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))), 0.16/0.39 introduced(choice_axiom,[])). 0.16/0.39 thf(f8,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ? [X3 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (? [X6] : (($true != (X1 @ X5 @ X3 @ X6)) & ($true != (X0 @ X5 @ X3 @ X6))) & ! [X7] : (($true = (X0 @ X5 @ X4 @ X7)) | ($true = (X1 @ X5 @ X4 @ X7))) & ! [X8] : (((X0 @ X4 @ X3 @ X8) = $true) | ((X1 @ X4 @ X3 @ X8) = $true))) | ? [X9 : $i > $o,X10] : (((X0 @ X9 @ X9 @ X10) != $true) & ($true != (X1 @ X9 @ X9 @ X10))))), 0.16/0.39 inference(rectify,[],[f7])). 0.16/0.39 thf(f7,plain,( 0.16/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X10] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X4 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (? [X7] : (($true != (X1 @ X3 @ X4 @ X7)) & ((X0 @ X3 @ X4 @ X7) != $true)) & ! [X5] : (((X0 @ X3 @ X2 @ X5) = $true) | ($true = (X1 @ X3 @ X2 @ X5))) & ! [X6] : (($true = (X0 @ X2 @ X4 @ X6)) | ((X1 @ X2 @ X4 @ X6) = $true))) | ? [X8 : $i > $o,X9] : (((X0 @ X8 @ X8 @ X9) != $true) & ($true != (X1 @ X8 @ X8 @ X9))))), 0.16/0.39 inference(flattening,[],[f6])). 0.16/0.39 thf(f6,plain,( 0.16/0.39 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (? [X4 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (? [X7] : (($true != (X1 @ X3 @ X4 @ X7)) & ((X0 @ X3 @ X4 @ X7) != $true)) & (! [X6] : (($true = (X0 @ X2 @ X4 @ X6)) | ((X1 @ X2 @ X4 @ X6) = $true)) & ! [X5] : (((X0 @ X3 @ X2 @ X5) = $true) | ($true = (X1 @ X3 @ X2 @ X5))))) | ! [X10] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X8 : $i > $o,X9] : (((X0 @ X8 @ X8 @ X9) != $true) & ($true != (X1 @ X8 @ X8 @ X9))))), 0.16/0.39 inference(ennf_transformation,[],[f5])). 0.16/0.39 thf(f5,plain,( 0.16/0.39 ~? [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X4 : $i > $o,X2 : $i > $o,X3 : $i > $o] : ((! [X6] : (($true = (X0 @ X2 @ X4 @ X6)) | ((X1 @ X2 @ X4 @ X6) = $true)) & ! [X5] : (((X0 @ X3 @ X2 @ X5) = $true) | ($true = (X1 @ X3 @ X2 @ X5)))) => ! [X7] : (($true = (X1 @ X3 @ X4 @ X7)) | ((X0 @ X3 @ X4 @ X7) = $true))) & ~! [X10] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) & ! [X8 : $i > $o,X9] : (($true = (X1 @ X8 @ X8 @ X9)) | ((X0 @ X8 @ X8 @ X9) = $true)))), 0.16/0.39 inference(fool_elimination,[],[f4])). 0.16/0.39 thf(f4,plain,( 0.16/0.39 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2 : $i > $o,X3 : $i > $o,X4 : $i > $o] : ((! [X5] : ((X1 @ X3 @ X2 @ X5) | (X0 @ X3 @ X2 @ X5)) & ! [X6] : ((X0 @ X2 @ X4 @ X6) | (X1 @ X2 @ X4 @ X6))) => ! [X7] : ((X0 @ X3 @ X4 @ X7) | (X1 @ X3 @ X4 @ X7))) & ! [X8 : $i > $o,X9] : ((X1 @ X8 @ X8 @ X9) | (X0 @ X8 @ X8 @ X9)) & ~! [X10] : ((X0 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X1 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))), 0.16/0.39 inference(rectify,[],[f2])). 0.16/0.39 thf(f2,negated_conjecture,( 0.16/0.39 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X4 : $i > $o,X3 : $i > $o,X5 : $i > $o] : ((! [X2] : ((X1 @ X3 @ X4 @ X2) | (X0 @ X3 @ X4 @ X2)) & ! [X2] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2))) => ! [X2] : ((X0 @ X3 @ X5 @ X2) | (X1 @ X3 @ X5 @ X2))) & ! [X3 : $i > $o,X2] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ~! [X2] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)))), 0.16/0.39 inference(negated_conjecture,[],[f1])). 0.16/0.39 thf(f1,conjecture,( 0.16/0.39 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X4 : $i > $o,X3 : $i > $o,X5 : $i > $o] : ((! [X2] : ((X1 @ X3 @ X4 @ X2) | (X0 @ X3 @ X4 @ X2)) & ! [X2] : ((X0 @ X4 @ X5 @ X2) | (X1 @ X4 @ X5 @ X2))) => ! [X2] : ((X0 @ X3 @ X5 @ X2) | (X1 @ X3 @ X5 @ X2))) & ! [X3 : $i > $o,X2] : ((X1 @ X3 @ X3 @ X2) | (X0 @ X3 @ X3 @ X2)) & ~! [X2] : ((X0 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2) | (X1 @ (^[X3 : $i] : ($true)) @ (^[X3 : $i] : ($false)) @ X2)))), 0.16/0.39 file('/export/starexec/sandbox2/tmp/tmp.ONBg3Qy975/Vampire---4.8_30202',cTHM120C_pme)). 0.16/0.39 thf(f339,plain,( 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(subsumption_resolution,[],[f338,f42])). 0.16/0.39 thf(f338,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(duplicate_literal_removal,[],[f337])). 0.16/0.39 thf(f337,plain,( 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(equality_proxy_clausification,[],[f336])). 0.16/0.39 thf(f336,plain,( 0.16/0.39 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | spl6_1), 0.16/0.39 inference(equality_proxy_clausification,[],[f335])). 0.16/0.39 thf(f335,plain,( 0.16/0.39 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_1), 0.16/0.39 inference(beta_eta_normalization,[],[f315])). 0.16/0.39 thf(f315,plain,( 0.16/0.39 ( ! [X2 : $i,X7 : $i] : (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ($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]: (Y1 = Y0))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X7)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) ) | spl6_1), 0.16/0.39 inference(primitive_instantiation,[],[f235])). 0.16/0.39 thf(f235,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) ) | spl6_1), 0.16/0.39 inference(subsumption_resolution,[],[f234,f42])). 0.16/0.39 thf(f234,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,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 = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )), 0.16/0.39 inference(equality_proxy_clausification,[],[f233])). 0.16/0.39 thf(f233,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[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)) )), 0.16/0.39 inference(equality_proxy_clausification,[],[f232])). 0.16/0.39 thf(f232,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[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) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(trivial_inequality_removal,[],[f231])). 0.16/0.39 thf(f231,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (($true != $true) | ($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((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) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(boolean_simplification,[],[f230])). 0.16/0.39 thf(f230,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $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) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) = $true) | ($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(beta_eta_normalization,[],[f210])). 0.16/0.39 thf(f210,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : ((((^[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)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X7))) )), 0.16/0.39 inference(primitive_instantiation,[],[f15])). 0.16/0.39 thf(f15,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X7 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7) = $true) | ($true = (X0 @ (sK2 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ X7)) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )), 0.16/0.39 inference(cnf_transformation,[],[f12])). 0.16/0.39 thf(f75,plain,( 0.16/0.39 ~spl6_4 | spl6_1 | ~spl6_2), 0.16/0.39 inference(avatar_split_clause,[],[f55,f45,f41,f72])). 0.16/0.39 thf(f45,plain,( 0.16/0.39 spl6_2 <=> ! [X2,X0 : ($i > $o) > ($i > $o) > $i > $o] : (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true))), 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])). 0.16/0.39 thf(f55,plain,( 0.16/0.39 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[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]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2), 0.16/0.39 inference(equality_proxy_clausification,[],[f54])). 0.16/0.39 thf(f54,plain,( 0.16/0.39 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ~spl6_2), 0.16/0.39 inference(equality_proxy_clausification,[],[f53])). 0.16/0.39 thf(f53,plain,( 0.16/0.39 (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl6_2), 0.16/0.39 inference(beta_eta_normalization,[],[f48])). 0.16/0.39 thf(f48,plain,( 0.16/0.39 ( ! [X2 : $i] : (($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]: (Y1 = Y0))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) ) | ~spl6_2), 0.16/0.39 inference(primitive_instantiation,[],[f46])). 0.16/0.39 thf(f46,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) ) | ~spl6_2), 0.16/0.39 inference(avatar_component_clause,[],[f45])). 0.16/0.39 thf(f47,plain,( 0.16/0.39 spl6_1 | spl6_2), 0.16/0.39 inference(avatar_split_clause,[],[f32,f45,f41])). 0.16/0.39 thf(f32,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(equality_proxy_clausification,[],[f31])). 0.16/0.39 thf(f31,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true) | ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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))) = $true)) )), 0.16/0.39 inference(trivial_inequality_removal,[],[f30])). 0.16/0.39 thf(f30,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(boolean_simplification,[],[f29])). 0.16/0.39 thf(f29,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $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) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )), 0.16/0.39 inference(beta_eta_normalization,[],[f21])). 0.16/0.39 thf(f21,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : ((((^[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) | ((X0 @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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)))))) @ (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)) != $true)) )), 0.16/0.39 inference(primitive_instantiation,[],[f17])). 0.16/0.39 thf(f17,plain,( 0.16/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (((X1 @ (sK4 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK2 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK3 @ X1 @ X0)) != $true) | ((X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2) = $true)) )), 0.16/0.39 inference(cnf_transformation,[],[f12])). 0.16/0.39 % SZS output end Proof for Vampire---4 0.16/0.39 % (30313)------------------------------ 0.16/0.39 % (30313)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.39 % (30313)Termination reason: Refutation 0.16/0.39 0.16/0.39 % (30313)Memory used [KB]: 6012 0.16/0.39 % (30313)Time elapsed: 0.055 s 0.16/0.39 % (30313)Instructions burned: 103 (million) 0.16/0.39 % (30313)------------------------------ 0.16/0.39 % (30313)------------------------------ 0.16/0.39 % (30309)Success in time 0.061 s 0.16/0.39 % Vampire---4.8 exiting 0.16/0.39 EOF