0.07/0.13 % Problem : Vampire---4.8_25369 : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.14/0.36 % Computer : n005.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1440 0.14/0.36 % WCLimit : 180 0.14/0.36 % DateTime : Mon Jul 3 12:44:45 EDT 2023 0.14/0.36 % CPUTime : 0.14/0.36 This is a THF_ problem 0.14/0.36 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/sandbox/tmp/tmp.fbV1Jytq4s/Vampire---4.8_25369 -m 12000 -t 180 0.14/0.37 % (25620)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi) 0.14/0.38 % (25618)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.14/0.38 % (25619)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.14/0.38 % (25621)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 (1799ds/385Mi) 0.14/0.38 % (25622)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.14/0.38 % (25623)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 (1799ds/74Mi) 0.14/0.38 % (25624)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi) 0.14/0.38 % (25625)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 (1799ds/915Mi) 0.14/0.38 % (25624)Instruction limit reached! 0.14/0.38 % (25624)------------------------------ 0.14/0.38 % (25624)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.38 % (25624)Termination reason: Unknown 0.14/0.38 % (25624)Termination phase: Preprocessing 3 0.14/0.38 0.14/0.38 % (25624)Memory used [KB]: 1023 0.14/0.38 % (25624)Time elapsed: 0.005 s 0.14/0.38 % (25624)Instructions burned: 5 (million) 0.14/0.38 % (25624)------------------------------ 0.14/0.38 % (25624)------------------------------ 0.14/0.39 % (25620)Instruction limit reached! 0.14/0.39 % (25620)------------------------------ 0.14/0.39 % (25620)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.39 % (25620)Termination reason: Unknown 0.14/0.39 % (25620)Termination phase: Saturation 0.14/0.39 0.14/0.39 % (25620)Memory used [KB]: 5884 0.14/0.39 % (25620)Time elapsed: 0.015 s 0.14/0.39 % (25620)Instructions burned: 36 (million) 0.14/0.39 % (25620)------------------------------ 0.14/0.39 % (25620)------------------------------ 0.14/0.39 % (25622)Instruction limit reached! 0.14/0.39 % (25622)------------------------------ 0.14/0.39 % (25622)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.39 % (25622)Termination reason: Unknown 0.14/0.39 % (25622)Termination phase: Saturation 0.14/0.39 0.14/0.39 % (25622)Memory used [KB]: 5756 0.14/0.39 % (25622)Time elapsed: 0.013 s 0.14/0.39 % (25622)Instructions burned: 18 (million) 0.14/0.39 % (25622)------------------------------ 0.14/0.39 % (25622)------------------------------ 0.22/0.40 % (25627)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.22/0.40 % (25626)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) 0.22/0.40 % (25627)Instruction limit reached! 0.22/0.40 % (25627)------------------------------ 0.22/0.40 % (25627)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.40 % (25627)Termination reason: Unknown 0.22/0.40 % (25627)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (25627)Memory used [KB]: 1151 0.22/0.40 % (25627)Time elapsed: 0.004 s 0.22/0.40 % (25627)Instructions burned: 10 (million) 0.22/0.40 % (25627)------------------------------ 0.22/0.40 % (25627)------------------------------ 0.22/0.40 % (25619)Instruction limit reached! 0.22/0.40 % (25619)------------------------------ 0.22/0.40 % (25619)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.40 % (25619)Termination reason: Unknown 0.22/0.40 % (25619)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (25619)Memory used [KB]: 5884 0.22/0.40 % (25619)Time elapsed: 0.024 s 0.22/0.40 % (25619)Instructions burned: 36 (million) 0.22/0.40 % (25619)------------------------------ 0.22/0.40 % (25619)------------------------------ 0.22/0.41 % (25628)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) 0.22/0.41 % (25629)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) 0.22/0.41 % (25626)Instruction limit reached! 0.22/0.41 % (25626)------------------------------ 0.22/0.41 % (25626)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.41 % (25626)Termination reason: Unknown 0.22/0.41 % (25626)Termination phase: Saturation 0.22/0.41 0.22/0.41 % (25626)Memory used [KB]: 5756 0.22/0.41 % (25626)Time elapsed: 0.014 s 0.22/0.41 % (25626)Instructions burned: 21 (million) 0.22/0.41 % (25626)------------------------------ 0.22/0.41 % (25626)------------------------------ 0.22/0.42 % (25630)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) 0.22/0.42 % (25630)Instruction limit reached! 0.22/0.42 % (25630)------------------------------ 0.22/0.42 % (25630)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.42 % (25630)Termination reason: Unknown 0.22/0.42 % (25630)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (25630)Memory used [KB]: 5628 0.22/0.42 % (25630)Time elapsed: 0.007 s 0.22/0.42 % (25630)Instructions burned: 9 (million) 0.22/0.42 % (25630)------------------------------ 0.22/0.42 % (25630)------------------------------ 0.22/0.42 % (25623)Instruction limit reached! 0.22/0.42 % (25623)------------------------------ 0.22/0.42 % (25623)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.42 % (25623)Termination reason: Unknown 0.22/0.42 % (25623)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (25623)Memory used [KB]: 5884 0.22/0.42 % (25623)Time elapsed: 0.045 s 0.22/0.42 % (25623)Instructions burned: 75 (million) 0.22/0.42 % (25623)------------------------------ 0.22/0.42 % (25623)------------------------------ 0.22/0.42 % (25631)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) 0.22/0.43 % (25629)Instruction limit reached! 0.22/0.43 % (25629)------------------------------ 0.22/0.43 % (25629)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.43 % (25629)Termination reason: Unknown 0.22/0.43 % (25629)Termination phase: Saturation 0.22/0.43 0.22/0.43 % (25629)Memory used [KB]: 6012 0.22/0.43 % (25629)Time elapsed: 0.027 s 0.22/0.43 % (25629)Instructions burned: 72 (million) 0.22/0.43 % (25629)------------------------------ 0.22/0.43 % (25629)------------------------------ 0.22/0.44 % (25632)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) 0.22/0.44 % (25618)Instruction limit reached! 0.22/0.44 % (25618)------------------------------ 0.22/0.44 % (25618)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.44 % (25618)Termination reason: Unknown 0.22/0.44 % (25618)Termination phase: Saturation 0.22/0.44 0.22/0.44 % (25618)Memory used [KB]: 6012 0.22/0.44 % (25618)Time elapsed: 0.059 s 0.22/0.44 % (25618)Instructions burned: 96 (million) 0.22/0.44 % (25618)------------------------------ 0.22/0.44 % (25618)------------------------------ 0.22/0.44 % (25633)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.22/0.44 % (25634)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.22/0.45 % (25634)Instruction limit reached! 0.22/0.45 % (25634)------------------------------ 0.22/0.45 % (25634)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.45 % (25634)Termination reason: Unknown 0.22/0.45 % (25634)Termination phase: Saturation 0.22/0.45 0.22/0.45 % (25634)Memory used [KB]: 5628 0.22/0.45 % (25634)Time elapsed: 0.006 s 0.22/0.45 % (25634)Instructions burned: 16 (million) 0.22/0.45 % (25634)------------------------------ 0.22/0.45 % (25634)------------------------------ 0.22/0.45 % (25635)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on Vampire---4 for (1799ds/2Mi) 0.22/0.45 % (25635)Instruction limit reached! 0.22/0.45 % (25635)------------------------------ 0.22/0.45 % (25635)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.45 % (25635)Termination reason: Unknown 0.22/0.45 % (25635)Termination phase: shuffling 0.22/0.45 0.22/0.45 % (25635)Memory used [KB]: 1023 0.22/0.45 % (25635)Time elapsed: 0.003 s 0.22/0.45 % (25635)Instructions burned: 3 (million) 0.22/0.45 % (25635)------------------------------ 0.22/0.45 % (25635)------------------------------ 0.22/0.46 % (25637)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (1799ds/1041Mi) 0.22/0.47 % (25641)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1799ds/11Mi) 0.22/0.47 % (25641)Instruction limit reached! 0.22/0.47 % (25641)------------------------------ 0.22/0.47 % (25641)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.47 % (25641)Termination reason: Unknown 0.22/0.47 % (25641)Termination phase: Saturation 0.22/0.47 0.22/0.47 % (25641)Memory used [KB]: 5500 0.22/0.47 % (25641)Time elapsed: 0.008 s 0.22/0.47 % (25641)Instructions burned: 11 (million) 0.22/0.47 % (25641)------------------------------ 0.22/0.47 % (25641)------------------------------ 0.22/0.48 % (25633)Instruction limit reached! 0.22/0.48 % (25633)------------------------------ 0.22/0.48 % (25633)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.48 % (25633)Termination reason: Unknown 0.22/0.48 % (25633)Termination phase: Saturation 0.22/0.48 0.22/0.48 % (25633)Memory used [KB]: 6012 0.22/0.48 % (25633)Time elapsed: 0.041 s 0.22/0.48 % (25633)Instructions burned: 61 (million) 0.22/0.48 % (25633)------------------------------ 0.22/0.48 % (25633)------------------------------ 0.22/0.49 % (25646)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1798ds/140Mi) 0.22/0.49 % (25647)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (1798ds/26Mi) 0.22/0.50 % (25647)Instruction limit reached! 0.22/0.50 % (25647)------------------------------ 0.22/0.50 % (25647)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.50 % (25647)Termination reason: Unknown 0.22/0.50 % (25647)Termination phase: Saturation 0.22/0.50 0.22/0.50 % (25647)Memory used [KB]: 5500 0.22/0.50 % (25647)Time elapsed: 0.010 s 0.22/0.50 % (25647)Instructions burned: 26 (million) 0.22/0.50 % (25647)------------------------------ 0.22/0.50 % (25647)------------------------------ 1.27/0.51 % (25632)Instruction limit reached! 1.27/0.51 % (25632)------------------------------ 1.27/0.51 % (25632)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.27/0.51 % (25632)Termination reason: Unknown 1.27/0.51 % (25632)Termination phase: Saturation 1.27/0.51 1.27/0.51 % (25632)Memory used [KB]: 6268 1.27/0.51 % (25632)Time elapsed: 0.065 s 1.27/0.51 % (25632)Instructions burned: 129 (million) 1.27/0.51 % (25632)------------------------------ 1.27/0.51 % (25632)------------------------------ 1.27/0.51 % (25666)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi) 1.27/0.52 % (25673)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (1798ds/275Mi) 1.41/0.53 % (25666)Instruction limit reached! 1.41/0.53 % (25666)------------------------------ 1.41/0.53 % (25666)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.53 % (25666)Termination reason: Unknown 1.41/0.53 % (25666)Termination phase: Saturation 1.41/0.53 1.41/0.53 % (25666)Memory used [KB]: 1535 1.41/0.53 % (25666)Time elapsed: 0.025 s 1.41/0.53 % (25666)Instructions burned: 57 (million) 1.41/0.53 % (25666)------------------------------ 1.41/0.53 % (25666)------------------------------ 1.41/0.54 % (25646)Instruction limit reached! 1.41/0.54 % (25646)------------------------------ 1.41/0.54 % (25646)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.54 % (25646)Termination reason: Unknown 1.41/0.54 % (25646)Termination phase: Saturation 1.41/0.54 1.41/0.54 % (25646)Memory used [KB]: 6268 1.41/0.54 % (25646)Time elapsed: 0.051 s 1.41/0.54 % (25646)Instructions burned: 140 (million) 1.41/0.54 % (25646)------------------------------ 1.41/0.54 % (25646)------------------------------ 1.41/0.54 % (25696)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1798ds/3Mi) 1.41/0.54 % (25696)Instruction limit reached! 1.41/0.54 % (25696)------------------------------ 1.41/0.54 % (25696)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.54 % (25696)Termination reason: Unknown 1.41/0.54 % (25696)Termination phase: Preprocessing 1 1.41/0.54 1.41/0.54 % (25696)Memory used [KB]: 1023 1.41/0.54 % (25696)Time elapsed: 0.003 s 1.41/0.54 % (25696)Instructions burned: 3 (million) 1.41/0.54 % (25696)------------------------------ 1.41/0.54 % (25696)------------------------------ 1.41/0.55 % (25699)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (1798ds/19Mi) 1.41/0.55 % (25699)Instruction limit reached! 1.41/0.55 % (25699)------------------------------ 1.41/0.55 % (25699)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.55 % (25699)Termination reason: Unknown 1.41/0.55 % (25699)Termination phase: Saturation 1.41/0.55 1.41/0.55 % (25699)Memory used [KB]: 5500 1.41/0.55 % (25699)Time elapsed: 0.006 s 1.41/0.55 % (25699)Instructions burned: 19 (million) 1.41/0.55 % (25699)------------------------------ 1.41/0.55 % (25699)------------------------------ 1.41/0.55 % (25711)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (1798ds/44Mi) 1.41/0.56 % (25714)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on Vampire---4 for (1798ds/191Mi) 1.41/0.56 % (25621)Instruction limit reached! 1.41/0.56 % (25621)------------------------------ 1.41/0.56 % (25621)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.56 % (25621)Termination reason: Unknown 1.41/0.56 % (25621)Termination phase: Saturation 1.41/0.56 1.41/0.56 % (25621)Memory used [KB]: 7036 1.41/0.56 % (25621)Time elapsed: 0.183 s 1.41/0.56 % (25621)Instructions burned: 386 (million) 1.41/0.56 % (25621)------------------------------ 1.41/0.56 % (25621)------------------------------ 1.41/0.57 % (25711)Instruction limit reached! 1.41/0.57 % (25711)------------------------------ 1.41/0.57 % (25711)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.57 % (25711)Termination reason: Unknown 1.41/0.57 % (25711)Termination phase: Saturation 1.41/0.57 1.41/0.57 % (25711)Memory used [KB]: 1151 1.41/0.57 % (25711)Time elapsed: 0.016 s 1.41/0.57 % (25711)Instructions burned: 45 (million) 1.41/0.57 % (25711)------------------------------ 1.41/0.57 % (25711)------------------------------ 1.41/0.57 % (25720)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (1798ds/62Mi) 1.41/0.58 % (25725)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on Vampire---4 for (1798ds/105Mi) 1.41/0.59 % (25720)Instruction limit reached! 1.41/0.59 % (25720)------------------------------ 1.41/0.59 % (25720)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.59 % (25720)Termination reason: Unknown 1.41/0.59 % (25720)Termination phase: Saturation 1.41/0.59 1.41/0.59 % (25720)Memory used [KB]: 5756 1.41/0.59 % (25720)Time elapsed: 0.020 s 1.41/0.59 % (25720)Instructions burned: 62 (million) 1.41/0.59 % (25720)------------------------------ 1.41/0.59 % (25720)------------------------------ 1.41/0.60 % (25741)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 1.41/0.60 % (25741)Instruction limit reached! 1.41/0.60 % (25741)------------------------------ 1.41/0.60 % (25741)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.60 % (25741)Termination reason: Unknown 1.41/0.60 % (25741)Termination phase: shuffling 1.41/0.60 1.41/0.60 % (25741)Memory used [KB]: 1023 1.41/0.60 % (25741)Time elapsed: 0.002 s 1.41/0.60 % (25741)Instructions burned: 3 (million) 1.41/0.60 % (25741)------------------------------ 1.41/0.60 % (25741)------------------------------ 1.41/0.61 % (25742)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=238:si=on:rtra=on_0 on Vampire---4 for (1797ds/238Mi) 1.41/0.62 % (25725)Instruction limit reached! 1.41/0.62 % (25725)------------------------------ 1.41/0.62 % (25725)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.62 % (25725)Termination reason: Unknown 1.41/0.62 % (25725)Termination phase: Saturation 1.41/0.62 1.41/0.62 % (25725)Memory used [KB]: 6140 1.41/0.62 % (25725)Time elapsed: 0.040 s 1.41/0.62 % (25725)Instructions burned: 107 (million) 1.41/0.62 % (25725)------------------------------ 1.41/0.62 % (25725)------------------------------ 1.41/0.62 % (25673)Instruction limit reached! 1.41/0.62 % (25673)------------------------------ 1.41/0.62 % (25673)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.62 % (25673)Termination reason: Unknown 1.41/0.62 % (25673)Termination phase: Saturation 1.41/0.62 1.41/0.62 % (25673)Memory used [KB]: 6396 1.41/0.62 % (25673)Time elapsed: 0.102 s 1.41/0.62 % (25673)Instructions burned: 275 (million) 1.41/0.62 % (25673)------------------------------ 1.41/0.62 % (25673)------------------------------ 1.41/0.62 % (25714)Instruction limit reached! 1.41/0.62 % (25714)------------------------------ 1.41/0.62 % (25714)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.41/0.62 % (25714)Termination reason: Unknown 1.41/0.62 % (25714)Termination phase: Saturation 1.41/0.62 1.41/0.62 % (25714)Memory used [KB]: 6652 1.41/0.62 % (25714)Time elapsed: 0.064 s 1.41/0.62 % (25714)Instructions burned: 192 (million) 1.41/0.62 % (25714)------------------------------ 1.41/0.62 % (25714)------------------------------ 2.20/0.63 % (25743)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 2.20/0.63 % (25743)Instruction limit reached! 2.20/0.63 % (25743)------------------------------ 2.20/0.63 % (25743)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.20/0.63 % (25743)Termination reason: Unknown 2.20/0.63 % (25743)Termination phase: shuffling 2.20/0.63 2.20/0.63 % (25743)Memory used [KB]: 1023 2.20/0.63 % (25743)Time elapsed: 0.002 s 2.20/0.63 % (25743)Instructions burned: 3 (million) 2.20/0.63 % (25743)------------------------------ 2.20/0.63 % (25743)------------------------------ 2.20/0.63 % (25744)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (1797ds/4Mi) 2.20/0.63 % (25744)Instruction limit reached! 2.20/0.63 % (25744)------------------------------ 2.20/0.63 % (25744)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.20/0.63 % (25744)Termination reason: Unknown 2.20/0.63 % (25744)Termination phase: Preprocessing 3 2.20/0.63 2.20/0.63 % (25744)Memory used [KB]: 1023 2.20/0.63 % (25744)Time elapsed: 0.003 s 2.20/0.63 % (25744)Instructions burned: 5 (million) 2.20/0.63 % (25744)------------------------------ 2.20/0.63 % (25744)------------------------------ 2.20/0.63 % (25637)First to succeed. 2.20/0.63 % (25745)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (1797ds/149Mi) 2.20/0.64 % (25746)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (1797ds/150Mi) 2.20/0.64 % (25747)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=199:si=on:rtra=on_0 on Vampire---4 for (1797ds/199Mi) 2.20/0.65 % (25637)Refutation found. Thanks to Tanya! 2.20/0.65 % SZS status Theorem for Vampire---4 2.20/0.65 % SZS output start Proof for Vampire---4 2.20/0.65 thf(type_def_5, type, a: $tType). 2.20/0.65 thf(func_def_0, type, a: $tType). 2.20/0.65 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)). 2.20/0.65 thf(func_def_22, type, sK2: a > a > $o). 2.20/0.65 thf(func_def_23, type, sK3: a). 2.20/0.65 thf(func_def_24, type, sK4: a). 2.20/0.65 thf(func_def_25, type, sK5: a > a > $o). 2.20/0.65 thf(func_def_26, type, sK6: a > $o). 2.20/0.65 thf(func_def_27, type, sK7: a). 2.20/0.65 thf(func_def_28, type, sK8: a). 2.20/0.65 thf(func_def_29, type, sK9: a). 2.20/0.65 thf(func_def_30, type, sK10: a). 2.20/0.65 thf(func_def_31, type, sK11: a). 2.20/0.65 thf(func_def_32, type, sK12: a). 2.20/0.65 thf(func_def_33, type, sK13: a > $o). 2.20/0.65 thf(func_def_34, type, sK14: a). 2.20/0.65 thf(func_def_35, type, sK15: a). 2.20/0.65 thf(func_def_36, type, sK16: a). 2.20/0.65 thf(func_def_37, type, sK17: a). 2.20/0.65 thf(func_def_38, type, sK18: a > $o). 2.20/0.65 thf(func_def_39, type, sK19: a). 2.20/0.65 thf(func_def_40, type, sK20: a). 2.20/0.65 thf(func_def_41, type, sK21: a). 2.20/0.65 thf(func_def_42, type, sK22: a). 2.20/0.65 thf(func_def_43, type, sK23: a). 2.20/0.65 thf(func_def_44, type, sK24: a). 2.20/0.65 thf(func_def_45, type, sK25: a). 2.20/0.65 thf(func_def_46, type, sK26: a). 2.20/0.65 thf(func_def_47, type, sK27: a). 2.20/0.65 thf(func_def_48, type, sK28: a). 2.20/0.65 thf(func_def_49, type, sK29: a). 2.20/0.65 thf(func_def_50, type, sK30: a). 2.20/0.65 thf(func_def_51, type, sK31: a). 2.20/0.65 thf(func_def_52, type, sK32: a). 2.20/0.65 thf(f3105,plain,( 2.20/0.65 $false), 2.20/0.65 inference(avatar_sat_refutation,[],[f57,f137,f191,f223,f229,f236,f247,f285,f393,f431,f637,f1450,f1561,f1577,f1618,f1661,f1706,f2039,f2461,f2953,f2983,f3091,f3104])). 2.20/0.65 thf(f3104,plain,( 2.20/0.65 spl0_50 | spl0_49 | ~spl0_5), 2.20/0.65 inference(avatar_split_clause,[],[f3098,f186,f1613,f1616])). 2.20/0.65 thf(f1616,plain,( 2.20/0.65 spl0_50 <=> ((sK6 @ sK7) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_50])])). 2.20/0.65 thf(f1613,plain,( 2.20/0.65 spl0_49 <=> ((sK6 @ sK9) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_49])])). 2.20/0.65 thf(f186,plain,( 2.20/0.65 spl0_5 <=> ((sK5 @ sK9 @ sK7) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 2.20/0.65 thf(f3098,plain,( 2.20/0.65 ((sK6 @ sK7) = $true) | ((sK6 @ sK9) = $false) | ~spl0_5), 2.20/0.65 inference(trivial_inequality_removal,[],[f3097])). 2.20/0.65 thf(f3097,plain,( 2.20/0.65 ($true = $false) | ((sK6 @ sK7) = $true) | ((sK6 @ sK9) = $false) | ~spl0_5), 2.20/0.65 inference(boolean_simplification,[],[f3094])). 2.20/0.65 thf(f3094,plain,( 2.20/0.65 ((sK6 @ sK7) = $true) | ((sK6 @ sK9) = $false) | (((sK2 @ sK9 @ sK7) | $true) = $false) | ~spl0_5), 2.20/0.65 inference(superposition,[],[f1016,f187])). 2.20/0.65 thf(f187,plain,( 2.20/0.65 ((sK5 @ sK9 @ sK7) = $true) | ~spl0_5), 2.20/0.65 inference(avatar_component_clause,[],[f186])). 2.20/0.65 thf(f1016,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($false = ((sK2 @ X1 @ X2) | (sK5 @ X1 @ X2))) | ((sK6 @ X1) = $false) | ($true = (sK6 @ X2))) )), 2.20/0.65 inference(binary_proxy_clausification,[],[f41])). 2.20/0.65 thf(f41,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (((((sK2 @ X1 @ X2) | (sK5 @ X1 @ X2)) & (sK6 @ X1)) = $false) | ($true = (sK6 @ X2))) )), 2.20/0.65 inference(binary_proxy_clausification,[],[f37])). 2.20/0.65 thf(f37,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : ((((((sK2 @ X1 @ X2) | (sK5 @ X1 @ X2)) & (sK6 @ X1)) => (sK6 @ X2)) = $true)) )), 2.20/0.65 inference(beta_eta_normalization,[],[f36])). 2.20/0.65 thf(f36,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: ((((sK2 @ X1 @ Y0) | (sK5 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0))) @ X2))) )), 2.20/0.65 inference(pi_clausification,[],[f33])). 2.20/0.65 thf(f33,plain,( 2.20/0.65 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((((sK2 @ X1 @ Y0) | (sK5 @ X1 @ Y0)) & (sK6 @ X1)) => (sK6 @ Y0)))) = $true)) )), 2.20/0.65 inference(beta_eta_normalization,[],[f32])). 2.20/0.65 thf(f32,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ X1) = $true)) )), 2.20/0.65 inference(pi_clausification,[],[f31])). 2.20/0.65 thf(f31,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) = $true)), 2.20/0.65 inference(boolean_simplification,[],[f30])). 2.20/0.65 thf(f30,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & $true) = $true)), 2.20/0.65 inference(backward_demodulation,[],[f25,f28])). 2.20/0.65 thf(f28,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0)))) = $true)), 2.20/0.65 inference(binary_proxy_clausification,[],[f25])). 2.20/0.65 thf(f25,plain,( 2.20/0.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))))))), 2.20/0.65 inference(binary_proxy_clausification,[],[f23])). 2.20/0.65 thf(f23,plain,( 2.20/0.65 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1)) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK3)))), 2.20/0.65 inference(beta_eta_normalization,[],[f22])). 2.20/0.65 thf(f22,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3))) @ sK6) = $false)), 2.20/0.65 inference(sigma_clausification,[],[f21])). 2.20/0.65 thf(f21,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3)))) = $false)), 2.20/0.65 inference(boolean_simplification,[],[f20])). 2.20/0.65 thf(f20,plain,( 2.20/0.65 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3)))) | $false))), 2.20/0.65 inference(backward_demodulation,[],[f17,f18])). 2.20/0.65 thf(f18,plain,( 2.20/0.65 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) & (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3)))))))), 2.20/0.65 inference(binary_proxy_clausification,[],[f17])). 2.20/0.65 thf(f17,plain,( 2.20/0.65 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2)) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3)))) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) & (~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))))))) = $false)), 2.20/0.65 inference(beta_eta_normalization,[],[f16])). 2.20/0.65 thf(f16,plain,( 2.20/0.65 (((^[Y0 : a > a > $o]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((Y0 @ sK4 @ Y2) | (sK2 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK3)))) | (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK2 @ Y1 @ Y5) | (Y0 @ Y1 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y0 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))) & (~ (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK4 @ Y2) | (Y0 @ sK4 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((Y0 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK3)))))))) @ sK5) = $false)), 2.20/0.65 inference(sigma_clausification,[],[f15])). 2.20/0.65 thf(f15,plain,( 2.20/0.65 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y2 @ Y3) | (Y0 @ Y2 @ Y3)) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((Y0 @ sK4 @ Y2) | (sK2 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK3)))) | (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (Y0 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ Y2 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y1)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((sK2 @ Y2 @ Y4) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK2 @ Y4 @ Y5)) => (Y3 @ Y5))))))) => (Y3 @ Y1))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y0 @ Y2 @ Y4) | (sK2 @ Y2 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y1))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((sK2 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y1)))) & (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((sK2 @ Y1 @ Y5) | (Y0 @ Y1 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y0 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6))))))) => (Y4 @ Y3))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((sK2 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (sK2 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y3)))))))))))) & (~ (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK4 @ Y2) | (Y0 @ sK4 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((Y0 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2))))))) => (Y1 @ sK3))))))))) = $false)), 2.20/0.65 inference(beta_eta_normalization,[],[f14])). 2.20/0.65 thf(f14,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((Y1 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK3)))) | (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y1 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y1 @ Y3 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK2 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK2 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK2 @ Y6 @ Y7) | (Y1 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y2)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK2 @ Y2 @ Y6) | (Y1 @ Y2 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y1 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y4))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK2 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((Y1 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y4)))))))))))) & (~ (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ Y0 @ Y3) | (Y1 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((Y1 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ sK3)))))))))) @ sK4) = $false)), 2.20/0.65 inference(sigma_clausification,[],[f13])). 2.20/0.65 thf(f13,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y3 @ Y4) | (Y1 @ Y3 @ Y4)) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((Y1 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK3)))) | (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y1 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y1 @ Y3 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y2)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((sK2 @ Y3 @ Y5) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (sK2 @ Y5 @ Y6)) => (Y4 @ Y6))))))) => (Y4 @ Y2))))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & ((Y1 @ Y5 @ Y6) | (sK2 @ Y5 @ Y6))) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y1 @ Y3 @ Y5) | (sK2 @ Y3 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y2))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((Y1 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((sK2 @ Y6 @ Y7) | (Y1 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y2)))) & (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (((sK2 @ Y2 @ Y6) | (Y1 @ Y2 @ Y6)) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y1 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7))))))) => (Y5 @ Y4))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((((sK2 @ Y7 @ Y6) | (Y1 @ Y7 @ Y6)) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (((Y1 @ Y3 @ Y6) | (sK2 @ Y3 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y4)))))))))))) & (~ (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ Y0 @ Y3) | (Y1 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((Y1 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3))))))) => (Y2 @ sK3))))))))))) = $false)), 2.20/0.65 inference(beta_eta_normalization,[],[f12])). 2.20/0.65 thf(f12,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y2 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0)))) | (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y2 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y2 @ Y4 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK2 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (sK2 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y2 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((Y2 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y4 @ Y7) | (sK2 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((sK2 @ Y7 @ Y8) | (Y2 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y3)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((sK2 @ Y3 @ Y7) | (Y2 @ Y3 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y2 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((sK2 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y2 @ Y4 @ Y7) | (sK2 @ Y4 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y5)))))))))))) & (~ (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y1 @ Y4) | (Y2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y2 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y0)))))))))))) @ sK3) = $false)), 2.20/0.65 inference(sigma_clausification,[],[f11])). 2.20/0.65 thf(f11,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y4 @ Y5) | (Y2 @ Y4 @ Y5)) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((Y2 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0)))) | (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y2 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y2 @ Y4 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y3)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: ((sK2 @ Y4 @ Y6) => (Y5 @ Y6)))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (sK2 @ Y6 @ Y7)) => (Y5 @ Y7))))))) => (Y5 @ Y3))))) => (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & ((Y2 @ Y6 @ Y7) | (sK2 @ Y6 @ Y7))) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (((Y2 @ Y4 @ Y6) | (sK2 @ Y4 @ Y6)) => (Y5 @ Y6))))) => (Y5 @ Y3))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((Y2 @ Y4 @ Y7) | (sK2 @ Y4 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((sK2 @ Y7 @ Y8) | (Y2 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y3)))) & (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (((sK2 @ Y3 @ Y7) | (Y2 @ Y3 @ Y7)) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y2 @ Y7 @ Y8) | (sK2 @ Y7 @ Y8))) => (Y6 @ Y8))))))) => (Y6 @ Y5))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((((sK2 @ Y8 @ Y7) | (Y2 @ Y8 @ Y7)) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (((Y2 @ Y4 @ Y7) | (sK2 @ Y4 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y5)))))))))))) & (~ (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y1 @ Y4) | (Y2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y2 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4))))))) => (Y3 @ Y0))))))))))))) = $false)), 2.20/0.65 inference(beta_eta_normalization,[],[f10])). 2.20/0.65 thf(f10,plain,( 2.20/0.65 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))) | (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y3 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y0 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y3 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y3 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y3 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y0 @ Y4 @ Y8) | (Y3 @ Y4 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y3 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y0 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))))))))))) & (~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y3 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y1)))))))))))))) @ sK2))), 2.20/0.65 inference(sigma_clausification,[],[f7])). 2.20/0.65 thf(f7,plain,( 2.20/0.65 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))) | (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y3 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y0 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y3 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y3 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y3 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y0 @ Y4 @ Y8) | (Y3 @ Y4 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y3 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y0 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))))))))))) & (~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y3 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y1))))))))))))))) = $false)), 2.20/0.65 inference(not_proxy_clausification,[],[f6])). 2.20/0.65 thf(f6,plain,( 2.20/0.65 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))) | (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y3 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y0 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y3 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y3 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y3 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y0 @ Y4 @ Y8) | (Y3 @ Y4 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y3 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y0 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))))))))))) & (~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y3 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y1)))))))))))))))))), 2.20/0.65 inference(cnf_transformation,[],[f5])). 2.20/0.65 thf(f5,plain,( 2.20/0.65 ($true = (~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((Y0 @ Y5 @ Y6) | (Y3 @ Y5 @ Y6)) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))) | (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y3 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y5 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y4)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: ((Y0 @ Y5 @ Y7) => (Y6 @ Y7)))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y0 @ Y7 @ Y8)) => (Y6 @ Y8))))))) => (Y6 @ Y4))))) => (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & ((Y3 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8))) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (((Y3 @ Y5 @ Y7) | (Y0 @ Y5 @ Y7)) => (Y6 @ Y7))))) => (Y6 @ Y4))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y0 @ Y8 @ Y9) | (Y3 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y4)))) & (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (((Y0 @ Y4 @ Y8) | (Y3 @ Y4 @ Y8)) => (Y7 @ Y8)))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & ((Y3 @ Y8 @ Y9) | (Y0 @ Y8 @ Y9))) => (Y7 @ Y9))))))) => (Y7 @ Y6))))) => (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((((Y0 @ Y9 @ Y8) | (Y3 @ Y9 @ Y8)) & (Y7 @ Y9)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (((Y3 @ Y5 @ Y8) | (Y0 @ Y5 @ Y8)) => (Y7 @ Y8))))) => (Y7 @ Y6)))))))))))) & (~ (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (((Y0 @ Y2 @ Y5) | (Y3 @ Y2 @ Y5)) => (Y4 @ Y5)))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5))))))) => (Y4 @ Y1)))))))))))))))))), 2.20/0.65 inference(fool_elimination,[],[f4])). 2.20/0.65 thf(f4,plain,( 2.20/0.65 ~! [X0 : a > a > $o,X1 : a,X2 : a,X3 : a > a > $o] : ((~! [X4 : a > $o] : ((! [X5 : a,X6 : a] : ((((X3 @ X5 @ X6) | (X0 @ X5 @ X6)) & (X4 @ X5)) => (X4 @ X6)) & ! [X7 : a] : (((X0 @ X1 @ X7) | (X3 @ X1 @ X7)) => (X4 @ X7))) => (X4 @ X2)) & ! [X8 : a,X9 : a,X10 : a] : ((! [X11 : a > $o] : ((! [X12 : a,X13 : a] : ((((X3 @ X13 @ X12) | (X0 @ X13 @ X12)) & (X11 @ X13)) => (X11 @ X12)) & ! [X14 : a] : (((X0 @ X10 @ X14) | (X3 @ X10 @ X14)) => (X11 @ X14))) => (X11 @ X8)) & ! [X15 : a > $o] : ((! [X16 : a,X17 : a] : ((((X0 @ X17 @ X16) | (X3 @ X17 @ X16)) & (X15 @ X17)) => (X15 @ X16)) & ! [X18 : a] : (((X3 @ X9 @ X18) | (X0 @ X9 @ X18)) => (X15 @ X18))) => (X15 @ X10))) => ! [X19 : a > $o] : ((! [X20 : a] : (((X3 @ X9 @ X20) | (X0 @ X9 @ X20)) => (X19 @ X20)) & ! [X21 : a,X22 : a] : (((X19 @ X21) & ((X0 @ X21 @ X22) | (X3 @ X21 @ X22))) => (X19 @ X22))) => (X19 @ X8))) & ! [X23 : a,X24 : a] : ((! [X25 : a > $o] : ((! [X26 : a,X27 : a] : (((X3 @ X27 @ X26) & (X25 @ X27)) => (X25 @ X26)) & ! [X28 : a] : ((X3 @ X23 @ X28) => (X25 @ X28))) => (X25 @ X24)) | ! [X29 : a > $o] : ((! [X30 : a] : ((X0 @ X23 @ X30) => (X29 @ X30)) & ! [X31 : a,X32 : a] : (((X0 @ X32 @ X31) & (X29 @ X32)) => (X29 @ X31))) => (X29 @ X24))) => ! [X33 : a > $o] : ((! [X34 : a] : (((X3 @ X23 @ X34) | (X0 @ X23 @ X34)) => (X33 @ X34)) & ! [X35 : a,X36 : a] : ((((X3 @ X36 @ X35) | (X0 @ X36 @ X35)) & (X33 @ X36)) => (X33 @ X35))) => (X33 @ X24)))) | ! [X37 : a > $o] : ((! [X38 : a] : (((X3 @ X1 @ X38) | (X0 @ X1 @ X38)) => (X37 @ X38)) & ! [X39 : a,X40 : a] : (((X37 @ X40) & ((X0 @ X40 @ X39) | (X3 @ X40 @ X39))) => (X37 @ X39))) => (X37 @ X2)))), 2.20/0.65 inference(rectify,[],[f2])). 2.20/0.65 thf(f2,negated_conjecture,( 2.20/0.65 ~! [X1 : a > a > $o,X2 : a,X3 : a,X0 : a > a > $o] : ((~! [X6 : a > $o] : ((! [X8 : a,X9 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X2 @ X7) | (X0 @ X2 @ X7)) => (X6 @ X7))) => (X6 @ X3)) & ! [X10 : a,X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X5 @ X7) | (X0 @ X5 @ X7)) => (X6 @ X7))) => (X6 @ X10)) & ! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : (((X6 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X6 @ X9))) => (X6 @ X10))) & ! [X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : (((X0 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : ((X0 @ X4 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X1 @ X4 @ X7) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7)) & ! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5)))) | ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X6 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X6 @ X9))) => (X6 @ X3)))), 2.20/0.65 inference(negated_conjecture,[],[f1])). 2.20/0.65 thf(f1,conjecture,( 2.20/0.65 ! [X1 : a > a > $o,X2 : a,X3 : a,X0 : a > a > $o] : ((~! [X6 : a > $o] : ((! [X8 : a,X9 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X2 @ X7) | (X0 @ X2 @ X7)) => (X6 @ X7))) => (X6 @ X3)) & ! [X10 : a,X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X1 @ X5 @ X7) | (X0 @ X5 @ X7)) => (X6 @ X7))) => (X6 @ X10)) & ! [X6 : a > $o] : ((! [X9 : a,X8 : a] : ((((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7)) & ! [X8 : a,X9 : a] : (((X6 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X6 @ X9))) => (X6 @ X10))) & ! [X4 : a,X5 : a] : ((! [X6 : a > $o] : ((! [X9 : a,X8 : a] : (((X0 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9)) & ! [X7 : a] : ((X0 @ X4 @ X7) => (X6 @ X7))) => (X6 @ X5)) | ! [X6 : a > $o] : ((! [X7 : a] : ((X1 @ X4 @ X7) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5))) => ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X4 @ X7) | (X1 @ X4 @ X7)) => (X6 @ X7)) & ! [X9 : a,X8 : a] : ((((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5)))) | ! [X6 : a > $o] : ((! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X6 @ X7)) & ! [X9 : a,X8 : a] : (((X6 @ X8) & ((X1 @ X8 @ X9) | (X0 @ X8 @ X9))) => (X6 @ X9))) => (X6 @ X3)))), 2.20/0.65 file('/export/starexec/sandbox/tmp/tmp.fbV1Jytq4s/Vampire---4.8_25369',cTHM251H_pme)). 2.20/0.65 thf(f3091,plain,( 2.20/0.65 ~spl0_10 | ~spl0_11 | ~spl0_67), 2.20/0.65 inference(avatar_contradiction_clause,[],[f3090])). 2.20/0.65 thf(f3090,plain,( 2.20/0.65 $false | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(trivial_inequality_removal,[],[f3089])). 2.20/0.65 thf(f3089,plain,( 2.20/0.65 ($true = $false) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(forward_demodulation,[],[f3088,f3045])). 2.20/0.65 thf(f3045,plain,( 2.20/0.65 ((sK13 @ sK32) = $false) | ~spl0_67), 2.20/0.65 inference(boolean_simplification,[],[f3044])). 2.20/0.65 thf(f3044,plain,( 2.20/0.65 (($true => (sK13 @ sK32)) = $false) | ~spl0_67), 2.20/0.65 inference(backward_demodulation,[],[f3021,f3043])). 2.20/0.65 thf(f3043,plain,( 2.20/0.65 ($true = ((sK13 @ sK31) & (sK2 @ sK31 @ sK32))) | ~spl0_67), 2.20/0.65 inference(binary_proxy_clausification,[],[f3021])). 2.20/0.65 thf(f3021,plain,( 2.20/0.65 ($false = (((sK13 @ sK31) & (sK2 @ sK31 @ sK32)) => (sK13 @ sK32))) | ~spl0_67), 2.20/0.65 inference(beta_eta_normalization,[],[f3020])). 2.20/0.65 thf(f3020,plain,( 2.20/0.65 (((^[Y0 : a]: (((sK13 @ sK31) & (sK2 @ sK31 @ Y0)) => (sK13 @ Y0))) @ sK32) = $false) | ~spl0_67), 2.20/0.65 inference(sigma_clausification,[],[f2997])). 2.20/0.65 thf(f2997,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK13 @ sK31) & (sK2 @ sK31 @ Y0)) => (sK13 @ Y0)))) = $false) | ~spl0_67), 2.20/0.65 inference(beta_eta_normalization,[],[f2995])). 2.20/0.65 thf(f2995,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1))))) @ sK31) = $false) | ~spl0_67), 2.20/0.65 inference(sigma_clausification,[],[f2952])). 2.20/0.65 thf(f2952,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ~spl0_67), 2.20/0.65 inference(avatar_component_clause,[],[f2951])). 2.20/0.65 thf(f2951,plain,( 2.20/0.65 spl0_67 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_67])])). 2.20/0.65 thf(f3088,plain,( 2.20/0.65 ((sK13 @ sK32) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(boolean_simplification,[],[f3087])). 2.20/0.65 thf(f3087,plain,( 2.20/0.65 (($true => (sK13 @ sK32)) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(forward_demodulation,[],[f3072,f3056])). 2.20/0.65 thf(f3056,plain,( 2.20/0.65 ((sK13 @ sK31) = $true) | ~spl0_67), 2.20/0.65 inference(binary_proxy_clausification,[],[f3043])). 2.20/0.65 thf(f3072,plain,( 2.20/0.65 (((sK13 @ sK31) => (sK13 @ sK32)) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(boolean_simplification,[],[f3071])). 2.20/0.65 thf(f3071,plain,( 2.20/0.65 ((((sK13 @ sK31) & $true) => (sK13 @ sK32)) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(boolean_simplification,[],[f3067])). 2.20/0.65 thf(f3067,plain,( 2.20/0.65 ((((sK13 @ sK31) & ((sK5 @ sK31 @ sK32) | $true)) => (sK13 @ sK32)) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_67)), 2.20/0.65 inference(superposition,[],[f2611,f3058])). 2.20/0.65 thf(f3058,plain,( 2.20/0.65 ((sK2 @ sK31 @ sK32) = $true) | ~spl0_67), 2.20/0.65 inference(boolean_simplification,[],[f3057])). 2.20/0.65 thf(f3057,plain,( 2.20/0.65 (($true & (sK2 @ sK31 @ sK32)) = $true) | ~spl0_67), 2.20/0.65 inference(backward_demodulation,[],[f3043,f3056])). 2.20/0.65 thf(f2611,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($true = (((sK13 @ X1) & ((sK5 @ X1 @ X2) | (sK2 @ X1 @ X2))) => (sK13 @ X2)))) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(beta_eta_normalization,[],[f2610])). 2.20/0.65 thf(f2610,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK13 @ X1) & ((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK13 @ Y0))) @ X2) = $true)) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(pi_clausification,[],[f2594])). 2.20/0.65 thf(f2594,plain,( 2.20/0.65 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK13 @ X1) & ((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK13 @ Y0)))) = $true)) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(beta_eta_normalization,[],[f2593])). 2.20/0.65 thf(f2593,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1))))) @ X1) = $true)) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(pi_clausification,[],[f2577])). 2.20/0.65 thf(f2577,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) = $true) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(boolean_simplification,[],[f2576])). 2.20/0.65 thf(f2576,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & $true) = $true) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(backward_demodulation,[],[f2483,f2574])). 2.20/0.65 thf(f2574,plain,( 2.20/0.65 ($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2483])). 2.20/0.65 thf(f2483,plain,( 2.20/0.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0)))))) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2468])). 2.20/0.65 thf(f2468,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) => (sK13 @ sK11)) = $false) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(beta_eta_normalization,[],[f2467])). 2.20/0.65 thf(f2467,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ sK13) = $false) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(sigma_clausification,[],[f2466])). 2.20/0.65 thf(f2466,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $false) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(boolean_simplification,[],[f2465])). 2.20/0.65 thf(f2465,plain,( 2.20/0.65 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))))) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(boolean_simplification,[],[f2464])). 2.20/0.65 thf(f2464,plain,( 2.20/0.65 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | $true) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))))) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(backward_demodulation,[],[f2089,f281])). 2.20/0.65 thf(f281,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11)))) = $true) | ~spl0_11), 2.20/0.65 inference(avatar_component_clause,[],[f280])). 2.20/0.65 thf(f280,plain,( 2.20/0.65 spl0_11 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11)))) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])). 2.20/0.65 thf(f2089,plain,( 2.20/0.65 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))))) = $false) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f2088])). 2.20/0.65 thf(f2088,plain,( 2.20/0.65 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK11)))))) @ sK12) = $false) | ~spl0_10), 2.20/0.65 inference(sigma_clausification,[],[f2078])). 2.20/0.65 thf(f2078,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK11))))))) = $false) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f2077])). 2.20/0.65 thf(f2077,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))) @ sK11) = $false) | ~spl0_10), 2.20/0.65 inference(sigma_clausification,[],[f246])). 2.20/0.65 thf(f246,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ~spl0_10), 2.20/0.65 inference(avatar_component_clause,[],[f245])). 2.20/0.65 thf(f245,plain,( 2.20/0.65 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])). 2.20/0.65 thf(f2983,plain,( 2.20/0.65 ~spl0_10 | ~spl0_11 | ~spl0_66), 2.20/0.65 inference(avatar_contradiction_clause,[],[f2982])). 2.20/0.65 thf(f2982,plain,( 2.20/0.65 $false | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(trivial_inequality_removal,[],[f2981])). 2.20/0.65 thf(f2981,plain,( 2.20/0.65 ($true = $false) | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(boolean_simplification,[],[f2980])). 2.20/0.65 thf(f2980,plain,( 2.20/0.65 ($true = (~ $true)) | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(boolean_simplification,[],[f2979])). 2.20/0.65 thf(f2979,plain,( 2.20/0.65 ((~ ((sK5 @ sK12 @ sK30) | $true)) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(forward_demodulation,[],[f2978,f2965])). 2.20/0.65 thf(f2965,plain,( 2.20/0.65 ((sK2 @ sK12 @ sK30) = $true) | ~spl0_66), 2.20/0.65 inference(binary_proxy_clausification,[],[f2963])). 2.20/0.65 thf(f2963,plain,( 2.20/0.65 (((sK2 @ sK12 @ sK30) => (sK13 @ sK30)) = $false) | ~spl0_66), 2.20/0.65 inference(beta_eta_normalization,[],[f2959])). 2.20/0.65 thf(f2959,plain,( 2.20/0.65 (((^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0))) @ sK30) = $false) | ~spl0_66), 2.20/0.65 inference(sigma_clausification,[],[f2949])). 2.20/0.65 thf(f2949,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ~spl0_66), 2.20/0.65 inference(avatar_component_clause,[],[f2948])). 2.20/0.65 thf(f2948,plain,( 2.20/0.65 spl0_66 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_66])])). 2.20/0.65 thf(f2978,plain,( 2.20/0.65 ((~ ((sK5 @ sK12 @ sK30) | (sK2 @ sK12 @ sK30))) = $true) | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(boolean_simplification,[],[f2970])). 2.20/0.65 thf(f2970,plain,( 2.20/0.65 ($true = (((sK5 @ sK12 @ sK30) | (sK2 @ sK12 @ sK30)) => $false)) | (~spl0_10 | ~spl0_11 | ~spl0_66)), 2.20/0.65 inference(superposition,[],[f2874,f2964])). 2.20/0.65 thf(f2964,plain,( 2.20/0.65 ((sK13 @ sK30) = $false) | ~spl0_66), 2.20/0.65 inference(binary_proxy_clausification,[],[f2963])). 2.20/0.65 thf(f2874,plain,( 2.20/0.65 ( ! [X1 : a] : (((((sK5 @ sK12 @ X1) | (sK2 @ sK12 @ X1)) => (sK13 @ X1)) = $true)) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(beta_eta_normalization,[],[f2873])). 2.20/0.65 thf(f2873,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))) @ X1) = $true)) ) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(pi_clausification,[],[f2574])). 2.20/0.65 thf(f2953,plain,( 2.20/0.65 spl0_66 | spl0_67 | ~spl0_10 | ~spl0_11), 2.20/0.65 inference(avatar_split_clause,[],[f2944,f280,f245,f2951,f2948])). 2.20/0.65 thf(f2944,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2918])). 2.20/0.65 thf(f2918,plain,( 2.20/0.65 ($false = ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1)))))))) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(not_proxy_clausification,[],[f2496])). 2.20/0.65 thf(f2496,plain,( 2.20/0.65 ((~ ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1)))))))) = $true) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(boolean_simplification,[],[f2495])). 2.20/0.65 thf(f2495,plain,( 2.20/0.65 ($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (sK13 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK2 @ Y0 @ Y1)) => (sK13 @ Y1))))))) => $false)) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(superposition,[],[f2489,f2482])). 2.20/0.65 thf(f2482,plain,( 2.20/0.65 ((sK13 @ sK11) = $false) | (~spl0_10 | ~spl0_11)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2468])). 2.20/0.65 thf(f2489,plain,( 2.20/0.65 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: ((sK2 @ sK12 @ Y0) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK2 @ Y0 @ Y1)) => (X1 @ Y1))))))) => (X1 @ sK11)))) ) | ~spl0_11), 2.20/0.65 inference(beta_eta_normalization,[],[f2488])). 2.20/0.65 thf(f2488,plain,( 2.20/0.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))) @ X1) = $true)) ) | ~spl0_11), 2.20/0.65 inference(pi_clausification,[],[f281])). 2.20/0.65 thf(f2461,plain,( 2.20/0.65 ~spl0_10 | ~spl0_12 | ~spl0_13), 2.20/0.65 inference(avatar_contradiction_clause,[],[f2460])). 2.20/0.65 thf(f2460,plain,( 2.20/0.65 $false | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(trivial_inequality_removal,[],[f2459])). 2.20/0.65 thf(f2459,plain,( 2.20/0.65 ($true = $false) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(forward_demodulation,[],[f2458,f2405])). 2.20/0.65 thf(f2405,plain,( 2.20/0.65 ((sK13 @ sK29) = $false) | ~spl0_13), 2.20/0.65 inference(binary_proxy_clausification,[],[f2391])). 2.20/0.65 thf(f2391,plain,( 2.20/0.65 ((((sK13 @ sK28) & (sK5 @ sK28 @ sK29)) => (sK13 @ sK29)) = $false) | ~spl0_13), 2.20/0.65 inference(beta_eta_normalization,[],[f2390])). 2.20/0.65 thf(f2390,plain,( 2.20/0.65 ($false = ((^[Y0 : a]: (((sK13 @ sK28) & (sK5 @ sK28 @ Y0)) => (sK13 @ Y0))) @ sK29)) | ~spl0_13), 2.20/0.65 inference(sigma_clausification,[],[f2380])). 2.20/0.65 thf(f2380,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK13 @ sK28) & (sK5 @ sK28 @ Y0)) => (sK13 @ Y0)))) = $false) | ~spl0_13), 2.20/0.65 inference(beta_eta_normalization,[],[f2376])). 2.20/0.65 thf(f2376,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1))))) @ sK28) = $false) | ~spl0_13), 2.20/0.65 inference(sigma_clausification,[],[f389])). 2.20/0.65 thf(f389,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ~spl0_13), 2.20/0.65 inference(avatar_component_clause,[],[f388])). 2.20/0.65 thf(f388,plain,( 2.20/0.65 spl0_13 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_13])])). 2.20/0.65 thf(f2458,plain,( 2.20/0.65 ((sK13 @ sK29) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(boolean_simplification,[],[f2457])). 2.20/0.65 thf(f2457,plain,( 2.20/0.65 (($true => (sK13 @ sK29)) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(forward_demodulation,[],[f2445,f2432])). 2.20/0.65 thf(f2432,plain,( 2.20/0.65 ((sK13 @ sK28) = $true) | ~spl0_13), 2.20/0.65 inference(boolean_simplification,[],[f2431])). 2.20/0.65 thf(f2431,plain,( 2.20/0.65 (((sK13 @ sK28) & $true) = $true) | ~spl0_13), 2.20/0.65 inference(backward_demodulation,[],[f2406,f2429])). 2.20/0.65 thf(f2429,plain,( 2.20/0.65 ((sK5 @ sK28 @ sK29) = $true) | ~spl0_13), 2.20/0.65 inference(binary_proxy_clausification,[],[f2406])). 2.20/0.65 thf(f2406,plain,( 2.20/0.65 (((sK13 @ sK28) & (sK5 @ sK28 @ sK29)) = $true) | ~spl0_13), 2.20/0.65 inference(binary_proxy_clausification,[],[f2391])). 2.20/0.65 thf(f2445,plain,( 2.20/0.65 (((sK13 @ sK28) => (sK13 @ sK29)) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(boolean_simplification,[],[f2444])). 2.20/0.65 thf(f2444,plain,( 2.20/0.65 ((((sK13 @ sK28) & $true) => (sK13 @ sK29)) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(boolean_simplification,[],[f2441])). 2.20/0.65 thf(f2441,plain,( 2.20/0.65 ((((sK13 @ sK28) & ($true | (sK2 @ sK28 @ sK29))) => (sK13 @ sK29)) = $true) | (~spl0_10 | ~spl0_12 | ~spl0_13)), 2.20/0.65 inference(superposition,[],[f2149,f2429])). 2.20/0.65 thf(f2149,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($true = (((sK13 @ X1) & ((sK5 @ X1 @ X2) | (sK2 @ X1 @ X2))) => (sK13 @ X2)))) ) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(beta_eta_normalization,[],[f2148])). 2.20/0.65 thf(f2148,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK13 @ X1) & ((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK13 @ Y0))) @ X2) = $true)) ) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(pi_clausification,[],[f2144])). 2.20/0.65 thf(f2144,plain,( 2.20/0.65 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK13 @ X1) & ((sK5 @ X1 @ Y0) | (sK2 @ X1 @ Y0))) => (sK13 @ Y0)))) = $true)) ) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(beta_eta_normalization,[],[f2143])). 2.20/0.65 thf(f2143,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1))))) @ X1) = $true)) ) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(pi_clausification,[],[f2125])). 2.20/0.65 thf(f2125,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) = $true) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(boolean_simplification,[],[f2124])). 2.20/0.65 thf(f2124,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & $true) = $true) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(backward_demodulation,[],[f2114,f2122])). 2.20/0.65 thf(f2122,plain,( 2.20/0.65 ($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2114])). 2.20/0.65 thf(f2114,plain,( 2.20/0.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0)))))) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(binary_proxy_clausification,[],[f2099])). 2.20/0.65 thf(f2099,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) => (sK13 @ sK11)) = $false) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(beta_eta_normalization,[],[f2098])). 2.20/0.65 thf(f2098,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ sK13) = $false) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(sigma_clausification,[],[f2092])). 2.20/0.65 thf(f2092,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $false) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(boolean_simplification,[],[f2091])). 2.20/0.65 thf(f2091,plain,( 2.20/0.65 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))))) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(boolean_simplification,[],[f2090])). 2.20/0.65 thf(f2090,plain,( 2.20/0.65 ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))))) = $false) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(forward_demodulation,[],[f2089,f284])). 2.20/0.65 thf(f284,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true) | ~spl0_12), 2.20/0.65 inference(avatar_component_clause,[],[f283])). 2.20/0.65 thf(f283,plain,( 2.20/0.65 spl0_12 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])). 2.20/0.65 thf(f2039,plain,( 2.20/0.65 ~spl0_9 | ~spl0_20 | ~spl0_45), 2.20/0.65 inference(avatar_contradiction_clause,[],[f2038])). 2.20/0.65 thf(f2038,plain,( 2.20/0.65 $false | (~spl0_9 | ~spl0_20 | ~spl0_45)), 2.20/0.65 inference(trivial_inequality_removal,[],[f2037])). 2.20/0.65 thf(f2037,plain,( 2.20/0.65 ($true = $false) | (~spl0_9 | ~spl0_20 | ~spl0_45)), 2.20/0.65 inference(forward_demodulation,[],[f2036,f1523])). 2.20/0.65 thf(f1523,plain,( 2.20/0.65 ((sK18 @ sK26) = $false) | ~spl0_20), 2.20/0.65 inference(binary_proxy_clausification,[],[f1507])). 2.20/0.65 thf(f1507,plain,( 2.20/0.65 ((((sK18 @ sK25) & ((sK5 @ sK25 @ sK26) | (sK2 @ sK25 @ sK26))) => (sK18 @ sK26)) = $false) | ~spl0_20), 2.20/0.65 inference(beta_eta_normalization,[],[f1506])). 2.20/0.65 thf(f1506,plain,( 2.20/0.65 ($false = ((^[Y0 : a]: (((sK18 @ sK25) & ((sK5 @ sK25 @ Y0) | (sK2 @ sK25 @ Y0))) => (sK18 @ Y0))) @ sK26)) | ~spl0_20), 2.20/0.65 inference(sigma_clausification,[],[f1497])). 2.20/0.65 thf(f1497,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK18 @ sK25) & ((sK5 @ sK25 @ Y0) | (sK2 @ sK25 @ Y0))) => (sK18 @ Y0)))) = $false) | ~spl0_20), 2.20/0.65 inference(beta_eta_normalization,[],[f1493])). 2.20/0.65 thf(f1493,plain,( 2.20/0.65 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1))))) @ sK25)) | ~spl0_20), 2.20/0.65 inference(sigma_clausification,[],[f636])). 2.20/0.65 thf(f636,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1)))))) = $false) | ~spl0_20), 2.20/0.65 inference(avatar_component_clause,[],[f635])). 2.20/0.65 thf(f635,plain,( 2.20/0.65 spl0_20 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1)))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])). 2.20/0.65 thf(f2036,plain,( 2.20/0.65 ($true = (sK18 @ sK26)) | (~spl0_9 | ~spl0_20 | ~spl0_45)), 2.20/0.65 inference(boolean_simplification,[],[f2035])). 2.20/0.65 thf(f2035,plain,( 2.20/0.65 ($true = ($true => (sK18 @ sK26))) | (~spl0_9 | ~spl0_20 | ~spl0_45)), 2.20/0.65 inference(forward_demodulation,[],[f1994,f1541])). 2.20/0.65 thf(f1541,plain,( 2.20/0.65 ((sK18 @ sK25) = $true) | ~spl0_20), 2.20/0.65 inference(binary_proxy_clausification,[],[f1524])). 2.20/0.65 thf(f1524,plain,( 2.20/0.65 ($true = ((sK18 @ sK25) & ((sK5 @ sK25 @ sK26) | (sK2 @ sK25 @ sK26)))) | ~spl0_20), 2.20/0.65 inference(binary_proxy_clausification,[],[f1507])). 2.20/0.65 thf(f1994,plain,( 2.20/0.65 (((sK18 @ sK25) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_45)), 2.20/0.65 inference(boolean_simplification,[],[f1993])). 2.20/0.65 thf(f1993,plain,( 2.20/0.65 ((($true & (sK18 @ sK25)) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_45)), 2.20/0.65 inference(boolean_simplification,[],[f1975])). 2.20/0.65 thf(f1975,plain,( 2.20/0.65 (((($true | (sK5 @ sK25 @ sK26)) & (sK18 @ sK25)) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_45)), 2.20/0.65 inference(superposition,[],[f1941,f1557])). 2.20/0.65 thf(f1557,plain,( 2.20/0.65 ((sK2 @ sK25 @ sK26) = $true) | ~spl0_45), 2.20/0.65 inference(avatar_component_clause,[],[f1556])). 2.20/0.65 thf(f1556,plain,( 2.20/0.65 spl0_45 <=> ((sK2 @ sK25 @ sK26) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_45])])). 2.20/0.65 thf(f1941,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($true = ((((sK2 @ X2 @ X1) | (sK5 @ X2 @ X1)) & (sK18 @ X2)) => (sK18 @ X1)))) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1940])). 2.20/0.65 thf(f1940,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK5 @ Y0 @ X1)) & (sK18 @ Y0)) => (sK18 @ X1))) @ X2) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f1926])). 2.20/0.65 thf(f1926,plain,( 2.20/0.65 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK5 @ Y0 @ X1)) & (sK18 @ Y0)) => (sK18 @ X1)))) = $true)) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1925])). 2.20/0.65 thf(f1925,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0))))) @ X1) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f1823])). 2.20/0.65 thf(f1823,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f1819])). 2.20/0.65 thf(f1819,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f1804])). 2.20/0.65 thf(f1804,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0))))) => (sK18 @ sK17)) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1803])). 2.20/0.65 thf(f1803,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))) @ sK18) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f1764])). 2.20/0.65 thf(f1764,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17)))) = $false) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f1763])). 2.20/0.65 thf(f1763,plain,( 2.20/0.65 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))))) = $false) | ~spl0_9), 2.20/0.65 inference(backward_demodulation,[],[f1749,f1762])). 2.20/0.65 thf(f1762,plain,( 2.20/0.65 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f1749])). 2.20/0.65 thf(f1749,plain,( 2.20/0.65 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))))) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1748])). 2.20/0.65 thf(f1748,plain,( 2.20/0.65 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK5 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK15 @ Y2) | (sK5 @ sK15 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) @ sK17) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f1738])). 2.20/0.65 thf(f1738,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK5 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK15 @ Y2) | (sK5 @ sK15 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0))))))) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1737])). 2.20/0.65 thf(f1737,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK5 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK15)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ sK15 @ Y3) | (sK5 @ sK15 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))) @ sK16) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f1728])). 2.20/0.65 thf(f1728,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK5 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK15)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ sK15 @ Y3) | (sK5 @ sK15 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))))) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f1727])). 2.20/0.65 thf(f1727,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))) @ sK15) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f243])). 2.20/0.65 thf(f243,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) | ~spl0_9), 2.20/0.65 inference(avatar_component_clause,[],[f242])). 2.20/0.65 thf(f242,plain,( 2.20/0.65 spl0_9 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2))))))))))))), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])). 2.20/0.65 thf(f1706,plain,( 2.20/0.65 ~spl0_3 | ~spl0_49), 2.20/0.65 inference(avatar_contradiction_clause,[],[f1705])). 2.20/0.65 thf(f1705,plain,( 2.20/0.65 $false | (~spl0_3 | ~spl0_49)), 2.20/0.65 inference(trivial_inequality_removal,[],[f1704])). 2.20/0.65 thf(f1704,plain,( 2.20/0.65 ($true = $false) | (~spl0_3 | ~spl0_49)), 2.20/0.65 inference(boolean_simplification,[],[f1703])). 2.20/0.65 thf(f1703,plain,( 2.20/0.65 ((~ $false) = $false) | (~spl0_3 | ~spl0_49)), 2.20/0.65 inference(boolean_simplification,[],[f1702])). 2.20/0.65 thf(f1702,plain,( 2.20/0.65 ((~ ($false & ((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)))) = $false) | (~spl0_3 | ~spl0_49)), 2.20/0.65 inference(forward_demodulation,[],[f1701,f1614])). 2.20/0.65 thf(f1614,plain,( 2.20/0.65 ((sK6 @ sK9) = $false) | ~spl0_49), 2.20/0.65 inference(avatar_component_clause,[],[f1613])). 2.20/0.65 thf(f1701,plain,( 2.20/0.65 ((~ ((sK6 @ sK9) & ((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)))) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f1700])). 2.20/0.65 thf(f1700,plain,( 2.20/0.65 (((^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))))) @ sK9) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f1683])). 2.20/0.65 thf(f1683,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7)))))) = $false) | ~spl0_3), 2.20/0.65 inference(boolean_simplification,[],[f1682])). 2.20/0.65 thf(f1682,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => $false))) = $false) | ~spl0_3), 2.20/0.65 inference(backward_demodulation,[],[f1653,f1679])). 2.20/0.65 thf(f1679,plain,( 2.20/0.65 ((sK6 @ sK7) = $false) | ~spl0_3), 2.20/0.65 inference(binary_proxy_clausification,[],[f1665])). 2.20/0.65 thf(f1665,plain,( 2.20/0.65 ((((sK6 @ sK8) & ((sK5 @ sK8 @ sK7) | (sK2 @ sK8 @ sK7))) => (sK6 @ sK7)) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f1664])). 2.20/0.65 thf(f1664,plain,( 2.20/0.65 (((^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => (sK6 @ sK7))) @ sK8) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f1653])). 2.20/0.65 thf(f1653,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => (sK6 @ sK7)))) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f1651])). 2.20/0.65 thf(f1651,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))) @ sK7) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f133])). 2.20/0.65 thf(f133,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false) | ~spl0_3), 2.20/0.65 inference(avatar_component_clause,[],[f132])). 2.20/0.65 thf(f132,plain,( 2.20/0.65 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 2.20/0.65 thf(f1661,plain,( 2.20/0.65 ~spl0_3 | ~spl0_50), 2.20/0.65 inference(avatar_contradiction_clause,[],[f1660])). 2.20/0.65 thf(f1660,plain,( 2.20/0.65 $false | (~spl0_3 | ~spl0_50)), 2.20/0.65 inference(trivial_inequality_removal,[],[f1659])). 2.20/0.65 thf(f1659,plain,( 2.20/0.65 ($true = $false) | (~spl0_3 | ~spl0_50)), 2.20/0.65 inference(beta_eta_normalization,[],[f1658])). 2.20/0.65 thf(f1658,plain,( 2.20/0.65 (((^[Y0 : a]: ($true)) @ sK27) = $false) | (~spl0_3 | ~spl0_50)), 2.20/0.65 inference(sigma_clausification,[],[f1657])). 2.20/0.65 thf(f1657,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: ($true))) = $false) | (~spl0_3 | ~spl0_50)), 2.20/0.65 inference(boolean_simplification,[],[f1656])). 2.20/0.65 thf(f1656,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => $true))) = $false) | (~spl0_3 | ~spl0_50)), 2.20/0.65 inference(forward_demodulation,[],[f1653,f1617])). 2.20/0.65 thf(f1617,plain,( 2.20/0.65 ((sK6 @ sK7) = $true) | ~spl0_50), 2.20/0.65 inference(avatar_component_clause,[],[f1616])). 2.20/0.65 thf(f1618,plain,( 2.20/0.65 spl0_49 | spl0_50 | ~spl0_6), 2.20/0.65 inference(avatar_split_clause,[],[f1609,f189,f1616,f1613])). 2.20/0.65 thf(f189,plain,( 2.20/0.65 spl0_6 <=> ((sK2 @ sK9 @ sK7) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])). 2.20/0.65 thf(f1609,plain,( 2.20/0.65 ((sK6 @ sK9) = $false) | ((sK6 @ sK7) = $true) | ~spl0_6), 2.20/0.65 inference(boolean_simplification,[],[f1608])). 2.20/0.65 thf(f1608,plain,( 2.20/0.65 (($true & (sK6 @ sK9)) = $false) | ((sK6 @ sK7) = $true) | ~spl0_6), 2.20/0.65 inference(boolean_simplification,[],[f1606])). 2.20/0.65 thf(f1606,plain,( 2.20/0.65 ((sK6 @ sK7) = $true) | ($false = (($true | (sK5 @ sK9 @ sK7)) & (sK6 @ sK9))) | ~spl0_6), 2.20/0.65 inference(superposition,[],[f41,f190])). 2.20/0.65 thf(f190,plain,( 2.20/0.65 ((sK2 @ sK9 @ sK7) = $true) | ~spl0_6), 2.20/0.65 inference(avatar_component_clause,[],[f189])). 2.20/0.65 thf(f1577,plain,( 2.20/0.65 ~spl0_9 | ~spl0_20 | ~spl0_46), 2.20/0.65 inference(avatar_contradiction_clause,[],[f1576])). 2.20/0.65 thf(f1576,plain,( 2.20/0.65 $false | (~spl0_9 | ~spl0_20 | ~spl0_46)), 2.20/0.65 inference(trivial_inequality_removal,[],[f1575])). 2.20/0.65 thf(f1575,plain,( 2.20/0.65 ($true = $false) | (~spl0_9 | ~spl0_20 | ~spl0_46)), 2.20/0.65 inference(forward_demodulation,[],[f1574,f1523])). 2.20/0.65 thf(f1574,plain,( 2.20/0.65 ($true = (sK18 @ sK26)) | (~spl0_9 | ~spl0_20 | ~spl0_46)), 2.20/0.65 inference(boolean_simplification,[],[f1573])). 2.20/0.65 thf(f1573,plain,( 2.20/0.65 ($true = ($true => (sK18 @ sK26))) | (~spl0_9 | ~spl0_20 | ~spl0_46)), 2.20/0.65 inference(forward_demodulation,[],[f1570,f1541])). 2.20/0.65 thf(f1570,plain,( 2.20/0.65 (((sK18 @ sK25) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_46)), 2.20/0.65 inference(boolean_simplification,[],[f1569])). 2.20/0.65 thf(f1569,plain,( 2.20/0.65 ((($true & (sK18 @ sK25)) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_46)), 2.20/0.65 inference(boolean_simplification,[],[f1565])). 2.20/0.65 thf(f1565,plain,( 2.20/0.65 (((((sK2 @ sK25 @ sK26) | $true) & (sK18 @ sK25)) => (sK18 @ sK26)) = $true) | (~spl0_9 | ~spl0_46)), 2.20/0.65 inference(superposition,[],[f552,f1560])). 2.20/0.65 thf(f1560,plain,( 2.20/0.65 ($true = (sK5 @ sK25 @ sK26)) | ~spl0_46), 2.20/0.65 inference(avatar_component_clause,[],[f1559])). 2.20/0.65 thf(f1559,plain,( 2.20/0.65 spl0_46 <=> ($true = (sK5 @ sK25 @ sK26))), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_46])])). 2.20/0.65 thf(f552,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : (($true = ((((sK2 @ X2 @ X1) | (sK5 @ X2 @ X1)) & (sK18 @ X2)) => (sK18 @ X1)))) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f551])). 2.20/0.65 thf(f551,plain,( 2.20/0.65 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK5 @ Y0 @ X1)) & (sK18 @ Y0)) => (sK18 @ X1))) @ X2) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f539])). 2.20/0.65 thf(f539,plain,( 2.20/0.65 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((((sK2 @ Y0 @ X1) | (sK5 @ Y0 @ X1)) & (sK18 @ Y0)) => (sK18 @ X1)))) = $true)) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f538])). 2.20/0.65 thf(f538,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0))))) @ X1) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f492])). 2.20/0.65 thf(f492,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f486])). 2.20/0.65 thf(f486,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f475])). 2.20/0.65 thf(f475,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((sK2 @ Y1 @ Y0) | (sK5 @ Y1 @ Y0)) & (sK18 @ Y1)) => (sK18 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0))))) => (sK18 @ sK17)) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f474])). 2.20/0.65 thf(f474,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))) @ sK18) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f464])). 2.20/0.65 thf(f464,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17)))) = $false) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f463])). 2.20/0.65 thf(f463,plain,( 2.20/0.65 (($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))))) = $false) | ~spl0_9), 2.20/0.65 inference(backward_demodulation,[],[f452,f462])). 2.20/0.65 thf(f462,plain,( 2.20/0.65 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))))) = $true) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f452])). 2.20/0.65 thf(f452,plain,( 2.20/0.65 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15)))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((sK2 @ Y2 @ Y1) | (sK5 @ Y2 @ Y1)) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK17))))) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f451])). 2.20/0.65 thf(f451,plain,( 2.20/0.65 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK5 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK15 @ Y2) | (sK5 @ sK15 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0)))))) @ sK17) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f440])). 2.20/0.65 thf(f440,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK2 @ Y2 @ Y3) | (sK5 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ sK15)))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (((sK2 @ sK15 @ Y2) | (sK5 @ sK15 @ Y2)) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3))))))) => (Y1 @ Y0))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((sK2 @ Y3 @ Y2) | (sK5 @ Y3 @ Y2)) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ sK16 @ Y2) | (sK2 @ sK16 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ Y0))))))) = $false) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f439])). 2.20/0.65 thf(f439,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK5 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK15)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ sK15 @ Y3) | (sK5 @ sK15 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))) @ sK16) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f435])). 2.20/0.65 thf(f435,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK2 @ Y3 @ Y4) | (sK5 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ sK15)))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (((sK2 @ sK15 @ Y3) | (sK5 @ sK15 @ Y3)) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4))))))) => (Y2 @ Y1))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((sK2 @ Y4 @ Y3) | (sK5 @ Y4 @ Y3)) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y1)))))))))) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f434])). 2.20/0.65 thf(f434,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))) @ sK15) = $false) | ~spl0_9), 2.20/0.65 inference(sigma_clausification,[],[f243])). 2.20/0.65 thf(f1561,plain,( 2.20/0.65 spl0_45 | spl0_46 | ~spl0_20), 2.20/0.65 inference(avatar_split_clause,[],[f1554,f635,f1559,f1556])). 2.20/0.65 thf(f1554,plain,( 2.20/0.65 ($true = (sK5 @ sK25 @ sK26)) | ((sK2 @ sK25 @ sK26) = $true) | ~spl0_20), 2.20/0.65 inference(binary_proxy_clausification,[],[f1543])). 2.20/0.65 thf(f1543,plain,( 2.20/0.65 (((sK5 @ sK25 @ sK26) | (sK2 @ sK25 @ sK26)) = $true) | ~spl0_20), 2.20/0.65 inference(boolean_simplification,[],[f1542])). 2.20/0.65 thf(f1542,plain,( 2.20/0.65 (($true & ((sK5 @ sK25 @ sK26) | (sK2 @ sK25 @ sK26))) = $true) | ~spl0_20), 2.20/0.65 inference(backward_demodulation,[],[f1524,f1541])). 2.20/0.65 thf(f1450,plain,( 2.20/0.65 ~spl0_9 | ~spl0_19), 2.20/0.65 inference(avatar_contradiction_clause,[],[f1449])). 2.20/0.65 thf(f1449,plain,( 2.20/0.65 $false | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(trivial_inequality_removal,[],[f1448])). 2.20/0.65 thf(f1448,plain,( 2.20/0.65 ($true = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(forward_demodulation,[],[f1447,f1083])). 2.20/0.65 thf(f1083,plain,( 2.20/0.65 ((sK18 @ sK21) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(binary_proxy_clausification,[],[f1012])). 2.20/0.65 thf(f1012,plain,( 2.20/0.65 ((((sK18 @ sK20) & ((sK2 @ sK20 @ sK21) | (sK5 @ sK20 @ sK21))) => (sK18 @ sK21)) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(beta_eta_normalization,[],[f1011])). 2.20/0.65 thf(f1011,plain,( 2.20/0.65 (((^[Y0 : a]: (((sK18 @ sK20) & ((sK2 @ sK20 @ Y0) | (sK5 @ sK20 @ Y0))) => (sK18 @ Y0))) @ sK21) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(sigma_clausification,[],[f988])). 2.20/0.65 thf(f988,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (((sK18 @ sK20) & ((sK2 @ sK20 @ Y0) | (sK5 @ sK20 @ Y0))) => (sK18 @ Y0))))) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(beta_eta_normalization,[],[f984])). 2.20/0.65 thf(f984,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1))))) @ sK20) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(sigma_clausification,[],[f959])). 2.20/0.65 thf(f959,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1)))))) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(not_proxy_clausification,[],[f698])). 2.20/0.65 thf(f698,plain,( 2.20/0.65 ((~ (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1))))))) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f696])). 2.20/0.65 thf(f696,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1)))))) => $false) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(backward_demodulation,[],[f694,f695])). 2.20/0.65 thf(f695,plain,( 2.20/0.65 ((sK18 @ sK15) = $false) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(not_proxy_clausification,[],[f689])). 2.20/0.65 thf(f689,plain,( 2.20/0.65 ((~ (sK18 @ sK15)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f688])). 2.20/0.65 thf(f688,plain,( 2.20/0.65 (((sK18 @ sK15) => $false) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(forward_demodulation,[],[f679,f664])). 2.20/0.65 thf(f664,plain,( 2.20/0.65 ((sK18 @ sK19) = $false) | ~spl0_19), 2.20/0.65 inference(boolean_simplification,[],[f663])). 2.20/0.65 thf(f663,plain,( 2.20/0.65 (($true => (sK18 @ sK19)) = $false) | ~spl0_19), 2.20/0.65 inference(backward_demodulation,[],[f655,f662])). 2.20/0.65 thf(f662,plain,( 2.20/0.65 (((sK2 @ sK15 @ sK19) | (sK5 @ sK15 @ sK19)) = $true) | ~spl0_19), 2.20/0.65 inference(binary_proxy_clausification,[],[f655])). 2.20/0.65 thf(f655,plain,( 2.20/0.65 ((((sK2 @ sK15 @ sK19) | (sK5 @ sK15 @ sK19)) => (sK18 @ sK19)) = $false) | ~spl0_19), 2.20/0.65 inference(beta_eta_normalization,[],[f653])). 2.20/0.65 thf(f653,plain,( 2.20/0.65 ($false = ((^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0))) @ sK19)) | ~spl0_19), 2.20/0.65 inference(sigma_clausification,[],[f633])). 2.20/0.65 thf(f633,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) = $false) | ~spl0_19), 2.20/0.65 inference(avatar_component_clause,[],[f632])). 2.20/0.65 thf(f632,plain,( 2.20/0.65 spl0_19 <=> ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])). 2.20/0.65 thf(f679,plain,( 2.20/0.65 (((sK18 @ sK15) => (sK18 @ sK19)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f678])). 2.20/0.65 thf(f678,plain,( 2.20/0.65 ((($true & (sK18 @ sK15)) => (sK18 @ sK19)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(superposition,[],[f552,f662])). 2.20/0.65 thf(f694,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1)))))) => (sK18 @ sK15)) = $true) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f693])). 2.20/0.65 thf(f693,plain,( 2.20/0.65 ((($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (sK18 @ Y1))))))) => (sK18 @ sK15)) = $true) | ~spl0_9), 2.20/0.65 inference(superposition,[],[f675,f494])). 2.20/0.65 thf(f494,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0)))) = $true) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f493])). 2.20/0.65 thf(f493,plain,( 2.20/0.65 ($true = ($true & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (sK18 @ Y0)))))) | ~spl0_9), 2.20/0.65 inference(backward_demodulation,[],[f486,f492])). 2.20/0.65 thf(f675,plain,( 2.20/0.65 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((sK5 @ sK16 @ Y0) | (sK2 @ sK16 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK2 @ Y0 @ Y1) | (sK5 @ Y0 @ Y1))) => (X1 @ Y1))))))) => (X1 @ sK15)))) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f674])). 2.20/0.65 thf(f674,plain,( 2.20/0.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15))) @ X1) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f510])). 2.20/0.65 thf(f510,plain,( 2.20/0.65 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK5 @ sK16 @ Y1) | (sK2 @ sK16 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK2 @ Y1 @ Y2) | (sK5 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK15))))) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f462])). 2.20/0.65 thf(f1447,plain,( 2.20/0.65 ($true = (sK18 @ sK21)) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f1446])). 2.20/0.65 thf(f1446,plain,( 2.20/0.65 (($true => (sK18 @ sK21)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(forward_demodulation,[],[f1445,f1277])). 2.20/0.65 thf(f1277,plain,( 2.20/0.65 ((sK18 @ sK20) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f1276])). 2.20/0.65 thf(f1276,plain,( 2.20/0.65 ($true = ((sK18 @ sK20) & $true)) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(backward_demodulation,[],[f1084,f1274])). 2.20/0.65 thf(f1274,plain,( 2.20/0.65 (((sK2 @ sK20 @ sK21) | (sK5 @ sK20 @ sK21)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(binary_proxy_clausification,[],[f1084])). 2.20/0.65 thf(f1084,plain,( 2.20/0.65 (((sK18 @ sK20) & ((sK2 @ sK20 @ sK21) | (sK5 @ sK20 @ sK21))) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(binary_proxy_clausification,[],[f1012])). 2.20/0.65 thf(f1445,plain,( 2.20/0.65 (((sK18 @ sK20) => (sK18 @ sK21)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(boolean_simplification,[],[f1442])). 2.20/0.65 thf(f1442,plain,( 2.20/0.65 ((($true & (sK18 @ sK20)) => (sK18 @ sK21)) = $true) | (~spl0_9 | ~spl0_19)), 2.20/0.65 inference(superposition,[],[f552,f1274])). 2.20/0.65 thf(f637,plain,( 2.20/0.65 spl0_19 | spl0_20 | ~spl0_9), 2.20/0.65 inference(avatar_split_clause,[],[f628,f242,f635,f632])). 2.20/0.65 thf(f628,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1)))))) = $false) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f619])). 2.20/0.65 thf(f619,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1))))))) = $false) | ~spl0_9), 2.20/0.65 inference(not_proxy_clausification,[],[f526])). 2.20/0.65 thf(f526,plain,( 2.20/0.65 ($true = (~ ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1))))))))) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f525])). 2.20/0.65 thf(f525,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (sK18 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK18 @ Y1))))))) => $false) = $true) | ~spl0_9), 2.20/0.65 inference(superposition,[],[f517,f485])). 2.20/0.65 thf(f485,plain,( 2.20/0.65 ((sK18 @ sK17) = $false) | ~spl0_9), 2.20/0.65 inference(binary_proxy_clausification,[],[f475])). 2.20/0.65 thf(f517,plain,( 2.20/0.65 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (((sK2 @ sK15 @ Y0) | (sK5 @ sK15 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (X1 @ Y1))))))) => (X1 @ sK17)) = $true)) ) | ~spl0_9), 2.20/0.65 inference(beta_eta_normalization,[],[f516])). 2.20/0.65 thf(f516,plain,( 2.20/0.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))) @ X1) = $true)) ) | ~spl0_9), 2.20/0.65 inference(pi_clausification,[],[f512])). 2.20/0.65 thf(f512,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17)))) = $true) | ~spl0_9), 2.20/0.65 inference(boolean_simplification,[],[f511])). 2.20/0.65 thf(f511,plain,( 2.20/0.65 (($true & (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK15 @ Y1) | (sK5 @ sK15 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2))))))) => (Y0 @ sK17))))) = $true) | ~spl0_9), 2.20/0.65 inference(backward_demodulation,[],[f462,f510])). 2.20/0.65 thf(f431,plain,( 2.20/0.65 ~spl0_10 | ~spl0_14), 2.20/0.65 inference(avatar_contradiction_clause,[],[f430])). 2.20/0.65 thf(f430,plain,( 2.20/0.65 $false | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(trivial_inequality_removal,[],[f429])). 2.20/0.65 thf(f429,plain,( 2.20/0.65 ($true = $false) | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(boolean_simplification,[],[f428])). 2.20/0.65 thf(f428,plain,( 2.20/0.65 ($true = (~ $true)) | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(boolean_simplification,[],[f427])). 2.20/0.65 thf(f427,plain,( 2.20/0.65 ((~ ($true | (sK2 @ sK12 @ sK14))) = $true) | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(forward_demodulation,[],[f425,f415])). 2.20/0.65 thf(f415,plain,( 2.20/0.65 ((sK5 @ sK12 @ sK14) = $true) | ~spl0_14), 2.20/0.65 inference(binary_proxy_clausification,[],[f413])). 2.20/0.65 thf(f413,plain,( 2.20/0.65 ($false = ((sK5 @ sK12 @ sK14) => (sK13 @ sK14))) | ~spl0_14), 2.20/0.65 inference(beta_eta_normalization,[],[f409])). 2.20/0.65 thf(f409,plain,( 2.20/0.65 (((^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0))) @ sK14) = $false) | ~spl0_14), 2.20/0.65 inference(sigma_clausification,[],[f392])). 2.20/0.65 thf(f392,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | ~spl0_14), 2.20/0.65 inference(avatar_component_clause,[],[f391])). 2.20/0.65 thf(f391,plain,( 2.20/0.65 spl0_14 <=> ((!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_14])])). 2.20/0.65 thf(f425,plain,( 2.20/0.65 ((~ ((sK5 @ sK12 @ sK14) | (sK2 @ sK12 @ sK14))) = $true) | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(boolean_simplification,[],[f421])). 2.20/0.65 thf(f421,plain,( 2.20/0.65 ((((sK5 @ sK12 @ sK14) | (sK2 @ sK12 @ sK14)) => $false) = $true) | (~spl0_10 | ~spl0_14)), 2.20/0.65 inference(superposition,[],[f271,f417])). 2.20/0.65 thf(f417,plain,( 2.20/0.65 ((sK13 @ sK14) = $false) | ~spl0_14), 2.20/0.65 inference(boolean_simplification,[],[f416])). 2.20/0.65 thf(f416,plain,( 2.20/0.65 (($true => (sK13 @ sK14)) = $false) | ~spl0_14), 2.20/0.65 inference(backward_demodulation,[],[f413,f415])). 2.20/0.65 thf(f271,plain,( 2.20/0.65 ( ! [X1 : a] : (((((sK5 @ sK12 @ X1) | (sK2 @ sK12 @ X1)) => (sK13 @ X1)) = $true)) ) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f270])). 2.20/0.65 thf(f270,plain,( 2.20/0.65 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))) @ X1) = $true)) ) | ~spl0_10), 2.20/0.65 inference(pi_clausification,[],[f269])). 2.20/0.65 thf(f269,plain,( 2.20/0.65 ($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) | ~spl0_10), 2.20/0.65 inference(boolean_simplification,[],[f268])). 2.20/0.65 thf(f268,plain,( 2.20/0.65 (($true & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) = $true) | ~spl0_10), 2.20/0.65 inference(backward_demodulation,[],[f261,f267])). 2.20/0.65 thf(f267,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) = $true) | ~spl0_10), 2.20/0.65 inference(binary_proxy_clausification,[],[f261])). 2.20/0.65 thf(f261,plain,( 2.20/0.65 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0)))))) | ~spl0_10), 2.20/0.65 inference(binary_proxy_clausification,[],[f259])). 2.20/0.65 thf(f259,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & ((sK5 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1))) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK12 @ Y0) | (sK2 @ sK12 @ Y0)) => (sK13 @ Y0))))) => (sK13 @ sK11)) = $false) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f258])). 2.20/0.65 thf(f258,plain,( 2.20/0.65 (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ sK13) = $false) | ~spl0_10), 2.20/0.65 inference(sigma_clausification,[],[f257])). 2.20/0.65 thf(f257,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $false) | ~spl0_10), 2.20/0.65 inference(boolean_simplification,[],[f256])). 2.20/0.65 thf(f256,plain,( 2.20/0.65 ($false = ($true => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11)))))) | ~spl0_10), 2.20/0.65 inference(backward_demodulation,[],[f253,f255])). 2.20/0.65 thf(f255,plain,( 2.20/0.65 (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) = $true) | ~spl0_10), 2.20/0.65 inference(binary_proxy_clausification,[],[f253])). 2.20/0.65 thf(f253,plain,( 2.20/0.65 ((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11))))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & ((sK5 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2))) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK12 @ Y1) | (sK2 @ sK12 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK11))))) = $false) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f252])). 2.20/0.65 thf(f252,plain,( 2.20/0.65 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK11)))))) @ sK12) = $false) | ~spl0_10), 2.20/0.65 inference(sigma_clausification,[],[f251])). 2.20/0.65 thf(f251,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ Y0 @ Y2) => (Y1 @ Y2))))) => (Y1 @ sK11)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((sK2 @ Y0 @ Y2) => (Y1 @ Y2)))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK2 @ Y2 @ Y3)) => (Y1 @ Y3))))))) => (Y1 @ sK11))))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & ((sK5 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3))) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((sK5 @ Y0 @ Y2) | (sK2 @ Y0 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK11))))))) = $false) | ~spl0_10), 2.20/0.65 inference(beta_eta_normalization,[],[f250])). 2.20/0.65 thf(f250,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0)))))))) @ sK11) = $false) | ~spl0_10), 2.20/0.65 inference(sigma_clausification,[],[f246])). 2.20/0.65 thf(f393,plain,( 2.20/0.65 spl0_13 | spl0_14 | ~spl0_10 | ~spl0_12), 2.20/0.65 inference(avatar_split_clause,[],[f384,f283,f245,f391,f388])). 2.20/0.65 thf(f384,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0)))) = $false) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(binary_proxy_clausification,[],[f368])). 2.20/0.65 thf(f368,plain,( 2.20/0.65 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0)))))) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(not_proxy_clausification,[],[f310])). 2.20/0.65 thf(f310,plain,( 2.20/0.65 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0)))))) = $true) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(boolean_simplification,[],[f306])). 2.20/0.65 thf(f306,plain,( 2.20/0.65 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK13 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK13 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (sK13 @ Y0))))) => $false) = $true) | (~spl0_10 | ~spl0_12)), 2.20/0.65 inference(superposition,[],[f295,f260])). 2.20/0.65 thf(f260,plain,( 2.20/0.65 ((sK13 @ sK11) = $false) | ~spl0_10), 2.20/0.65 inference(binary_proxy_clausification,[],[f259])). 2.20/0.65 thf(f295,plain,( 2.20/0.65 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK5 @ Y0 @ Y1)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK12 @ Y0) => (X1 @ Y0))))) => (X1 @ sK11)) = $true)) ) | ~spl0_12), 2.20/0.65 inference(beta_eta_normalization,[],[f294])). 2.20/0.65 thf(f294,plain,( 2.20/0.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ X1) = $true)) ) | ~spl0_12), 2.20/0.65 inference(pi_clausification,[],[f284])). 2.20/0.65 thf(f285,plain,( 2.20/0.65 spl0_11 | spl0_12 | ~spl0_10), 2.20/0.65 inference(avatar_split_clause,[],[f278,f245,f283,f280])). 2.20/0.65 thf(f278,plain,( 2.20/0.65 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((sK2 @ sK12 @ Y1) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK2 @ Y1 @ Y2)) => (Y0 @ Y2))))))) => (Y0 @ sK11)))) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK12 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true) | ~spl0_10), 2.20/0.65 inference(binary_proxy_clausification,[],[f255])). 2.20/0.65 thf(f247,plain,( 2.20/0.65 spl0_9 | spl0_10 | ~spl0_1), 2.20/0.65 inference(avatar_split_clause,[],[f240,f52,f245,f242])). 2.20/0.65 thf(f52,plain,( 2.20/0.65 spl0_1 <=> (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 2.20/0.65 thf(f240,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) | ~spl0_1), 2.20/0.65 inference(binary_proxy_clausification,[],[f53])). 2.20/0.65 thf(f53,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) = $false) | ~spl0_1), 2.20/0.65 inference(avatar_component_clause,[],[f52])). 2.20/0.65 thf(f236,plain,( 2.20/0.65 ~spl0_4 | ~spl0_8), 2.20/0.65 inference(avatar_contradiction_clause,[],[f235])). 2.20/0.65 thf(f235,plain,( 2.20/0.65 $false | (~spl0_4 | ~spl0_8)), 2.20/0.65 inference(trivial_inequality_removal,[],[f234])). 2.20/0.65 thf(f234,plain,( 2.20/0.65 ($true = $false) | (~spl0_4 | ~spl0_8)), 2.20/0.65 inference(boolean_simplification,[],[f233])). 2.20/0.65 thf(f233,plain,( 2.20/0.65 ($true = (~ $true)) | (~spl0_4 | ~spl0_8)), 2.20/0.65 inference(boolean_simplification,[],[f231])). 2.20/0.65 thf(f231,plain,( 2.20/0.65 ((~ ((sK5 @ sK4 @ sK10) | $true)) = $true) | (~spl0_4 | ~spl0_8)), 2.20/0.65 inference(backward_demodulation,[],[f211,f222])). 2.20/0.65 thf(f222,plain,( 2.20/0.65 ($true = (sK2 @ sK4 @ sK10)) | ~spl0_8), 2.20/0.65 inference(avatar_component_clause,[],[f221])). 2.20/0.65 thf(f221,plain,( 2.20/0.65 spl0_8 <=> ($true = (sK2 @ sK4 @ sK10))), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 2.20/0.65 thf(f211,plain,( 2.20/0.65 ($true = (~ ((sK5 @ sK4 @ sK10) | (sK2 @ sK4 @ sK10)))) | ~spl0_4), 2.20/0.65 inference(boolean_simplification,[],[f206])). 2.20/0.65 thf(f206,plain,( 2.20/0.65 ($true = (((sK5 @ sK4 @ sK10) | (sK2 @ sK4 @ sK10)) => $false)) | ~spl0_4), 2.20/0.65 inference(superposition,[],[f35,f202])). 2.20/0.65 thf(f202,plain,( 2.20/0.65 ($false = (sK6 @ sK10)) | ~spl0_4), 2.20/0.65 inference(boolean_simplification,[],[f201])). 2.20/0.65 thf(f201,plain,( 2.20/0.65 (($true => (sK6 @ sK10)) = $false) | ~spl0_4), 2.20/0.65 inference(backward_demodulation,[],[f198,f200])). 2.20/0.65 thf(f200,plain,( 2.20/0.65 ($true = ((sK2 @ sK4 @ sK10) | (sK5 @ sK4 @ sK10))) | ~spl0_4), 2.20/0.65 inference(binary_proxy_clausification,[],[f198])). 2.20/0.65 thf(f198,plain,( 2.20/0.65 ((((sK2 @ sK4 @ sK10) | (sK5 @ sK4 @ sK10)) => (sK6 @ sK10)) = $false) | ~spl0_4), 2.20/0.65 inference(beta_eta_normalization,[],[f194])). 2.20/0.65 thf(f194,plain,( 2.20/0.65 (((^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0))) @ sK10) = $false) | ~spl0_4), 2.20/0.65 inference(sigma_clausification,[],[f136])). 2.20/0.65 thf(f136,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0))))) | ~spl0_4), 2.20/0.65 inference(avatar_component_clause,[],[f135])). 2.20/0.65 thf(f135,plain,( 2.20/0.65 spl0_4 <=> ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0)))))), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 2.20/0.65 thf(f35,plain,( 2.20/0.65 ( ! [X1 : a] : (((((sK5 @ sK4 @ X1) | (sK2 @ sK4 @ X1)) => (sK6 @ X1)) = $true)) )), 2.20/0.65 inference(beta_eta_normalization,[],[f34])). 2.20/0.65 thf(f34,plain,( 2.20/0.65 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))) @ X1))) )), 2.20/0.65 inference(pi_clausification,[],[f28])). 2.20/0.65 thf(f229,plain,( 2.20/0.65 ~spl0_4 | ~spl0_7), 2.20/0.65 inference(avatar_contradiction_clause,[],[f228])). 2.20/0.65 thf(f228,plain,( 2.20/0.65 $false | (~spl0_4 | ~spl0_7)), 2.20/0.65 inference(trivial_inequality_removal,[],[f227])). 2.20/0.65 thf(f227,plain,( 2.20/0.65 ($true = $false) | (~spl0_4 | ~spl0_7)), 2.20/0.65 inference(boolean_simplification,[],[f226])). 2.20/0.65 thf(f226,plain,( 2.20/0.65 ($true = (~ $true)) | (~spl0_4 | ~spl0_7)), 2.20/0.65 inference(boolean_simplification,[],[f224])). 2.20/0.65 thf(f224,plain,( 2.20/0.65 ((~ ($true | (sK2 @ sK4 @ sK10))) = $true) | (~spl0_4 | ~spl0_7)), 2.20/0.65 inference(backward_demodulation,[],[f211,f219])). 2.20/0.65 thf(f219,plain,( 2.20/0.65 ((sK5 @ sK4 @ sK10) = $true) | ~spl0_7), 2.20/0.65 inference(avatar_component_clause,[],[f218])). 2.20/0.65 thf(f218,plain,( 2.20/0.65 spl0_7 <=> ((sK5 @ sK4 @ sK10) = $true)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])). 2.20/0.65 thf(f223,plain,( 2.20/0.65 spl0_7 | spl0_8 | ~spl0_4), 2.20/0.65 inference(avatar_split_clause,[],[f212,f135,f221,f218])). 2.20/0.65 thf(f212,plain,( 2.20/0.65 ((sK5 @ sK4 @ sK10) = $true) | ($true = (sK2 @ sK4 @ sK10)) | ~spl0_4), 2.20/0.65 inference(binary_proxy_clausification,[],[f200])). 2.20/0.65 thf(f191,plain,( 2.20/0.65 spl0_5 | spl0_6 | ~spl0_3), 2.20/0.65 inference(avatar_split_clause,[],[f184,f132,f189,f186])). 2.20/0.65 thf(f184,plain,( 2.20/0.65 ((sK2 @ sK9 @ sK7) = $true) | ((sK5 @ sK9 @ sK7) = $true) | ~spl0_3), 2.20/0.65 inference(binary_proxy_clausification,[],[f175])). 2.20/0.65 thf(f175,plain,( 2.20/0.65 (((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)) = $true) | ~spl0_3), 2.20/0.65 inference(boolean_simplification,[],[f174])). 2.20/0.65 thf(f174,plain,( 2.20/0.65 ($true = ($true & ((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)))) | ~spl0_3), 2.20/0.65 inference(backward_demodulation,[],[f166,f173])). 2.20/0.65 thf(f173,plain,( 2.20/0.65 ((sK6 @ sK9) = $true) | ~spl0_3), 2.20/0.65 inference(binary_proxy_clausification,[],[f166])). 2.20/0.65 thf(f166,plain,( 2.20/0.65 ($true = ((sK6 @ sK9) & ((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)))) | ~spl0_3), 2.20/0.65 inference(not_proxy_clausification,[],[f156])). 2.20/0.65 thf(f156,plain,( 2.20/0.65 ((~ ((sK6 @ sK9) & ((sK5 @ sK9 @ sK7) | (sK2 @ sK9 @ sK7)))) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f155])). 2.20/0.65 thf(f155,plain,( 2.20/0.65 (((^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))))) @ sK9) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f152])). 2.20/0.65 thf(f152,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7)))))) = $false) | ~spl0_3), 2.20/0.65 inference(boolean_simplification,[],[f150])). 2.20/0.65 thf(f150,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => $false))) = $false) | ~spl0_3), 2.20/0.65 inference(backward_demodulation,[],[f142,f147])). 2.20/0.65 thf(f147,plain,( 2.20/0.65 ((sK6 @ sK7) = $false) | ~spl0_3), 2.20/0.65 inference(binary_proxy_clausification,[],[f146])). 2.20/0.65 thf(f146,plain,( 2.20/0.65 ((((sK6 @ sK8) & ((sK5 @ sK8 @ sK7) | (sK2 @ sK8 @ sK7))) => (sK6 @ sK7)) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f145])). 2.20/0.65 thf(f145,plain,( 2.20/0.65 (((^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => (sK6 @ sK7))) @ sK8) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f142])). 2.20/0.65 thf(f142,plain,( 2.20/0.65 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ sK7) | (sK2 @ Y0 @ sK7))) => (sK6 @ sK7)))) = $false) | ~spl0_3), 2.20/0.65 inference(beta_eta_normalization,[],[f140])). 2.20/0.65 thf(f140,plain,( 2.20/0.65 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))) @ sK7) = $false) | ~spl0_3), 2.20/0.65 inference(sigma_clausification,[],[f133])). 2.20/0.65 thf(f137,plain,( 2.20/0.65 spl0_3 | spl0_4 | ~spl0_2), 2.20/0.65 inference(avatar_split_clause,[],[f128,f55,f135,f132])). 2.20/0.65 thf(f55,plain,( 2.20/0.65 spl0_2 <=> ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))))) = $false)), 2.20/0.65 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 2.20/0.65 thf(f128,plain,( 2.20/0.65 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $false) | ~spl0_2), 2.20/0.65 inference(binary_proxy_clausification,[],[f125])). 2.20/0.65 thf(f125,plain,( 2.20/0.65 (((!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))))) = $false) | ~spl0_2), 2.20/0.65 inference(not_proxy_clausification,[],[f94])). 2.20/0.65 thf(f94,plain,( 2.20/0.65 ((~ ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))))) = $true) | ~spl0_2), 2.20/0.65 inference(boolean_simplification,[],[f90])). 2.20/0.65 thf(f90,plain,( 2.20/0.65 ($true = (((!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (sK6 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))))) => $false)) | ~spl0_2), 2.20/0.65 inference(superposition,[],[f79,f27])). 2.20/0.65 thf(f27,plain,( 2.20/0.65 ((sK6 @ sK3) = $false)), 2.20/0.65 inference(boolean_simplification,[],[f26])). 2.20/0.65 thf(f26,plain,( 2.20/0.65 (($true => (sK6 @ sK3)) = $false)), 2.20/0.65 inference(backward_demodulation,[],[f23,f25])). 2.20/0.65 thf(f79,plain,( 2.20/0.65 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (((sK2 @ sK4 @ Y0) | (sK5 @ sK4 @ Y0)) => (X1 @ Y0)))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (X1 @ Y0))))))) => (X1 @ sK3)))) ) | ~spl0_2), 2.20/0.65 inference(beta_eta_normalization,[],[f78])). 2.20/0.65 thf(f78,plain,( 2.20/0.65 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))) @ X1) = $true)) ) | ~spl0_2), 2.20/0.65 inference(pi_clausification,[],[f66])). 2.20/0.65 thf(f66,plain,( 2.20/0.65 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))))) | ~spl0_2), 2.20/0.65 inference(not_proxy_clausification,[],[f56])). 2.20/0.65 thf(f56,plain,( 2.20/0.65 ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))))) = $false) | ~spl0_2), 2.20/0.65 inference(avatar_component_clause,[],[f55])). 2.20/0.65 thf(f57,plain,( 2.20/0.65 spl0_1 | spl0_2), 2.20/0.65 inference(avatar_split_clause,[],[f50,f55,f52])). 2.20/0.65 thf(f50,plain,( 2.20/0.65 ((~ (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (((sK2 @ sK4 @ Y1) | (sK5 @ sK4 @ Y1)) => (Y0 @ Y1)))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1))))))) => (Y0 @ sK3))))) = $false) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y1 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y0)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((sK2 @ Y1 @ Y3) => (Y2 @ Y3)))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK2 @ Y3 @ Y4)) => (Y2 @ Y4))))))) => (Y2 @ Y0))))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & ((sK5 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4))) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((sK5 @ Y1 @ Y3) | (sK2 @ Y1 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ Y0))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK2 @ Y4 @ Y5) | (sK5 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y0)))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (((sK2 @ Y0 @ Y4) | (sK5 @ Y0 @ Y4)) => (Y3 @ Y4)))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & ((sK5 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5))) => (Y3 @ Y5))))))) => (Y3 @ Y2))))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((sK2 @ Y5 @ Y4) | (sK5 @ Y5 @ Y4)) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((sK5 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y2)))))))))))) = $false)), 2.20/0.65 inference(binary_proxy_clausification,[],[f18])). 2.20/0.65 % SZS output end Proof for Vampire---4 2.20/0.65 % (25637)------------------------------ 2.20/0.65 % (25637)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.20/0.65 % (25637)Termination reason: Refutation 2.20/0.65 2.20/0.65 % (25637)Memory used [KB]: 7419 2.20/0.65 % (25637)Time elapsed: 0.188 s 2.20/0.65 % (25637)Instructions burned: 419 (million) 2.20/0.65 % (25637)------------------------------ 2.20/0.65 % (25637)------------------------------ 2.20/0.65 % (25617)Success in time 0.267 s 2.20/0.65 % Vampire---4.8 exiting 2.20/0.65 EOF