0.07/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s 0.08/0.32 % Computer : n032.cluster.edu 0.08/0.32 % Model : x86_64 x86_64 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.32 % Memory : 8042.1875MB 0.08/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.32 % CPULimit : 300 0.08/0.32 % WCLimit : 300 0.08/0.32 % DateTime : Fri Jul 5 04:23:39 EDT 2024 0.08/0.32 % CPUTime : 0.08/0.33 This is a THF_ problem 0.08/0.33 Running vampire_ho --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.08/0.34 % (18811)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (3000ds/96Mi) 0.08/0.35 % (18815)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (3000ds/17Mi) 0.08/0.35 % (18812)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (3000ds/36Mi) 0.08/0.35 % (18813)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (3000ds/34Mi) 0.08/0.35 % (18814)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on theBenchmark for (3000ds/385Mi) 0.08/0.35 % (18816)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 theBenchmark for (3000ds/74Mi) 0.08/0.35 % (18818)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on theBenchmark for (3000ds/915Mi) 0.08/0.35 % (18817)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi) 0.08/0.35 % (18817)Instruction limit reached! 0.08/0.35 % (18817)------------------------------ 0.08/0.35 % (18817)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.35 % (18817)Termination reason: Unknown 0.08/0.35 % (18817)Termination phase: Naming 0.08/0.35 0.08/0.35 % (18817)Memory used [KB]: 1023 0.08/0.35 % (18817)Time elapsed: 0.004 s 0.08/0.35 % (18817)Instructions burned: 4 (million) 0.08/0.35 % (18817)------------------------------ 0.08/0.35 % (18817)------------------------------ 0.08/0.35 % (18815)Instruction limit reached! 0.08/0.35 % (18815)------------------------------ 0.08/0.35 % (18815)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.35 % (18815)Termination reason: Unknown 0.08/0.35 % (18815)Termination phase: Saturation 0.08/0.35 0.08/0.35 % (18815)Memory used [KB]: 5756 0.08/0.35 % (18815)Time elapsed: 0.010 s 0.08/0.35 % (18815)Instructions burned: 17 (million) 0.08/0.35 % (18815)------------------------------ 0.08/0.35 % (18815)------------------------------ 0.08/0.36 % (18819)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 theBenchmark for (2999ds/21Mi) 0.08/0.36 % (18812)Instruction limit reached! 0.08/0.36 % (18812)------------------------------ 0.08/0.36 % (18812)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.36 % (18812)Termination reason: Unknown 0.08/0.36 % (18812)Termination phase: Saturation 0.08/0.36 0.08/0.36 % (18812)Memory used [KB]: 5756 0.08/0.36 % (18812)Time elapsed: 0.020 s 0.08/0.36 % (18812)Instructions burned: 36 (million) 0.08/0.36 % (18812)------------------------------ 0.08/0.36 % (18812)------------------------------ 0.08/0.37 % (18813)Instruction limit reached! 0.08/0.37 % (18813)------------------------------ 0.08/0.37 % (18813)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.37 % (18813)Termination reason: Unknown 0.08/0.37 % (18813)Termination phase: Saturation 0.08/0.37 0.08/0.37 % (18813)Memory used [KB]: 5884 0.08/0.37 % (18813)Time elapsed: 0.021 s 0.08/0.37 % (18813)Instructions burned: 35 (million) 0.08/0.37 % (18813)------------------------------ 0.08/0.37 % (18813)------------------------------ 0.08/0.37 % (18820)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.08/0.37 % (18820)Instruction limit reached! 0.08/0.37 % (18820)------------------------------ 0.08/0.37 % (18820)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.37 % (18820)Termination reason: Unknown 0.08/0.37 % (18820)Termination phase: Property scanning 0.08/0.37 0.08/0.37 % (18820)Memory used [KB]: 1151 0.08/0.37 % (18820)Time elapsed: 0.005 s 0.08/0.37 % (18820)Instructions burned: 8 (million) 0.08/0.37 % (18820)------------------------------ 0.08/0.37 % (18820)------------------------------ 0.08/0.37 % (18811)Instruction limit reached! 0.08/0.37 % (18811)------------------------------ 0.08/0.37 % (18811)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.37 % (18811)Termination reason: Unknown 0.08/0.37 % (18811)Termination phase: Saturation 0.08/0.37 0.08/0.37 % (18811)Memory used [KB]: 6012 0.08/0.37 % (18811)Time elapsed: 0.034 s 0.08/0.37 % (18811)Instructions burned: 99 (million) 0.08/0.37 % (18811)------------------------------ 0.08/0.37 % (18811)------------------------------ 0.08/0.37 % (18819)Instruction limit reached! 0.08/0.37 % (18819)------------------------------ 0.08/0.37 % (18819)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.37 % (18819)Termination reason: Unknown 0.08/0.37 % (18819)Termination phase: Saturation 0.08/0.37 0.08/0.37 % (18819)Memory used [KB]: 5756 0.08/0.37 % (18819)Time elapsed: 0.012 s 0.08/0.37 % (18819)Instructions burned: 21 (million) 0.08/0.37 % (18819)------------------------------ 0.08/0.37 % (18819)------------------------------ 0.08/0.38 % (18821)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 theBenchmark for (2999ds/1021Mi) 0.08/0.38 % (18824)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on theBenchmark for (2999ds/1044Mi) 0.08/0.38 % (18816)Instruction limit reached! 0.08/0.38 % (18816)------------------------------ 0.08/0.38 % (18816)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.08/0.38 % (18816)Termination reason: Unknown 0.08/0.38 % (18816)Termination phase: Saturation 0.08/0.38 0.08/0.38 % (18816)Memory used [KB]: 5884 0.08/0.38 % (18816)Time elapsed: 0.038 s 0.08/0.38 % (18816)Instructions burned: 74 (million) 0.08/0.38 % (18816)------------------------------ 0.08/0.38 % (18816)------------------------------ 0.08/0.38 % (18823)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 theBenchmark for (2999ds/9Mi) 0.14/0.39 % (18822)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2999ds/71Mi) 0.14/0.39 % (18823)Instruction limit reached! 0.14/0.39 % (18823)------------------------------ 0.14/0.39 % (18823)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.39 % (18823)Termination reason: Unknown 0.14/0.39 % (18823)Termination phase: Property scanning 0.14/0.39 0.14/0.39 % (18823)Memory used [KB]: 1151 0.14/0.39 % (18823)Time elapsed: 0.005 s 0.14/0.39 % (18823)Instructions burned: 9 (million) 0.14/0.39 % (18823)------------------------------ 0.14/0.39 % (18823)------------------------------ 0.14/0.39 % (18825)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on theBenchmark for (2999ds/128Mi) 0.14/0.40 % (18826)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.14/0.40 % (18827)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.14/0.41 % (18827)Instruction limit reached! 0.14/0.41 % (18827)------------------------------ 0.14/0.41 % (18827)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.41 % (18827)Termination reason: Unknown 0.14/0.41 % (18827)Termination phase: Saturation 0.14/0.41 0.14/0.41 % (18827)Memory used [KB]: 5628 0.14/0.41 % (18827)Time elapsed: 0.008 s 0.14/0.41 % (18827)Instructions burned: 14 (million) 0.14/0.41 % (18827)------------------------------ 0.14/0.41 % (18827)------------------------------ 0.14/0.42 % (18828)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 theBenchmark for (2999ds/2Mi) 0.14/0.42 % (18828)Instruction limit reached! 0.14/0.42 % (18828)------------------------------ 0.14/0.42 % (18828)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.42 % (18828)Termination reason: Unknown 0.14/0.42 % (18828)Termination phase: shuffling 0.14/0.42 0.14/0.42 % (18828)Memory used [KB]: 1023 0.14/0.42 % (18828)Time elapsed: 0.003 s 0.14/0.42 % (18828)Instructions burned: 3 (million) 0.14/0.42 % (18828)------------------------------ 0.14/0.42 % (18828)------------------------------ 0.14/0.42 % (18822)Instruction limit reached! 0.14/0.42 % (18822)------------------------------ 0.14/0.42 % (18822)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.42 % (18822)Termination reason: Unknown 0.14/0.42 % (18822)Termination phase: Saturation 0.14/0.42 0.14/0.42 % (18822)Memory used [KB]: 6012 0.14/0.42 % (18822)Time elapsed: 0.038 s 0.14/0.42 % (18822)Instructions burned: 72 (million) 0.14/0.42 % (18822)------------------------------ 0.14/0.42 % (18822)------------------------------ 0.14/0.43 % (18826)Instruction limit reached! 0.14/0.43 % (18826)------------------------------ 0.14/0.43 % (18826)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.43 % (18826)Termination reason: Unknown 0.14/0.43 % (18826)Termination phase: Saturation 0.14/0.43 0.14/0.43 % (18826)Memory used [KB]: 6012 0.14/0.43 % (18826)Time elapsed: 0.031 s 0.14/0.43 % (18826)Instructions burned: 61 (million) 0.14/0.43 % (18826)------------------------------ 0.14/0.43 % (18826)------------------------------ 0.14/0.43 % (18829)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi) 0.14/0.44 % (18831)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2999ds/140Mi) 0.14/0.44 % (18830)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2999ds/11Mi) 0.14/0.45 % (18830)Instruction limit reached! 0.14/0.45 % (18830)------------------------------ 0.14/0.45 % (18830)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.45 % (18830)Termination reason: Unknown 0.14/0.45 % (18830)Termination phase: Saturation 0.14/0.45 0.14/0.45 % (18830)Memory used [KB]: 5500 0.14/0.45 % (18830)Time elapsed: 0.031 s 0.14/0.45 % (18830)Instructions burned: 13 (million) 0.14/0.45 % (18830)------------------------------ 0.14/0.45 % (18830)------------------------------ 0.14/0.45 % (18825)Instruction limit reached! 0.14/0.45 % (18825)------------------------------ 0.14/0.45 % (18825)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.45 % (18825)Termination reason: Unknown 0.14/0.45 % (18825)Termination phase: Saturation 0.14/0.45 0.14/0.45 % (18825)Memory used [KB]: 6268 0.14/0.45 % (18825)Time elapsed: 0.061 s 0.14/0.45 % (18825)Instructions burned: 129 (million) 0.14/0.45 % (18825)------------------------------ 0.14/0.45 % (18825)------------------------------ 0.14/0.45 % (18832)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 theBenchmark for (2998ds/26Mi) 0.14/0.46 % (18832)Instruction limit reached! 0.14/0.46 % (18832)------------------------------ 0.14/0.46 % (18832)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.46 % (18832)Termination reason: Unknown 0.14/0.46 % (18832)Termination phase: Saturation 0.14/0.46 0.14/0.46 % (18832)Memory used [KB]: 5500 0.14/0.46 % (18832)Time elapsed: 0.008 s 0.14/0.46 % (18832)Instructions burned: 28 (million) 0.14/0.46 % (18832)------------------------------ 0.14/0.46 % (18832)------------------------------ 0.14/0.46 % (18833)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on theBenchmark for (2998ds/56Mi) 0.14/0.47 % (18834)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2998ds/275Mi) 0.14/0.49 % (18833)Instruction limit reached! 0.14/0.49 % (18833)------------------------------ 0.14/0.49 % (18833)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.49 % (18833)Termination reason: Unknown 0.14/0.49 % (18833)Termination phase: Saturation 0.14/0.49 0.14/0.49 % (18833)Memory used [KB]: 1407 0.14/0.49 % (18833)Time elapsed: 0.030 s 0.14/0.49 % (18833)Instructions burned: 56 (million) 0.14/0.49 % (18833)------------------------------ 0.14/0.49 % (18833)------------------------------ 0.14/0.51 % (18835)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi) 0.14/0.51 % (18831)Instruction limit reached! 0.14/0.51 % (18831)------------------------------ 0.14/0.51 % (18831)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.51 % (18831)Termination reason: Unknown 0.14/0.51 % (18831)Termination phase: Saturation 0.14/0.51 0.14/0.51 % (18831)Memory used [KB]: 6396 0.14/0.51 % (18831)Time elapsed: 0.068 s 0.14/0.51 % (18831)Instructions burned: 140 (million) 0.14/0.51 % (18831)------------------------------ 0.14/0.51 % (18831)------------------------------ 0.14/0.51 % (18835)Instruction limit reached! 0.14/0.51 % (18835)------------------------------ 0.14/0.51 % (18835)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.51 % (18835)Termination reason: Unknown 0.14/0.51 % (18835)Termination phase: Preprocessing 3 0.14/0.51 0.14/0.51 % (18835)Memory used [KB]: 1023 0.14/0.51 % (18835)Time elapsed: 0.004 s 0.14/0.51 % (18835)Instructions burned: 4 (million) 0.14/0.51 % (18835)------------------------------ 0.14/0.51 % (18835)------------------------------ 1.49/0.52 % (18836)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 theBenchmark for (2998ds/19Mi) 1.49/0.52 % (18837)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 theBenchmark for (2998ds/44Mi) 1.49/0.52 % (18814)Instruction limit reached! 1.49/0.52 % (18814)------------------------------ 1.49/0.52 % (18814)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.49/0.52 % (18814)Termination reason: Unknown 1.49/0.52 % (18814)Termination phase: Saturation 1.49/0.52 1.49/0.52 % (18814)Memory used [KB]: 6140 1.49/0.52 % (18814)Time elapsed: 0.179 s 1.49/0.52 % (18814)Instructions burned: 386 (million) 1.49/0.52 % (18814)------------------------------ 1.49/0.52 % (18814)------------------------------ 1.49/0.53 % (18836)Instruction limit reached! 1.49/0.53 % (18836)------------------------------ 1.49/0.53 % (18836)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.49/0.53 % (18836)Termination reason: Unknown 1.49/0.53 % (18836)Termination phase: Saturation 1.49/0.53 1.49/0.53 % (18836)Memory used [KB]: 5500 1.49/0.53 % (18836)Time elapsed: 0.010 s 1.49/0.53 % (18836)Instructions burned: 21 (million) 1.49/0.53 % (18836)------------------------------ 1.49/0.53 % (18836)------------------------------ 1.61/0.54 % (18838)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on theBenchmark for (2998ds/191Mi) 1.61/0.54 % (18837)Instruction limit reached! 1.61/0.54 % (18837)------------------------------ 1.61/0.54 % (18837)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.54 % (18837)Termination reason: Unknown 1.61/0.54 % (18837)Termination phase: Saturation 1.61/0.54 1.61/0.54 % (18837)Memory used [KB]: 1151 1.61/0.54 % (18837)Time elapsed: 0.019 s 1.61/0.54 % (18837)Instructions burned: 44 (million) 1.61/0.54 % (18837)------------------------------ 1.61/0.54 % (18837)------------------------------ 1.61/0.54 % (18839)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2998ds/62Mi) 1.61/0.55 % (18840)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on theBenchmark for (2998ds/105Mi) 1.61/0.57 % (18834)Instruction limit reached! 1.61/0.57 % (18834)------------------------------ 1.61/0.57 % (18834)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.57 % (18839)Instruction limit reached! 1.61/0.57 % (18839)------------------------------ 1.61/0.57 % (18839)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.57 % (18839)Termination reason: Unknown 1.61/0.57 % (18839)Termination phase: Saturation 1.61/0.57 1.61/0.57 % (18839)Memory used [KB]: 5628 1.61/0.57 % (18839)Time elapsed: 0.028 s 1.61/0.57 % (18839)Instructions burned: 62 (million) 1.61/0.57 % (18839)------------------------------ 1.61/0.57 % (18839)------------------------------ 1.61/0.57 % (18834)Termination reason: Unknown 1.61/0.57 % (18834)Termination phase: Saturation 1.61/0.57 1.61/0.57 % (18834)Memory used [KB]: 6396 1.61/0.57 % (18834)Time elapsed: 0.118 s 1.61/0.57 % (18834)Instructions burned: 277 (million) 1.61/0.57 % (18834)------------------------------ 1.61/0.57 % (18834)------------------------------ 1.61/0.58 % (18841)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi) 1.61/0.58 % (18841)Instruction limit reached! 1.61/0.58 % (18841)------------------------------ 1.61/0.58 % (18841)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.58 % (18841)Termination reason: Unknown 1.61/0.58 % (18841)Termination phase: Preprocessing 3 1.61/0.58 1.61/0.58 % (18841)Memory used [KB]: 1023 1.61/0.58 % (18841)Time elapsed: 0.003 s 1.61/0.58 % (18841)Instructions burned: 5 (million) 1.61/0.58 % (18841)------------------------------ 1.61/0.58 % (18841)------------------------------ 1.61/0.58 % (18842)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 theBenchmark for (2997ds/238Mi) 1.61/0.58 % (18843)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 theBenchmark for (2997ds/3Mi) 1.61/0.59 % (18843)Instruction limit reached! 1.61/0.59 % (18843)------------------------------ 1.61/0.59 % (18843)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.59 % (18843)Termination reason: Unknown 1.61/0.59 % (18843)Termination phase: Preprocessing 3 1.61/0.59 1.61/0.59 % (18843)Memory used [KB]: 1023 1.61/0.59 % (18843)Time elapsed: 0.003 s 1.61/0.59 % (18843)Instructions burned: 5 (million) 1.61/0.59 % (18843)------------------------------ 1.61/0.59 % (18843)------------------------------ 1.61/0.59 % (18844)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2997ds/4Mi) 1.61/0.60 % (18844)Instruction limit reached! 1.61/0.60 % (18844)------------------------------ 1.61/0.60 % (18844)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.60 % (18844)Termination reason: Unknown 1.61/0.60 % (18844)Termination phase: Preprocessing 3 1.61/0.60 1.61/0.60 % (18844)Memory used [KB]: 1023 1.61/0.60 % (18844)Time elapsed: 0.003 s 1.61/0.60 % (18844)Instructions burned: 5 (million) 1.61/0.60 % (18844)------------------------------ 1.61/0.60 % (18844)------------------------------ 1.61/0.60 % (18840)Instruction limit reached! 1.61/0.60 % (18840)------------------------------ 1.61/0.60 % (18840)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.61/0.60 % (18840)Termination reason: Unknown 1.61/0.60 % (18840)Termination phase: Saturation 1.61/0.60 1.61/0.60 % (18840)Memory used [KB]: 6012 1.61/0.60 % (18840)Time elapsed: 0.053 s 1.61/0.60 % (18840)Instructions burned: 105 (million) 1.61/0.60 % (18840)------------------------------ 1.61/0.60 % (18840)------------------------------ 1.61/0.60 % (18845)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 theBenchmark for (2997ds/149Mi) 1.61/0.62 % (18846)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2997ds/150Mi) 2.18/0.63 % (18838)Instruction limit reached! 2.18/0.63 % (18838)------------------------------ 2.18/0.63 % (18838)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.18/0.63 % (18838)Termination reason: Unknown 2.18/0.63 % (18838)Termination phase: Saturation 2.18/0.63 2.18/0.63 % (18838)Memory used [KB]: 6268 2.18/0.63 % (18838)Time elapsed: 0.090 s 2.18/0.63 % (18838)Instructions burned: 191 (million) 2.18/0.63 % (18838)------------------------------ 2.18/0.63 % (18838)------------------------------ 2.18/0.64 % (18845)Instruction limit reached! 2.18/0.64 % (18845)------------------------------ 2.18/0.64 % (18845)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.18/0.64 % (18845)Termination reason: Unknown 2.18/0.64 % (18845)Termination phase: Property scanning 2.18/0.64 2.18/0.64 % (18845)Memory used [KB]: 1918 2.18/0.64 % (18845)Time elapsed: 0.035 s 2.18/0.64 % (18845)Instructions burned: 150 (million) 2.18/0.64 % (18845)------------------------------ 2.18/0.64 % (18845)------------------------------ 2.18/0.65 % (18847)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 theBenchmark for (2997ds/199Mi) 2.18/0.66 % (18848)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi) 2.18/0.68 % (18848)Instruction limit reached! 2.18/0.68 % (18848)------------------------------ 2.18/0.68 % (18848)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.18/0.68 % (18848)Termination reason: Unknown 2.18/0.68 % (18848)Termination phase: Saturation 2.18/0.68 2.18/0.68 % (18848)Memory used [KB]: 5756 2.18/0.68 % (18848)Time elapsed: 0.058 s 2.18/0.68 % (18848)Instructions burned: 41 (million) 2.18/0.68 % (18848)------------------------------ 2.18/0.68 % (18848)------------------------------ 2.60/0.69 % (18842)Instruction limit reached! 2.60/0.69 % (18842)------------------------------ 2.60/0.69 % (18842)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.60/0.69 % (18842)Termination reason: Unknown 2.60/0.69 % (18842)Termination phase: Saturation 2.60/0.69 2.60/0.69 % (18842)Memory used [KB]: 5884 2.60/0.69 % (18842)Time elapsed: 0.107 s 2.60/0.69 % (18842)Instructions burned: 238 (million) 2.60/0.69 % (18842)------------------------------ 2.60/0.69 % (18842)------------------------------ 2.60/0.69 % (18846)Instruction limit reached! 2.60/0.69 % (18846)------------------------------ 2.60/0.69 % (18846)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.60/0.69 % (18846)Termination reason: Unknown 2.60/0.69 % (18846)Termination phase: Saturation 2.60/0.69 2.60/0.69 % (18846)Memory used [KB]: 6268 2.60/0.69 % (18846)Time elapsed: 0.093 s 2.60/0.69 % (18846)Instructions burned: 150 (million) 2.60/0.69 % (18846)------------------------------ 2.60/0.69 % (18846)------------------------------ 2.60/0.70 % (18849)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=721:si=on:rtra=on_0 on theBenchmark for (2996ds/721Mi) 2.60/0.70 % (18850)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=3:si=on:rtra=on_0 on theBenchmark for (2996ds/3Mi) 2.60/0.70 % (18850)Instruction limit reached! 2.60/0.70 % (18850)------------------------------ 2.60/0.70 % (18850)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.60/0.70 % (18850)Termination reason: Unknown 2.60/0.70 % (18850)Termination phase: Preprocessing 2 2.60/0.70 2.60/0.70 % (18850)Memory used [KB]: 1023 2.60/0.70 % (18850)Time elapsed: 0.003 s 2.60/0.70 % (18850)Instructions burned: 3 (million) 2.60/0.70 % (18850)------------------------------ 2.60/0.70 % (18850)------------------------------ 2.60/0.70 % (18829)First to succeed. 2.60/0.71 % (18852)lrs+10_1:1_au=on:c=on:sac=on:slsq=on:slsqc=2:i=218:si=on:rtra=on_0 on theBenchmark for (2996ds/218Mi) 2.60/0.72 % (18851)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2996ds/18Mi) 2.60/0.73 % (18829)Refutation found. Thanks to Tanya! 2.60/0.73 % SZS status Theorem for theBenchmark 2.60/0.73 % SZS output start Proof for theBenchmark 2.60/0.73 thf(type_def_5, type, a: $tType). 2.60/0.73 thf(func_def_0, type, a: $tType). 2.60/0.73 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)). 2.60/0.73 thf(func_def_21, type, sK2: a > a > $o). 2.60/0.73 thf(func_def_22, type, sK3: a > a > $o). 2.60/0.73 thf(func_def_23, type, sK4: a). 2.60/0.73 thf(func_def_24, type, sK5: a). 2.60/0.73 thf(func_def_25, type, sK6: a > a > $o). 2.60/0.73 thf(func_def_26, type, sK7: a). 2.60/0.73 thf(func_def_27, type, sK8: a). 2.60/0.73 thf(func_def_28, type, sK9: a). 2.60/0.73 thf(func_def_29, type, sK10: a). 2.60/0.73 thf(func_def_30, type, sK11: a). 2.60/0.73 thf(func_def_31, type, sK12: a). 2.60/0.73 thf(func_def_32, type, sK13: a). 2.60/0.73 thf(func_def_33, type, sK14: a). 2.60/0.73 thf(func_def_34, type, sK15: a > a > $o). 2.60/0.73 thf(func_def_35, type, sK16: a). 2.60/0.73 thf(func_def_36, type, sK17: a). 2.60/0.73 thf(func_def_37, type, sK18: a > a > $o). 2.60/0.73 thf(func_def_38, type, sK19: a). 2.60/0.73 thf(func_def_39, type, sK20: a). 2.60/0.73 thf(func_def_40, type, sK21: a). 2.60/0.73 thf(func_def_41, type, sK22: a). 2.60/0.73 thf(func_def_42, type, sK23: a). 2.60/0.73 thf(func_def_43, type, sK24: a). 2.60/0.73 thf(func_def_44, type, sK25: a). 2.60/0.73 thf(func_def_45, type, sK26: a). 2.60/0.73 thf(func_def_46, type, sK27: a). 2.60/0.73 thf(func_def_47, type, sK28: a). 2.60/0.73 thf(func_def_48, type, sK29: a). 2.60/0.73 thf(func_def_49, type, sK30: a). 2.60/0.73 thf(func_def_50, type, sK31: a). 2.60/0.73 thf(func_def_51, type, sK32: a). 2.60/0.73 thf(func_def_52, type, sK33: a). 2.60/0.73 thf(func_def_53, type, sK34: a). 2.60/0.73 thf(func_def_54, type, sK35: a). 2.60/0.73 thf(func_def_55, type, sK36: a). 2.60/0.73 thf(func_def_56, type, sK37: a). 2.60/0.73 thf(func_def_57, type, sK38: a). 2.60/0.73 thf(func_def_58, type, sK39: a). 2.60/0.73 thf(func_def_59, type, sK40: a). 2.60/0.73 thf(func_def_60, type, sK41: a). 2.60/0.73 thf(func_def_61, type, sK42: a). 2.60/0.73 thf(func_def_62, type, sK43: a). 2.60/0.73 thf(func_def_63, type, sK44: a). 2.60/0.73 thf(func_def_64, type, sK45: a). 2.60/0.73 thf(f3338,plain,( 2.60/0.73 $false), 2.60/0.73 inference(avatar_sat_refutation,[],[f60,f123,f202,f219,f233,f433,f446,f532,f601,f629,f911,f1133,f1183,f1507,f1566,f1790,f1898,f3051,f3069,f3158,f3164,f3302,f3337])). 2.60/0.73 thf(f3337,plain,( 2.60/0.73 ~spl0_6 | ~spl0_9 | ~spl0_51), 2.60/0.73 inference(avatar_contradiction_clause,[],[f3336])). 2.60/0.73 thf(f3336,plain,( 2.60/0.73 $false | (~spl0_6 | ~spl0_9 | ~spl0_51)), 2.60/0.73 inference(trivial_inequality_removal,[],[f3335])). 2.60/0.73 thf(f3335,plain,( 2.60/0.73 ($true = $false) | (~spl0_6 | ~spl0_9 | ~spl0_51)), 2.60/0.73 inference(backward_demodulation,[],[f3314,f3334])). 2.60/0.73 thf(f3334,plain,( 2.60/0.73 ((sK15 @ sK42 @ sK41) = $false) | (~spl0_9 | ~spl0_51)), 2.60/0.73 inference(boolean_simplification,[],[f3333])). 2.60/0.73 thf(f3333,plain,( 2.60/0.73 (($true => (sK15 @ sK42 @ sK41)) = $false) | (~spl0_9 | ~spl0_51)), 2.60/0.73 inference(boolean_simplification,[],[f3332])). 2.60/0.73 thf(f3332,plain,( 2.60/0.73 ((($true | (sK2 @ sK42 @ sK41)) => (sK15 @ sK42 @ sK41)) = $false) | (~spl0_9 | ~spl0_51)), 2.60/0.73 inference(forward_demodulation,[],[f3331,f3157])). 2.60/0.73 thf(f3157,plain,( 2.60/0.73 ((sK3 @ sK42 @ sK41) = $true) | ~spl0_51), 2.60/0.73 inference(avatar_component_clause,[],[f3156])). 2.60/0.73 thf(f3156,plain,( 2.60/0.73 spl0_51 <=> ((sK3 @ sK42 @ sK41) = $true)), 2.60/0.73 introduced(avatar_definition,[new_symbols(naming,[spl0_51])])). 2.60/0.73 thf(f3331,plain,( 2.60/0.73 ((((sK3 @ sK42 @ sK41) | (sK2 @ sK42 @ sK41)) => (sK15 @ sK42 @ sK41)) = $false) | ~spl0_9), 2.60/0.73 inference(beta_eta_normalization,[],[f3330])). 2.60/0.73 thf(f3330,plain,( 2.60/0.73 (((^[Y0 : a]: (((sK3 @ Y0 @ sK41) | (sK2 @ Y0 @ sK41)) => (sK15 @ Y0 @ sK41))) @ sK42) = $false) | ~spl0_9), 2.60/0.73 inference(sigma_clausification,[],[f3321])). 2.60/0.73 thf(f3321,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK41) | (sK2 @ Y0 @ sK41)) => (sK15 @ Y0 @ sK41)))) = $false) | ~spl0_9), 2.60/0.73 inference(beta_eta_normalization,[],[f3317])). 2.60/0.73 thf(f3317,plain,( 2.60/0.73 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ sK41) = $false) | ~spl0_9), 2.60/0.73 inference(sigma_clausification,[],[f442])). 2.60/0.73 thf(f442,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $false) | ~spl0_9), 2.60/0.73 inference(avatar_component_clause,[],[f441])). 2.60/0.73 thf(f441,plain,( 2.60/0.73 spl0_9 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $false)), 2.60/0.73 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])). 2.60/0.73 thf(f3314,plain,( 2.60/0.73 ((sK15 @ sK42 @ sK41) = $true) | (~spl0_6 | ~spl0_51)), 2.60/0.73 inference(boolean_simplification,[],[f3313])). 2.60/0.73 thf(f3313,plain,( 2.60/0.73 (($true => (sK15 @ sK42 @ sK41)) = $true) | (~spl0_6 | ~spl0_51)), 2.60/0.73 inference(boolean_simplification,[],[f3308])). 2.60/0.73 thf(f3308,plain,( 2.60/0.73 ((((sK2 @ sK42 @ sK41) | $true) => (sK15 @ sK42 @ sK41)) = $true) | (~spl0_6 | ~spl0_51)), 2.60/0.73 inference(superposition,[],[f2660,f3157])). 2.60/0.73 thf(f2660,plain,( 2.60/0.73 ( ! [X2 : a,X1 : a] : (($true = (((sK2 @ X2 @ X1) | (sK3 @ X2 @ X1)) => (sK15 @ X2 @ X1)))) ) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f2659])). 2.60/0.73 thf(f2659,plain,( 2.60/0.73 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK15 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_6), 2.60/0.73 inference(pi_clausification,[],[f2424])). 2.60/0.73 thf(f2424,plain,( 2.60/0.73 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK15 @ Y0 @ X1)))) = $true)) ) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f2423])). 2.60/0.73 thf(f2423,plain,( 2.60/0.73 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.73 inference(pi_clausification,[],[f2091])). 2.60/0.73 thf(f2091,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $true) | ~spl0_6), 2.60/0.73 inference(binary_proxy_clausification,[],[f2031])). 2.60/0.73 thf(f2031,plain,( 2.60/0.73 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) = $true) | ~spl0_6), 2.60/0.73 inference(binary_proxy_clausification,[],[f1999])). 2.60/0.73 thf(f1999,plain,( 2.60/0.73 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) => (sK15 @ sK14 @ sK13)) = $false) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f1998])). 2.60/0.73 thf(f1998,plain,( 2.60/0.73 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))) @ sK15) = $false) | ~spl0_6), 2.60/0.73 inference(sigma_clausification,[],[f1913])). 2.60/0.73 thf(f1913,plain,( 2.60/0.73 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13)))) = $false) | ~spl0_6), 2.60/0.73 inference(binary_proxy_clausification,[],[f1906])). 2.60/0.73 thf(f1906,plain,( 2.60/0.73 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))))) = $false) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f1905])). 2.60/0.73 thf(f1905,plain,( 2.60/0.73 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13)))))) @ sK14) = $false) | ~spl0_6), 2.60/0.73 inference(sigma_clausification,[],[f1904])). 2.60/0.73 thf(f1904,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13))))))) = $false) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f1903])). 2.60/0.73 thf(f1903,plain,( 2.60/0.73 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK13) = $false) | ~spl0_6), 2.60/0.73 inference(sigma_clausification,[],[f1902])). 2.60/0.73 thf(f1902,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_6), 2.60/0.73 inference(beta_eta_normalization,[],[f1901])). 2.60/0.73 thf(f1901,plain,( 2.60/0.73 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))))))))) @ sK12) = $false) | ~spl0_6), 2.60/0.73 inference(sigma_clausification,[],[f232])). 2.60/0.73 thf(f232,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) = $false) | ~spl0_6), 2.60/0.73 inference(avatar_component_clause,[],[f231])). 2.60/0.73 thf(f231,plain,( 2.60/0.73 spl0_6 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) = $false)), 2.60/0.73 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])). 2.60/0.73 thf(f3302,plain,( 2.60/0.73 ~spl0_6 | ~spl0_10), 2.60/0.73 inference(avatar_contradiction_clause,[],[f3301])). 2.60/0.73 thf(f3301,plain,( 2.60/0.73 $false | (~spl0_6 | ~spl0_10)), 2.60/0.73 inference(trivial_inequality_removal,[],[f3300])). 2.60/0.73 thf(f3300,plain,( 2.60/0.73 ($true = $false) | (~spl0_6 | ~spl0_10)), 2.60/0.73 inference(boolean_simplification,[],[f3299])). 2.60/0.73 thf(f3299,plain,( 2.60/0.73 ((~ $true) = $true) | (~spl0_6 | ~spl0_10)), 2.60/0.73 inference(forward_demodulation,[],[f3296,f3279])). 2.60/0.73 thf(f3279,plain,( 2.60/0.73 ((sK15 @ sK44 @ sK45) = $true) | ~spl0_10), 2.60/0.73 inference(binary_proxy_clausification,[],[f3265])). 2.60/0.73 thf(f3265,plain,( 2.60/0.73 (((sK15 @ sK44 @ sK45) & (sK15 @ sK43 @ sK44)) = $true) | ~spl0_10), 2.60/0.73 inference(binary_proxy_clausification,[],[f3263])). 2.60/0.73 thf(f3263,plain,( 2.60/0.73 ((((sK15 @ sK44 @ sK45) & (sK15 @ sK43 @ sK44)) => (sK15 @ sK43 @ sK45)) = $false) | ~spl0_10), 2.60/0.73 inference(beta_eta_normalization,[],[f3262])). 2.60/0.73 thf(f3262,plain,( 2.60/0.73 (((^[Y0 : a]: (((sK15 @ sK44 @ Y0) & (sK15 @ sK43 @ sK44)) => (sK15 @ sK43 @ Y0))) @ sK45) = $false) | ~spl0_10), 2.60/0.73 inference(sigma_clausification,[],[f3261])). 2.60/0.73 thf(f3261,plain,( 2.60/0.73 ((!! @ a @ (^[Y0 : a]: (((sK15 @ sK44 @ Y0) & (sK15 @ sK43 @ sK44)) => (sK15 @ sK43 @ Y0)))) = $false) | ~spl0_10), 2.60/0.74 inference(beta_eta_normalization,[],[f3260])). 2.60/0.74 thf(f3260,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ sK43 @ Y0)) => (sK15 @ sK43 @ Y1))))) @ sK44) = $false) | ~spl0_10), 2.60/0.74 inference(sigma_clausification,[],[f3224])). 2.60/0.74 thf(f3224,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ sK43 @ Y0)) => (sK15 @ sK43 @ Y1)))))) = $false) | ~spl0_10), 2.60/0.74 inference(beta_eta_normalization,[],[f3220])). 2.60/0.74 thf(f3220,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))) @ sK43) = $false) | ~spl0_10), 2.60/0.74 inference(sigma_clausification,[],[f445])). 2.60/0.74 thf(f445,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) = $false) | ~spl0_10), 2.60/0.74 inference(avatar_component_clause,[],[f444])). 2.60/0.74 thf(f444,plain,( 2.60/0.74 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])). 2.60/0.74 thf(f3296,plain,( 2.60/0.74 ((~ (sK15 @ sK44 @ sK45)) = $true) | (~spl0_6 | ~spl0_10)), 2.60/0.74 inference(boolean_simplification,[],[f3292])). 2.60/0.74 thf(f3292,plain,( 2.60/0.74 ((~ ($true & (sK15 @ sK44 @ sK45))) = $true) | (~spl0_6 | ~spl0_10)), 2.60/0.74 inference(superposition,[],[f3274,f3281])). 2.60/0.74 thf(f3281,plain,( 2.60/0.74 ((sK15 @ sK43 @ sK44) = $true) | ~spl0_10), 2.60/0.74 inference(boolean_simplification,[],[f3280])). 2.60/0.74 thf(f3280,plain,( 2.60/0.74 (($true & (sK15 @ sK43 @ sK44)) = $true) | ~spl0_10), 2.60/0.74 inference(backward_demodulation,[],[f3265,f3279])). 2.60/0.74 thf(f3274,plain,( 2.60/0.74 ( ! [X0 : a] : (((~ ((sK15 @ sK43 @ X0) & (sK15 @ X0 @ sK45))) = $true)) ) | (~spl0_6 | ~spl0_10)), 2.60/0.74 inference(boolean_simplification,[],[f3271])). 2.60/0.74 thf(f3271,plain,( 2.60/0.74 ( ! [X0 : a] : (((((sK15 @ sK43 @ X0) & (sK15 @ X0 @ sK45)) => $false) = $true)) ) | (~spl0_6 | ~spl0_10)), 2.60/0.74 inference(superposition,[],[f2168,f3267])). 2.60/0.74 thf(f3267,plain,( 2.60/0.74 ((sK15 @ sK43 @ sK45) = $false) | ~spl0_10), 2.60/0.74 inference(boolean_simplification,[],[f3266])). 2.60/0.74 thf(f3266,plain,( 2.60/0.74 (($true => (sK15 @ sK43 @ sK45)) = $false) | ~spl0_10), 2.60/0.74 inference(backward_demodulation,[],[f3263,f3265])). 2.60/0.74 thf(f2168,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK15 @ X3 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ X3 @ X2)) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f2167])). 2.60/0.74 thf(f2167,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2))) @ X3) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f2137])). 2.60/0.74 thf(f2137,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2)))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f2136])). 2.60/0.74 thf(f2136,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ X2) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f2095])). 2.60/0.74 thf(f2095,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f2094])). 2.60/0.74 thf(f2094,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f2093])). 2.60/0.74 thf(f2093,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1)))))))) = $true) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f2092])). 2.60/0.74 thf(f2092,plain,( 2.60/0.74 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) = $true) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f2031,f2091])). 2.60/0.74 thf(f3164,plain,( 2.60/0.74 ~spl0_6 | ~spl0_9 | ~spl0_50), 2.60/0.74 inference(avatar_contradiction_clause,[],[f3163])). 2.60/0.74 thf(f3163,plain,( 2.60/0.74 $false | (~spl0_6 | ~spl0_9 | ~spl0_50)), 2.60/0.74 inference(trivial_inequality_removal,[],[f3162])). 2.60/0.74 thf(f3162,plain,( 2.60/0.74 ($true = $false) | (~spl0_6 | ~spl0_9 | ~spl0_50)), 2.60/0.74 inference(boolean_simplification,[],[f3161])). 2.60/0.74 thf(f3161,plain,( 2.60/0.74 ((~ $true) = $true) | (~spl0_6 | ~spl0_9 | ~spl0_50)), 2.60/0.74 inference(boolean_simplification,[],[f3159])). 2.60/0.74 thf(f3159,plain,( 2.60/0.74 ((~ ($true | (sK3 @ sK42 @ sK41))) = $true) | (~spl0_6 | ~spl0_9 | ~spl0_50)), 2.60/0.74 inference(backward_demodulation,[],[f3116,f3154])). 2.60/0.74 thf(f3154,plain,( 2.60/0.74 ((sK2 @ sK42 @ sK41) = $true) | ~spl0_50), 2.60/0.74 inference(avatar_component_clause,[],[f3153])). 2.60/0.74 thf(f3153,plain,( 2.60/0.74 spl0_50 <=> ((sK2 @ sK42 @ sK41) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_50])])). 2.60/0.74 thf(f3116,plain,( 2.60/0.74 ((~ ((sK2 @ sK42 @ sK41) | (sK3 @ sK42 @ sK41))) = $true) | (~spl0_6 | ~spl0_9)), 2.60/0.74 inference(boolean_simplification,[],[f3109])). 2.60/0.74 thf(f3109,plain,( 2.60/0.74 ((((sK2 @ sK42 @ sK41) | (sK3 @ sK42 @ sK41)) => $false) = $true) | (~spl0_6 | ~spl0_9)), 2.60/0.74 inference(superposition,[],[f2660,f3100])). 2.60/0.74 thf(f3100,plain,( 2.60/0.74 ((sK15 @ sK42 @ sK41) = $false) | ~spl0_9), 2.60/0.74 inference(binary_proxy_clausification,[],[f3089])). 2.60/0.74 thf(f3089,plain,( 2.60/0.74 ((((sK3 @ sK42 @ sK41) | (sK2 @ sK42 @ sK41)) => (sK15 @ sK42 @ sK41)) = $false) | ~spl0_9), 2.60/0.74 inference(beta_eta_normalization,[],[f3088])). 2.60/0.74 thf(f3088,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK3 @ Y0 @ sK41) | (sK2 @ Y0 @ sK41)) => (sK15 @ Y0 @ sK41))) @ sK42) = $false) | ~spl0_9), 2.60/0.74 inference(sigma_clausification,[],[f3075])). 2.60/0.74 thf(f3075,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK41) | (sK2 @ Y0 @ sK41)) => (sK15 @ Y0 @ sK41)))) = $false) | ~spl0_9), 2.60/0.74 inference(beta_eta_normalization,[],[f3073])). 2.60/0.74 thf(f3073,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ sK41) = $false) | ~spl0_9), 2.60/0.74 inference(sigma_clausification,[],[f442])). 2.60/0.74 thf(f3158,plain,( 2.60/0.74 spl0_50 | spl0_51 | ~spl0_9), 2.60/0.74 inference(avatar_split_clause,[],[f3145,f441,f3156,f3153])). 2.60/0.74 thf(f3145,plain,( 2.60/0.74 ((sK2 @ sK42 @ sK41) = $true) | ((sK3 @ sK42 @ sK41) = $true) | ~spl0_9), 2.60/0.74 inference(binary_proxy_clausification,[],[f3101])). 2.60/0.74 thf(f3101,plain,( 2.60/0.74 (((sK3 @ sK42 @ sK41) | (sK2 @ sK42 @ sK41)) = $true) | ~spl0_9), 2.60/0.74 inference(binary_proxy_clausification,[],[f3089])). 2.60/0.74 thf(f3069,plain,( 2.60/0.74 ~spl0_6 | ~spl0_11 | ~spl0_15), 2.60/0.74 inference(avatar_contradiction_clause,[],[f3068])). 2.60/0.74 thf(f3068,plain,( 2.60/0.74 $false | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(trivial_inequality_removal,[],[f3067])). 2.60/0.74 thf(f3067,plain,( 2.60/0.74 ($true = $false) | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(boolean_simplification,[],[f3066])). 2.60/0.74 thf(f3066,plain,( 2.60/0.74 ((~ $true) = $true) | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(boolean_simplification,[],[f3065])). 2.60/0.74 thf(f3065,plain,( 2.60/0.74 ((~ ($true | (sK3 @ sK19 @ sK20))) = $true) | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(forward_demodulation,[],[f3064,f625])). 2.60/0.74 thf(f625,plain,( 2.60/0.74 ((sK2 @ sK19 @ sK20) = $true) | ~spl0_15), 2.60/0.74 inference(avatar_component_clause,[],[f624])). 2.60/0.74 thf(f624,plain,( 2.60/0.74 spl0_15 <=> ((sK2 @ sK19 @ sK20) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_15])])). 2.60/0.74 thf(f3064,plain,( 2.60/0.74 ((~ ((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20))) = $true) | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(boolean_simplification,[],[f3055])). 2.60/0.74 thf(f3055,plain,( 2.60/0.74 ((((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) => $false) = $true) | (~spl0_6 | ~spl0_11 | ~spl0_15)), 2.60/0.74 inference(superposition,[],[f2660,f3054])). 2.60/0.74 thf(f3054,plain,( 2.60/0.74 ((sK15 @ sK19 @ sK20) = $false) | (~spl0_11 | ~spl0_15)), 2.60/0.74 inference(boolean_simplification,[],[f3053])). 2.60/0.74 thf(f3053,plain,( 2.60/0.74 (($true => (sK15 @ sK19 @ sK20)) = $false) | (~spl0_11 | ~spl0_15)), 2.60/0.74 inference(boolean_simplification,[],[f3052])). 2.60/0.74 thf(f3052,plain,( 2.60/0.74 ((($true | (sK3 @ sK19 @ sK20)) => (sK15 @ sK19 @ sK20)) = $false) | (~spl0_11 | ~spl0_15)), 2.60/0.74 inference(backward_demodulation,[],[f3045,f625])). 2.60/0.74 thf(f3045,plain,( 2.60/0.74 ((((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) => (sK15 @ sK19 @ sK20)) = $false) | ~spl0_11), 2.60/0.74 inference(beta_eta_normalization,[],[f3044])). 2.60/0.74 thf(f3044,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) => (sK15 @ sK19 @ Y0))) @ sK20) = $false) | ~spl0_11), 2.60/0.74 inference(sigma_clausification,[],[f3031])). 2.60/0.74 thf(f3031,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) => (sK15 @ sK19 @ Y0)))) = $false) | ~spl0_11), 2.60/0.74 inference(beta_eta_normalization,[],[f3027])). 2.60/0.74 thf(f3027,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1))))) @ sK19) = $false) | ~spl0_11), 2.60/0.74 inference(sigma_clausification,[],[f528])). 2.60/0.74 thf(f528,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1)))))) = $false) | ~spl0_11), 2.60/0.74 inference(avatar_component_clause,[],[f527])). 2.60/0.74 thf(f527,plain,( 2.60/0.74 spl0_11 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1)))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])). 2.60/0.74 thf(f3051,plain,( 2.60/0.74 ~spl0_6 | ~spl0_11 | ~spl0_16), 2.60/0.74 inference(avatar_contradiction_clause,[],[f3050])). 2.60/0.74 thf(f3050,plain,( 2.60/0.74 $false | (~spl0_6 | ~spl0_11 | ~spl0_16)), 2.60/0.74 inference(trivial_inequality_removal,[],[f3049])). 2.60/0.74 thf(f3049,plain,( 2.60/0.74 ($true = $false) | (~spl0_6 | ~spl0_11 | ~spl0_16)), 2.60/0.74 inference(backward_demodulation,[],[f2701,f3048])). 2.60/0.74 thf(f3048,plain,( 2.60/0.74 ((sK15 @ sK19 @ sK20) = $false) | (~spl0_11 | ~spl0_16)), 2.60/0.74 inference(boolean_simplification,[],[f3047])). 2.60/0.74 thf(f3047,plain,( 2.60/0.74 (($true => (sK15 @ sK19 @ sK20)) = $false) | (~spl0_11 | ~spl0_16)), 2.60/0.74 inference(boolean_simplification,[],[f3046])). 2.60/0.74 thf(f3046,plain,( 2.60/0.74 ((((sK2 @ sK19 @ sK20) | $true) => (sK15 @ sK19 @ sK20)) = $false) | (~spl0_11 | ~spl0_16)), 2.60/0.74 inference(forward_demodulation,[],[f3045,f628])). 2.60/0.74 thf(f628,plain,( 2.60/0.74 ((sK3 @ sK19 @ sK20) = $true) | ~spl0_16), 2.60/0.74 inference(avatar_component_clause,[],[f627])). 2.60/0.74 thf(f627,plain,( 2.60/0.74 spl0_16 <=> ((sK3 @ sK19 @ sK20) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_16])])). 2.60/0.74 thf(f2701,plain,( 2.60/0.74 ((sK15 @ sK19 @ sK20) = $true) | (~spl0_6 | ~spl0_16)), 2.60/0.74 inference(boolean_simplification,[],[f2700])). 2.60/0.74 thf(f2700,plain,( 2.60/0.74 (($true => (sK15 @ sK19 @ sK20)) = $true) | (~spl0_6 | ~spl0_16)), 2.60/0.74 inference(boolean_simplification,[],[f2684])). 2.60/0.74 thf(f2684,plain,( 2.60/0.74 ((((sK2 @ sK19 @ sK20) | $true) => (sK15 @ sK19 @ sK20)) = $true) | (~spl0_6 | ~spl0_16)), 2.60/0.74 inference(superposition,[],[f2660,f628])). 2.60/0.74 thf(f1898,plain,( 2.60/0.74 ~spl0_5 | ~spl0_13 | ~spl0_27), 2.60/0.74 inference(avatar_contradiction_clause,[],[f1897])). 2.60/0.74 thf(f1897,plain,( 2.60/0.74 $false | (~spl0_5 | ~spl0_13 | ~spl0_27)), 2.60/0.74 inference(trivial_inequality_removal,[],[f1896])). 2.60/0.74 thf(f1896,plain,( 2.60/0.74 ($true = $false) | (~spl0_5 | ~spl0_13 | ~spl0_27)), 2.60/0.74 inference(forward_demodulation,[],[f1893,f1863])). 2.60/0.74 thf(f1863,plain,( 2.60/0.74 ((sK18 @ sK35 @ sK34) = $false) | ~spl0_27), 2.60/0.74 inference(binary_proxy_clausification,[],[f1860])). 2.60/0.74 thf(f1860,plain,( 2.60/0.74 ((((sK18 @ sK35 @ sK36) & (sK18 @ sK36 @ sK34)) => (sK18 @ sK35 @ sK34)) = $false) | ~spl0_27), 2.60/0.74 inference(beta_eta_normalization,[],[f1859])). 2.60/0.74 thf(f1859,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK18 @ sK35 @ Y0) & (sK18 @ Y0 @ sK34)) => (sK18 @ sK35 @ sK34))) @ sK36) = $false) | ~spl0_27), 2.60/0.74 inference(sigma_clausification,[],[f1856])). 2.60/0.74 thf(f1856,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK18 @ sK35 @ Y0) & (sK18 @ Y0 @ sK34)) => (sK18 @ sK35 @ sK34)))) = $false) | ~spl0_27), 2.60/0.74 inference(beta_eta_normalization,[],[f1855])). 2.60/0.74 thf(f1855,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ sK34)) => (sK18 @ Y0 @ sK34))))) @ sK35) = $false) | ~spl0_27), 2.60/0.74 inference(sigma_clausification,[],[f1797])). 2.60/0.74 thf(f1797,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ sK34)) => (sK18 @ Y0 @ sK34)))))) = $false) | ~spl0_27), 2.60/0.74 inference(beta_eta_normalization,[],[f1796])). 2.60/0.74 thf(f1796,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0))))))) @ sK34) = $false) | ~spl0_27), 2.60/0.74 inference(sigma_clausification,[],[f1506])). 2.60/0.74 thf(f1506,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0)))))))) = $false) | ~spl0_27), 2.60/0.74 inference(avatar_component_clause,[],[f1505])). 2.60/0.74 thf(f1505,plain,( 2.60/0.74 spl0_27 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0)))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_27])])). 2.60/0.74 thf(f1893,plain,( 2.60/0.74 ((sK18 @ sK35 @ sK34) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_27)), 2.60/0.74 inference(boolean_simplification,[],[f1892])). 2.60/0.74 thf(f1892,plain,( 2.60/0.74 (($true => (sK18 @ sK35 @ sK34)) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_27)), 2.60/0.74 inference(superposition,[],[f1872,f1864])). 2.60/0.74 thf(f1864,plain,( 2.60/0.74 (((sK18 @ sK35 @ sK36) & (sK18 @ sK36 @ sK34)) = $true) | ~spl0_27), 2.60/0.74 inference(binary_proxy_clausification,[],[f1860])). 2.60/0.74 thf(f1872,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK18 @ X3 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ X3 @ X1)) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1871])). 2.60/0.74 thf(f1871,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK18 @ Y0 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ Y0 @ X1))) @ X3) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(pi_clausification,[],[f1862])). 2.60/0.74 thf(f1862,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK18 @ Y0 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ Y0 @ X1)))) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1861])). 2.60/0.74 thf(f1861,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y0 @ X1)) => (sK18 @ Y1 @ X1))))) @ X2))) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(pi_clausification,[],[f1858])). 2.60/0.74 thf(f1858,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y0 @ X1)) => (sK18 @ Y1 @ X1)))))) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1857])). 2.60/0.74 thf(f1857,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))) @ X1) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(pi_clausification,[],[f1805])). 2.60/0.74 thf(f1805,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0)))))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1804])). 2.60/0.74 thf(f1804,plain,( 2.60/0.74 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(backward_demodulation,[],[f1799,f1803])). 2.60/0.74 thf(f1803,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1799])). 2.60/0.74 thf(f1799,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1795])). 2.60/0.74 thf(f1795,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1794])). 2.60/0.74 thf(f1794,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))) @ sK18) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(sigma_clausification,[],[f1793])). 2.60/0.74 thf(f1793,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1792])). 2.60/0.74 thf(f1792,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1791])). 2.60/0.74 thf(f1791,plain,( 2.60/0.74 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(forward_demodulation,[],[f919,f597])). 2.60/0.74 thf(f597,plain,( 2.60/0.74 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) | ~spl0_13), 2.60/0.74 inference(avatar_component_clause,[],[f596])). 2.60/0.74 thf(f596,plain,( 2.60/0.74 spl0_13 <=> ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))))), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_13])])). 2.60/0.74 thf(f919,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | ~spl0_5), 2.60/0.74 inference(beta_eta_normalization,[],[f918])). 2.60/0.74 thf(f918,plain,( 2.60/0.74 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))))) @ sK17) = $false) | ~spl0_5), 2.60/0.74 inference(sigma_clausification,[],[f915])). 2.60/0.74 thf(f915,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK16))))))) = $false) | ~spl0_5), 2.60/0.74 inference(beta_eta_normalization,[],[f914])). 2.60/0.74 thf(f914,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK16) = $false) | ~spl0_5), 2.60/0.74 inference(sigma_clausification,[],[f229])). 2.60/0.74 thf(f229,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_5), 2.60/0.74 inference(avatar_component_clause,[],[f228])). 2.60/0.74 thf(f228,plain,( 2.60/0.74 spl0_5 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 2.60/0.74 thf(f1790,plain,( 2.60/0.74 ~spl0_5 | ~spl0_14 | ~spl0_21), 2.60/0.74 inference(avatar_contradiction_clause,[],[f1789])). 2.60/0.74 thf(f1789,plain,( 2.60/0.74 $false | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(trivial_inequality_removal,[],[f1788])). 2.60/0.74 thf(f1788,plain,( 2.60/0.74 ($true = $false) | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(forward_demodulation,[],[f1781,f1731])). 2.60/0.74 thf(f1731,plain,( 2.60/0.74 ((sK18 @ sK31 @ sK33) = $false) | ~spl0_21), 2.60/0.74 inference(boolean_simplification,[],[f1730])). 2.60/0.74 thf(f1730,plain,( 2.60/0.74 (($true => (sK18 @ sK31 @ sK33)) = $false) | ~spl0_21), 2.60/0.74 inference(backward_demodulation,[],[f1727,f1729])). 2.60/0.74 thf(f1729,plain,( 2.60/0.74 ($true = ((sK18 @ sK31 @ sK32) & (sK18 @ sK32 @ sK33))) | ~spl0_21), 2.60/0.74 inference(binary_proxy_clausification,[],[f1727])). 2.60/0.74 thf(f1727,plain,( 2.60/0.74 ((((sK18 @ sK31 @ sK32) & (sK18 @ sK32 @ sK33)) => (sK18 @ sK31 @ sK33)) = $false) | ~spl0_21), 2.60/0.74 inference(beta_eta_normalization,[],[f1726])). 2.60/0.74 thf(f1726,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK18 @ sK31 @ sK32) & (sK18 @ sK32 @ Y0)) => (sK18 @ sK31 @ Y0))) @ sK33) = $false) | ~spl0_21), 2.60/0.74 inference(sigma_clausification,[],[f1725])). 2.60/0.74 thf(f1725,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK18 @ sK31 @ sK32) & (sK18 @ sK32 @ Y0)) => (sK18 @ sK31 @ Y0)))) = $false) | ~spl0_21), 2.60/0.74 inference(beta_eta_normalization,[],[f1724])). 2.60/0.74 thf(f1724,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ sK31 @ Y0) & (sK18 @ Y0 @ Y1)) => (sK18 @ sK31 @ Y1))))) @ sK32) = $false) | ~spl0_21), 2.60/0.74 inference(sigma_clausification,[],[f1711])). 2.60/0.74 thf(f1711,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ sK31 @ Y0) & (sK18 @ Y0 @ Y1)) => (sK18 @ sK31 @ Y1)))))) = $false) | ~spl0_21), 2.60/0.74 inference(beta_eta_normalization,[],[f1707])). 2.60/0.74 thf(f1707,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2))))))) @ sK31) = $false) | ~spl0_21), 2.60/0.74 inference(sigma_clausification,[],[f1129])). 2.60/0.74 thf(f1129,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2)))))))) = $false) | ~spl0_21), 2.60/0.74 inference(avatar_component_clause,[],[f1128])). 2.60/0.74 thf(f1128,plain,( 2.60/0.74 spl0_21 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2)))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])). 2.60/0.74 thf(f1781,plain,( 2.60/0.74 ((sK18 @ sK31 @ sK33) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(boolean_simplification,[],[f1780])). 2.60/0.74 thf(f1780,plain,( 2.60/0.74 (($true => (sK18 @ sK31 @ sK33)) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(superposition,[],[f1763,f1736])). 2.60/0.74 thf(f1736,plain,( 2.60/0.74 ($true = (sK18 @ sK32 @ sK33)) | ~spl0_21), 2.60/0.74 inference(binary_proxy_clausification,[],[f1729])). 2.60/0.74 thf(f1763,plain,( 2.60/0.74 ( ! [X0 : a] : ((((sK18 @ sK32 @ X0) => (sK18 @ sK31 @ X0)) = $true)) ) | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(boolean_simplification,[],[f1758])). 2.60/0.74 thf(f1758,plain,( 2.60/0.74 ( ! [X0 : a] : (((($true & (sK18 @ sK32 @ X0)) => (sK18 @ sK31 @ X0)) = $true)) ) | (~spl0_5 | ~spl0_14 | ~spl0_21)), 2.60/0.74 inference(superposition,[],[f1745,f1739])). 2.60/0.74 thf(f1739,plain,( 2.60/0.74 ((sK18 @ sK31 @ sK32) = $true) | ~spl0_21), 2.60/0.74 inference(boolean_simplification,[],[f1738])). 2.60/0.74 thf(f1738,plain,( 2.60/0.74 (((sK18 @ sK31 @ sK32) & $true) = $true) | ~spl0_21), 2.60/0.74 inference(backward_demodulation,[],[f1729,f1736])). 2.60/0.74 thf(f1745,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK18 @ X3 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ X3 @ X1)) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1744])). 2.60/0.74 thf(f1744,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK18 @ Y0 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ Y0 @ X1))) @ X3) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(pi_clausification,[],[f1741])). 2.60/0.74 thf(f1741,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK18 @ Y0 @ X2) & (sK18 @ X2 @ X1)) => (sK18 @ Y0 @ X1)))) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1740])). 2.60/0.74 thf(f1740,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y0 @ X1)) => (sK18 @ Y1 @ X1))))) @ X2))) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(pi_clausification,[],[f1735])). 2.60/0.74 thf(f1735,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK18 @ Y1 @ Y0) & (sK18 @ Y0 @ X1)) => (sK18 @ Y1 @ X1)))))) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1734])). 2.60/0.74 thf(f1734,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))) @ X1) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(pi_clausification,[],[f1609])). 2.60/0.74 thf(f1609,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0)))))))) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1604])). 2.60/0.74 thf(f1604,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1571])). 2.60/0.74 thf(f1571,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1570])). 2.60/0.74 thf(f1570,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))) @ sK18) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(sigma_clausification,[],[f1569])). 2.60/0.74 thf(f1569,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f1568])). 2.60/0.74 thf(f1568,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f1567])). 2.60/0.74 thf(f1567,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) | $true) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(forward_demodulation,[],[f919,f600])). 2.60/0.74 thf(f600,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16)))) = $true) | ~spl0_14), 2.60/0.74 inference(avatar_component_clause,[],[f599])). 2.60/0.74 thf(f599,plain,( 2.60/0.74 spl0_14 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16)))) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_14])])). 2.60/0.74 thf(f1566,plain,( 2.60/0.74 ~spl0_5 | ~spl0_13 | ~spl0_26), 2.60/0.74 inference(avatar_contradiction_clause,[],[f1565])). 2.60/0.74 thf(f1565,plain,( 2.60/0.74 $false | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(trivial_inequality_removal,[],[f1564])). 2.60/0.74 thf(f1564,plain,( 2.60/0.74 ($true = $false) | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(boolean_simplification,[],[f1563])). 2.60/0.74 thf(f1563,plain,( 2.60/0.74 ((~ $true) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(boolean_simplification,[],[f1562])). 2.60/0.74 thf(f1562,plain,( 2.60/0.74 ((~ ((sK2 @ sK29 @ sK30) | $true)) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(forward_demodulation,[],[f1560,f1549])). 2.60/0.74 thf(f1549,plain,( 2.60/0.74 ((sK3 @ sK29 @ sK30) = $true) | ~spl0_26), 2.60/0.74 inference(binary_proxy_clausification,[],[f1535])). 2.60/0.74 thf(f1535,plain,( 2.60/0.74 (((sK3 @ sK29 @ sK30) => (sK18 @ sK29 @ sK30)) = $false) | ~spl0_26), 2.60/0.74 inference(beta_eta_normalization,[],[f1534])). 2.60/0.74 thf(f1534,plain,( 2.60/0.74 (((^[Y0 : a]: ((sK3 @ sK29 @ Y0) => (sK18 @ sK29 @ Y0))) @ sK30) = $false) | ~spl0_26), 2.60/0.74 inference(sigma_clausification,[],[f1518])). 2.60/0.74 thf(f1518,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: ((sK3 @ sK29 @ Y0) => (sK18 @ sK29 @ Y0)))) = $false) | ~spl0_26), 2.60/0.74 inference(beta_eta_normalization,[],[f1516])). 2.60/0.74 thf(f1516,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1))))) @ sK29) = $false) | ~spl0_26), 2.60/0.74 inference(sigma_clausification,[],[f1503])). 2.60/0.74 thf(f1503,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) = $false) | ~spl0_26), 2.60/0.74 inference(avatar_component_clause,[],[f1502])). 2.60/0.74 thf(f1502,plain,( 2.60/0.74 spl0_26 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_26])])). 2.60/0.74 thf(f1560,plain,( 2.60/0.74 ((~ ((sK2 @ sK29 @ sK30) | (sK3 @ sK29 @ sK30))) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(boolean_simplification,[],[f1552])). 2.60/0.74 thf(f1552,plain,( 2.60/0.74 ((((sK2 @ sK29 @ sK30) | (sK3 @ sK29 @ sK30)) => $false) = $true) | (~spl0_5 | ~spl0_13 | ~spl0_26)), 2.60/0.74 inference(superposition,[],[f1397,f1551])). 2.60/0.74 thf(f1551,plain,( 2.60/0.74 ((sK18 @ sK29 @ sK30) = $false) | ~spl0_26), 2.60/0.74 inference(boolean_simplification,[],[f1550])). 2.60/0.74 thf(f1550,plain,( 2.60/0.74 (($true => (sK18 @ sK29 @ sK30)) = $false) | ~spl0_26), 2.60/0.74 inference(backward_demodulation,[],[f1535,f1549])). 2.60/0.74 thf(f1397,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((((sK2 @ X1 @ X2) | (sK3 @ X1 @ X2)) => (sK18 @ X1 @ X2)) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1396])). 2.60/0.74 thf(f1396,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0))) @ X2) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(pi_clausification,[],[f1388])). 2.60/0.74 thf(f1388,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0)))) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1387])). 2.60/0.74 thf(f1387,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))) @ X1) = $true)) ) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(pi_clausification,[],[f1230])). 2.60/0.74 thf(f1230,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1196])). 2.60/0.74 thf(f1196,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1188])). 2.60/0.74 thf(f1188,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(beta_eta_normalization,[],[f1187])). 2.60/0.74 thf(f1187,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))) @ sK18) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(sigma_clausification,[],[f1186])). 2.60/0.74 thf(f1186,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1185])). 2.60/0.74 thf(f1185,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1184])). 2.60/0.74 thf(f1184,plain,( 2.60/0.74 ((($true | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(forward_demodulation,[],[f919,f597])). 2.60/0.74 thf(f1507,plain,( 2.60/0.74 spl0_26 | spl0_27 | ~spl0_5 | ~spl0_13), 2.60/0.74 inference(avatar_split_clause,[],[f1498,f596,f228,f1505,f1502])). 2.60/0.74 thf(f1498,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1492])). 2.60/0.74 thf(f1492,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0))))))))) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(not_proxy_clausification,[],[f1359])). 2.60/0.74 thf(f1359,plain,( 2.60/0.74 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0)))))))))) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1357])). 2.60/0.74 thf(f1357,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y1 @ Y2) & (sK18 @ Y2 @ Y0)) => (sK18 @ Y1 @ Y0))))))))) => $false) = $true) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(superposition,[],[f1346,f1198])). 2.60/0.74 thf(f1198,plain,( 2.60/0.74 ((sK18 @ sK17 @ sK16) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(boolean_simplification,[],[f1197])). 2.60/0.74 thf(f1197,plain,( 2.60/0.74 (($true => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_13)), 2.60/0.74 inference(backward_demodulation,[],[f1188,f1196])). 2.60/0.74 thf(f1346,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (X1 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0))))))))) => (X1 @ sK17 @ sK16)) = $true)) ) | ~spl0_13), 2.60/0.74 inference(beta_eta_normalization,[],[f1345])). 2.60/0.74 thf(f1345,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16))) @ X1) = $true)) ) | ~spl0_13), 2.60/0.74 inference(pi_clausification,[],[f597])). 2.60/0.74 thf(f1183,plain,( 2.60/0.74 ~spl0_5 | ~spl0_14 | ~spl0_22), 2.60/0.74 inference(avatar_contradiction_clause,[],[f1182])). 2.60/0.74 thf(f1182,plain,( 2.60/0.74 $false | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(trivial_inequality_removal,[],[f1181])). 2.60/0.74 thf(f1181,plain,( 2.60/0.74 ($true = $false) | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(boolean_simplification,[],[f1180])). 2.60/0.74 thf(f1180,plain,( 2.60/0.74 ((~ $true) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(boolean_simplification,[],[f1179])). 2.60/0.74 thf(f1179,plain,( 2.60/0.74 ((~ ($true | (sK3 @ sK28 @ sK27))) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(forward_demodulation,[],[f1174,f1166])). 2.60/0.74 thf(f1166,plain,( 2.60/0.74 ((sK2 @ sK28 @ sK27) = $true) | ~spl0_22), 2.60/0.74 inference(binary_proxy_clausification,[],[f1151])). 2.60/0.74 thf(f1151,plain,( 2.60/0.74 (((sK2 @ sK28 @ sK27) => (sK18 @ sK28 @ sK27)) = $false) | ~spl0_22), 2.60/0.74 inference(beta_eta_normalization,[],[f1150])). 2.60/0.74 thf(f1150,plain,( 2.60/0.74 (((^[Y0 : a]: ((sK2 @ Y0 @ sK27) => (sK18 @ Y0 @ sK27))) @ sK28) = $false) | ~spl0_22), 2.60/0.74 inference(sigma_clausification,[],[f1143])). 2.60/0.74 thf(f1143,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK27) => (sK18 @ Y0 @ sK27)))) = $false) | ~spl0_22), 2.60/0.74 inference(beta_eta_normalization,[],[f1139])). 2.60/0.74 thf(f1139,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0))))) @ sK27) = $false) | ~spl0_22), 2.60/0.74 inference(sigma_clausification,[],[f1132])). 2.60/0.74 thf(f1132,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) = $false) | ~spl0_22), 2.60/0.74 inference(avatar_component_clause,[],[f1131])). 2.60/0.74 thf(f1131,plain,( 2.60/0.74 spl0_22 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])). 2.60/0.74 thf(f1174,plain,( 2.60/0.74 ((~ ((sK2 @ sK28 @ sK27) | (sK3 @ sK28 @ sK27))) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(boolean_simplification,[],[f1169])). 2.60/0.74 thf(f1169,plain,( 2.60/0.74 ((((sK2 @ sK28 @ sK27) | (sK3 @ sK28 @ sK27)) => $false) = $true) | (~spl0_5 | ~spl0_14 | ~spl0_22)), 2.60/0.74 inference(superposition,[],[f1059,f1168])). 2.60/0.74 thf(f1168,plain,( 2.60/0.74 ((sK18 @ sK28 @ sK27) = $false) | ~spl0_22), 2.60/0.74 inference(boolean_simplification,[],[f1167])). 2.60/0.74 thf(f1167,plain,( 2.60/0.74 (($true => (sK18 @ sK28 @ sK27)) = $false) | ~spl0_22), 2.60/0.74 inference(backward_demodulation,[],[f1151,f1166])). 2.60/0.74 thf(f1059,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((((sK2 @ X1 @ X2) | (sK3 @ X1 @ X2)) => (sK18 @ X1 @ X2)) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1058])). 2.60/0.74 thf(f1058,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0))) @ X2) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(pi_clausification,[],[f1035])). 2.60/0.74 thf(f1035,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK2 @ X1 @ Y0) | (sK3 @ X1 @ Y0)) => (sK18 @ X1 @ Y0)))) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f1034])). 2.60/0.74 thf(f1034,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1))))) @ X1) = $true)) ) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(pi_clausification,[],[f953])). 2.60/0.74 thf(f953,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(binary_proxy_clausification,[],[f947])). 2.60/0.74 thf(f947,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(binary_proxy_clausification,[],[f931])). 2.60/0.74 thf(f931,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK18 @ Y0 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y2 @ Y1) & (sK18 @ Y1 @ Y0)) => (sK18 @ Y2 @ Y0))))))))) => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(beta_eta_normalization,[],[f930])). 2.60/0.74 thf(f930,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))) @ sK18) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(sigma_clausification,[],[f922])). 2.60/0.74 thf(f922,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f921])). 2.60/0.74 thf(f921,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f920])). 2.60/0.74 thf(f920,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) | $true) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(forward_demodulation,[],[f919,f600])). 2.60/0.74 thf(f1133,plain,( 2.60/0.74 spl0_21 | spl0_22 | ~spl0_5 | ~spl0_14), 2.60/0.74 inference(avatar_split_clause,[],[f1124,f599,f228,f1131,f1128])). 2.60/0.74 thf(f1124,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(binary_proxy_clausification,[],[f1111])). 2.60/0.74 thf(f1111,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2))))))))) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(not_proxy_clausification,[],[f951])). 2.60/0.74 thf(f951,plain,( 2.60/0.74 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2)))))))))) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f950])). 2.60/0.74 thf(f950,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK18 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK18 @ Y0 @ Y1) & (sK18 @ Y1 @ Y2)) => (sK18 @ Y0 @ Y2))))))))) => $false) = $true) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(superposition,[],[f917,f949])). 2.60/0.74 thf(f949,plain,( 2.60/0.74 ((sK18 @ sK17 @ sK16) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(boolean_simplification,[],[f948])). 2.60/0.74 thf(f948,plain,( 2.60/0.74 (($true => (sK18 @ sK17 @ sK16)) = $false) | (~spl0_5 | ~spl0_14)), 2.60/0.74 inference(backward_demodulation,[],[f931,f947])). 2.60/0.74 thf(f917,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2))))))))) => (X1 @ sK17 @ sK16)) = $true)) ) | ~spl0_14), 2.60/0.74 inference(beta_eta_normalization,[],[f916])). 2.60/0.74 thf(f916,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))) @ X1) = $true)) ) | ~spl0_14), 2.60/0.74 inference(pi_clausification,[],[f600])). 2.60/0.74 thf(f911,plain,( 2.60/0.74 ~spl0_6 | ~spl0_12), 2.60/0.74 inference(avatar_contradiction_clause,[],[f910])). 2.60/0.74 thf(f910,plain,( 2.60/0.74 $false | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(trivial_inequality_removal,[],[f909])). 2.60/0.74 thf(f909,plain,( 2.60/0.74 ($true = $false) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(boolean_simplification,[],[f908])). 2.60/0.74 thf(f908,plain,( 2.60/0.74 ((~ $true) = $true) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(forward_demodulation,[],[f902,f876])). 2.60/0.74 thf(f876,plain,( 2.60/0.74 ((sK15 @ sK21 @ sK24) = $true) | ~spl0_12), 2.60/0.74 inference(binary_proxy_clausification,[],[f865])). 2.60/0.74 thf(f865,plain,( 2.60/0.74 (((sK15 @ sK24 @ sK22) & (sK15 @ sK21 @ sK24)) = $true) | ~spl0_12), 2.60/0.74 inference(not_proxy_clausification,[],[f856])). 2.60/0.74 thf(f856,plain,( 2.60/0.74 ((~ ((sK15 @ sK24 @ sK22) & (sK15 @ sK21 @ sK24))) = $false) | ~spl0_12), 2.60/0.74 inference(beta_eta_normalization,[],[f855])). 2.60/0.74 thf(f855,plain,( 2.60/0.74 (((^[Y0 : a]: (~ ((sK15 @ Y0 @ sK22) & (sK15 @ sK21 @ Y0)))) @ sK24) = $false) | ~spl0_12), 2.60/0.74 inference(sigma_clausification,[],[f840])). 2.60/0.74 thf(f840,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (~ ((sK15 @ Y0 @ sK22) & (sK15 @ sK21 @ Y0))))) = $false) | ~spl0_12), 2.60/0.74 inference(boolean_simplification,[],[f839])). 2.60/0.74 thf(f839,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ sK22) & (sK15 @ sK21 @ Y0)) => $false))) = $false) | ~spl0_12), 2.60/0.74 inference(backward_demodulation,[],[f643,f838])). 2.60/0.74 thf(f838,plain,( 2.60/0.74 ((sK15 @ sK21 @ sK22) = $false) | ~spl0_12), 2.60/0.74 inference(boolean_simplification,[],[f837])). 2.60/0.74 thf(f837,plain,( 2.60/0.74 (($true => (sK15 @ sK21 @ sK22)) = $false) | ~spl0_12), 2.60/0.74 inference(backward_demodulation,[],[f647,f836])). 2.60/0.74 thf(f836,plain,( 2.60/0.74 (((sK15 @ sK23 @ sK22) & (sK15 @ sK21 @ sK23)) = $true) | ~spl0_12), 2.60/0.74 inference(binary_proxy_clausification,[],[f647])). 2.60/0.74 thf(f647,plain,( 2.60/0.74 ((((sK15 @ sK23 @ sK22) & (sK15 @ sK21 @ sK23)) => (sK15 @ sK21 @ sK22)) = $false) | ~spl0_12), 2.60/0.74 inference(beta_eta_normalization,[],[f646])). 2.60/0.74 thf(f646,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK15 @ Y0 @ sK22) & (sK15 @ sK21 @ Y0)) => (sK15 @ sK21 @ sK22))) @ sK23) = $false) | ~spl0_12), 2.60/0.74 inference(sigma_clausification,[],[f643])). 2.60/0.74 thf(f643,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ sK22) & (sK15 @ sK21 @ Y0)) => (sK15 @ sK21 @ sK22)))) = $false) | ~spl0_12), 2.60/0.74 inference(beta_eta_normalization,[],[f642])). 2.60/0.74 thf(f642,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ Y0) & (sK15 @ sK21 @ Y1)) => (sK15 @ sK21 @ Y0))))) @ sK22) = $false) | ~spl0_12), 2.60/0.74 inference(sigma_clausification,[],[f633])). 2.60/0.74 thf(f633,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ Y0) & (sK15 @ sK21 @ Y1)) => (sK15 @ sK21 @ Y0)))))) = $false) | ~spl0_12), 2.60/0.74 inference(beta_eta_normalization,[],[f632])). 2.60/0.74 thf(f632,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1))))))) @ sK21) = $false) | ~spl0_12), 2.60/0.74 inference(sigma_clausification,[],[f531])). 2.60/0.74 thf(f531,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) = $false) | ~spl0_12), 2.60/0.74 inference(avatar_component_clause,[],[f530])). 2.60/0.74 thf(f530,plain,( 2.60/0.74 spl0_12 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])). 2.60/0.74 thf(f902,plain,( 2.60/0.74 ((~ (sK15 @ sK21 @ sK24)) = $true) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(boolean_simplification,[],[f897])). 2.60/0.74 thf(f897,plain,( 2.60/0.74 (((sK15 @ sK21 @ sK24) => $false) = $true) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(superposition,[],[f885,f838])). 2.60/0.74 thf(f885,plain,( 2.60/0.74 ( ! [X0 : a] : ((((sK15 @ X0 @ sK24) => (sK15 @ X0 @ sK22)) = $true)) ) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(boolean_simplification,[],[f881])). 2.60/0.74 thf(f881,plain,( 2.60/0.74 ( ! [X0 : a] : (((((sK15 @ X0 @ sK24) & $true) => (sK15 @ X0 @ sK22)) = $true)) ) | (~spl0_6 | ~spl0_12)), 2.60/0.74 inference(superposition,[],[f738,f879])). 2.60/0.74 thf(f879,plain,( 2.60/0.74 ((sK15 @ sK24 @ sK22) = $true) | ~spl0_12), 2.60/0.74 inference(boolean_simplification,[],[f878])). 2.60/0.74 thf(f878,plain,( 2.60/0.74 (((sK15 @ sK24 @ sK22) & $true) = $true) | ~spl0_12), 2.60/0.74 inference(backward_demodulation,[],[f865,f876])). 2.60/0.74 thf(f738,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK15 @ X3 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ X3 @ X2)) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f737])). 2.60/0.74 thf(f737,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2))) @ X3) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f733])). 2.60/0.74 thf(f733,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2)))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f732])). 2.60/0.74 thf(f732,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ X2) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f702])). 2.60/0.74 thf(f702,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f701])). 2.60/0.74 thf(f701,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f638])). 2.60/0.74 thf(f638,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1)))))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f635])). 2.60/0.74 thf(f635,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f631])). 2.60/0.74 thf(f631,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) => (sK15 @ sK14 @ sK13)) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f630])). 2.60/0.74 thf(f630,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))) @ sK15) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f621])). 2.60/0.74 thf(f621,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13)))) = $false) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f620])). 2.60/0.74 thf(f620,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))))) = $false) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f617,f619])). 2.60/0.74 thf(f619,plain,( 2.60/0.74 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f617])). 2.60/0.74 thf(f617,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f616])). 2.60/0.74 thf(f616,plain,( 2.60/0.74 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13)))))) @ sK14) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f611])). 2.60/0.74 thf(f611,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13))))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f610])). 2.60/0.74 thf(f610,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK13) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f607])). 2.60/0.74 thf(f607,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f606])). 2.60/0.74 thf(f606,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))))))))) @ sK12) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f232])). 2.60/0.74 thf(f629,plain,( 2.60/0.74 spl0_15 | spl0_16 | ~spl0_11), 2.60/0.74 inference(avatar_split_clause,[],[f622,f527,f627,f624])). 2.60/0.74 thf(f622,plain,( 2.60/0.74 ((sK3 @ sK19 @ sK20) = $true) | ((sK2 @ sK19 @ sK20) = $true) | ~spl0_11), 2.60/0.74 inference(binary_proxy_clausification,[],[f613])). 2.60/0.74 thf(f613,plain,( 2.60/0.74 (((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) = $true) | ~spl0_11), 2.60/0.74 inference(binary_proxy_clausification,[],[f609])). 2.60/0.74 thf(f609,plain,( 2.60/0.74 ((((sK2 @ sK19 @ sK20) | (sK3 @ sK19 @ sK20)) => (sK15 @ sK19 @ sK20)) = $false) | ~spl0_11), 2.60/0.74 inference(beta_eta_normalization,[],[f608])). 2.60/0.74 thf(f608,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) => (sK15 @ sK19 @ Y0))) @ sK20) = $false) | ~spl0_11), 2.60/0.74 inference(sigma_clausification,[],[f605])). 2.60/0.74 thf(f605,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK2 @ sK19 @ Y0) | (sK3 @ sK19 @ Y0)) => (sK15 @ sK19 @ Y0)))) = $false) | ~spl0_11), 2.60/0.74 inference(beta_eta_normalization,[],[f604])). 2.60/0.74 thf(f604,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1))))) @ sK19) = $false) | ~spl0_11), 2.60/0.74 inference(sigma_clausification,[],[f528])). 2.60/0.74 thf(f601,plain,( 2.60/0.74 spl0_13 | spl0_14 | ~spl0_5), 2.60/0.74 inference(avatar_split_clause,[],[f594,f228,f599,f596])). 2.60/0.74 thf(f594,plain,( 2.60/0.74 ($true = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16)))) = $true) | ~spl0_5), 2.60/0.74 inference(binary_proxy_clausification,[],[f540])). 2.60/0.74 thf(f540,plain,( 2.60/0.74 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))))) = $true) | ~spl0_5), 2.60/0.74 inference(binary_proxy_clausification,[],[f538])). 2.60/0.74 thf(f538,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) => (Y0 @ sK17 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK17 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK17 @ sK16))))) = $false) | ~spl0_5), 2.60/0.74 inference(beta_eta_normalization,[],[f537])). 2.60/0.74 thf(f537,plain,( 2.60/0.74 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))))) @ sK17) = $false) | ~spl0_5), 2.60/0.74 inference(sigma_clausification,[],[f536])). 2.60/0.74 thf(f536,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK3 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) => (Y1 @ Y0 @ sK16)))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK16))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ Y0 @ sK16))))))) = $false) | ~spl0_5), 2.60/0.74 inference(beta_eta_normalization,[],[f535])). 2.60/0.74 thf(f535,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK16) = $false) | ~spl0_5), 2.60/0.74 inference(sigma_clausification,[],[f229])). 2.60/0.74 thf(f532,plain,( 2.60/0.74 spl0_11 | spl0_12 | ~spl0_6 | ~spl0_8), 2.60/0.74 inference(avatar_split_clause,[],[f523,f431,f231,f530,f527])). 2.60/0.74 thf(f431,plain,( 2.60/0.74 spl0_8 <=> ((sK15 @ sK12 @ sK13) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 2.60/0.74 thf(f523,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1)))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) = $false) | (~spl0_6 | ~spl0_8)), 2.60/0.74 inference(binary_proxy_clausification,[],[f520])). 2.60/0.74 thf(f520,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1))))))) = $false) | (~spl0_6 | ~spl0_8)), 2.60/0.74 inference(not_proxy_clausification,[],[f455])). 2.60/0.74 thf(f455,plain,( 2.60/0.74 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) = $true) | (~spl0_6 | ~spl0_8)), 2.60/0.74 inference(boolean_simplification,[],[f452])). 2.60/0.74 thf(f452,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y0 @ Y2)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y1))))))) => $false) = $true) | (~spl0_6 | ~spl0_8)), 2.60/0.74 inference(superposition,[],[f349,f432])). 2.60/0.74 thf(f432,plain,( 2.60/0.74 ((sK15 @ sK12 @ sK13) = $false) | ~spl0_8), 2.60/0.74 inference(avatar_component_clause,[],[f431])). 2.60/0.74 thf(f349,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y1) & (X1 @ Y0 @ Y2)) => (X1 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y0 @ Y1) | (sK3 @ Y0 @ Y1)) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK12 @ sK13)) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f348])). 2.60/0.74 thf(f348,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f296])). 2.60/0.74 thf(f296,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f243])). 2.60/0.74 thf(f243,plain,( 2.60/0.74 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f241])). 2.60/0.74 thf(f241,plain,( 2.60/0.74 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y1 @ Y2) | (sK3 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f240])). 2.60/0.74 thf(f240,plain,( 2.60/0.74 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13)))))) @ sK14) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f239])). 2.60/0.74 thf(f239,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y2 @ Y3) | (sK3 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK12 @ sK13)))) & (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4))))))))) => (Y1 @ Y0 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) | (sK3 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y4 @ Y2) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y4 @ Y3))))))))) => (Y1 @ Y0 @ sK13))))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f238])). 2.60/0.74 thf(f238,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK13) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f237])). 2.60/0.74 thf(f237,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y3 @ Y5)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ sK12 @ Y0)))) & (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ sK12))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y3) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y5 @ Y4))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f236])). 2.60/0.74 thf(f236,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1)))))))))) @ sK12) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f232])). 2.60/0.74 thf(f446,plain,( 2.60/0.74 spl0_9 | spl0_10 | ~spl0_7), 2.60/0.74 inference(avatar_split_clause,[],[f437,f428,f444,f441])). 2.60/0.74 thf(f428,plain,( 2.60/0.74 spl0_7 <=> ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))))) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])). 2.60/0.74 thf(f437,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $false) | ~spl0_7), 2.60/0.74 inference(binary_proxy_clausification,[],[f434])). 2.60/0.74 thf(f434,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))))) = $false) | ~spl0_7), 2.60/0.74 inference(not_proxy_clausification,[],[f429])). 2.60/0.74 thf(f429,plain,( 2.60/0.74 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))))) = $true) | ~spl0_7), 2.60/0.74 inference(avatar_component_clause,[],[f428])). 2.60/0.74 thf(f433,plain,( 2.60/0.74 spl0_7 | spl0_8 | ~spl0_6), 2.60/0.74 inference(avatar_split_clause,[],[f422,f231,f431,f428])). 2.60/0.74 thf(f422,plain,( 2.60/0.74 ((sK15 @ sK12 @ sK13) = $false) | ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))))) = $true) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f417])). 2.60/0.74 thf(f417,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))))) => $false) = $true) | ((sK15 @ sK12 @ sK13) = $false) | ~spl0_6), 2.60/0.74 inference(superposition,[],[f308,f341])). 2.60/0.74 thf(f341,plain,( 2.60/0.74 ( ! [X0 : a] : (((sK15 @ sK14 @ X0) = $false) | ((sK15 @ X0 @ sK13) = $false)) ) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f332])). 2.60/0.74 thf(f332,plain,( 2.60/0.74 ( ! [X0 : a] : ((((sK15 @ sK14 @ X0) & (sK15 @ X0 @ sK13)) = $false)) ) | ~spl0_6), 2.60/0.74 inference(not_proxy_clausification,[],[f288])). 2.60/0.74 thf(f288,plain,( 2.60/0.74 ( ! [X0 : a] : (((~ ((sK15 @ sK14 @ X0) & (sK15 @ X0 @ sK13))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f281])). 2.60/0.74 thf(f281,plain,( 2.60/0.74 ( ! [X0 : a] : (((((sK15 @ sK14 @ X0) & (sK15 @ X0 @ sK13)) => $false) = $true)) ) | ~spl0_6), 2.60/0.74 inference(superposition,[],[f276,f251])). 2.60/0.74 thf(f251,plain,( 2.60/0.74 ((sK15 @ sK14 @ sK13) = $false) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f250])). 2.60/0.74 thf(f250,plain,( 2.60/0.74 (($true => (sK15 @ sK14 @ sK13)) = $false) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f247,f249])). 2.60/0.74 thf(f249,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f247])). 2.60/0.74 thf(f247,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) => (sK15 @ sK14 @ sK13)) = $false) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f246])). 2.60/0.74 thf(f246,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))) @ sK15) = $false) | ~spl0_6), 2.60/0.74 inference(sigma_clausification,[],[f245])). 2.60/0.74 thf(f245,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13)))) = $false) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f244])). 2.60/0.74 thf(f244,plain,( 2.60/0.74 (($true => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) | (sK3 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) => (Y0 @ sK14 @ sK13))))) = $false) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f241,f243])). 2.60/0.74 thf(f276,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK15 @ X3 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ X3 @ X2)) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f275])). 2.60/0.74 thf(f275,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2))) @ X3) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f263])). 2.60/0.74 thf(f263,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ X1) & (sK15 @ X1 @ X2)) => (sK15 @ Y0 @ X2)))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f262])). 2.60/0.74 thf(f262,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ X2) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f259])). 2.60/0.74 thf(f259,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ X1) & (sK15 @ X1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f258])). 2.60/0.74 thf(f258,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f255])). 2.60/0.74 thf(f255,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1)))))))) = $true) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f254])). 2.60/0.74 thf(f254,plain,( 2.60/0.74 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y2 @ Y1))))))))) = $true) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f249,f253])). 2.60/0.74 thf(f253,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0)))))) = $true) | ~spl0_6), 2.60/0.74 inference(binary_proxy_clausification,[],[f249])). 2.60/0.74 thf(f308,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y0 @ Y1)) => (X1 @ Y0 @ Y2))))))))) => (X1 @ sK14 @ sK12)) = $true)) ) | ~spl0_6), 2.60/0.74 inference(beta_eta_normalization,[],[f307])). 2.60/0.74 thf(f307,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))) @ X1) = $true)) ) | ~spl0_6), 2.60/0.74 inference(pi_clausification,[],[f298])). 2.60/0.74 thf(f298,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12)))) = $true) | ~spl0_6), 2.60/0.74 inference(boolean_simplification,[],[f297])). 2.60/0.74 thf(f297,plain,( 2.60/0.74 (($true & (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) => (Y0 @ sK14 @ sK12))))) = $true) | ~spl0_6), 2.60/0.74 inference(backward_demodulation,[],[f243,f296])). 2.60/0.74 thf(f233,plain,( 2.60/0.74 spl0_5 | spl0_6 | ~spl0_1), 2.60/0.74 inference(avatar_split_clause,[],[f226,f55,f231,f228])). 2.60/0.74 thf(f55,plain,( 2.60/0.74 spl0_1 <=> (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 2.60/0.74 thf(f226,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0))))))))) = $false) | ~spl0_1), 2.60/0.74 inference(binary_proxy_clausification,[],[f56])). 2.60/0.74 thf(f56,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false) | ~spl0_1), 2.60/0.74 inference(avatar_component_clause,[],[f55])). 2.60/0.74 thf(f219,plain,( 2.60/0.74 ~spl0_4), 2.60/0.74 inference(avatar_contradiction_clause,[],[f218])). 2.60/0.74 thf(f218,plain,( 2.60/0.74 $false | ~spl0_4), 2.60/0.74 inference(trivial_inequality_removal,[],[f215])). 2.60/0.74 thf(f215,plain,( 2.60/0.74 ($true = $false) | ~spl0_4), 2.60/0.74 inference(superposition,[],[f37,f211])). 2.60/0.74 thf(f211,plain,( 2.60/0.74 ((((sK3 @ sK11 @ sK10) | (sK2 @ sK11 @ sK10)) => (sK6 @ sK11 @ sK10)) = $false) | ~spl0_4), 2.60/0.74 inference(beta_eta_normalization,[],[f210])). 2.60/0.74 thf(f210,plain,( 2.60/0.74 ($false = ((^[Y0 : a]: (((sK3 @ Y0 @ sK10) | (sK2 @ Y0 @ sK10)) => (sK6 @ Y0 @ sK10))) @ sK11)) | ~spl0_4), 2.60/0.74 inference(sigma_clausification,[],[f207])). 2.60/0.74 thf(f207,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK3 @ Y0 @ sK10) | (sK2 @ Y0 @ sK10)) => (sK6 @ Y0 @ sK10)))) = $false) | ~spl0_4), 2.60/0.74 inference(beta_eta_normalization,[],[f205])). 2.60/0.74 thf(f205,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK10) = $false) | ~spl0_4), 2.60/0.74 inference(sigma_clausification,[],[f122])). 2.60/0.74 thf(f122,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ~spl0_4), 2.60/0.74 inference(avatar_component_clause,[],[f121])). 2.60/0.74 thf(f121,plain,( 2.60/0.74 spl0_4 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 2.60/0.74 thf(f37,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((((sK3 @ X1 @ X2) | (sK2 @ X1 @ X2)) => (sK6 @ X1 @ X2)) = $true)) )), 2.60/0.74 inference(beta_eta_normalization,[],[f36])). 2.60/0.74 thf(f36,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0))) @ X2) = $true)) )), 2.60/0.74 inference(pi_clausification,[],[f35])). 2.60/0.74 thf(f35,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK3 @ X1 @ Y0) | (sK2 @ X1 @ Y0)) => (sK6 @ X1 @ Y0)))) = $true)) )), 2.60/0.74 inference(beta_eta_normalization,[],[f34])). 2.60/0.74 thf(f34,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))) @ X1) = $true)) )), 2.60/0.74 inference(pi_clausification,[],[f33])). 2.60/0.74 thf(f33,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1)))))) = $true)), 2.60/0.74 inference(boolean_simplification,[],[f32])). 2.60/0.74 thf(f32,plain,( 2.60/0.74 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) = $true)), 2.60/0.74 inference(backward_demodulation,[],[f25,f31])). 2.60/0.74 thf(f31,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) = $true)), 2.60/0.74 inference(binary_proxy_clausification,[],[f25])). 2.60/0.74 thf(f25,plain,( 2.60/0.74 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))))), 2.60/0.74 inference(binary_proxy_clausification,[],[f23])). 2.60/0.74 thf(f23,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y0 @ Y1) | (sK2 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y1))))))) => (sK6 @ sK4 @ sK5)) = $false)), 2.60/0.74 inference(beta_eta_normalization,[],[f22])). 2.60/0.74 thf(f22,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))) @ sK6) = $false)), 2.60/0.74 inference(sigma_clausification,[],[f21])). 2.60/0.74 thf(f21,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5)))) = $false)), 2.60/0.74 inference(boolean_simplification,[],[f20])). 2.60/0.74 thf(f20,plain,( 2.60/0.74 (($false | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) = $false)), 2.60/0.74 inference(backward_demodulation,[],[f17,f19])). 2.60/0.74 thf(f19,plain,( 2.60/0.74 ((~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5)))))) = $false)), 2.60/0.74 inference(binary_proxy_clausification,[],[f17])). 2.60/0.74 thf(f17,plain,( 2.60/0.74 (((~ (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5)))))) | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y1 @ Y2) | (sK2 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK4 @ sK5))))) = $false)), 2.60/0.74 inference(beta_eta_normalization,[],[f16])). 2.60/0.74 thf(f16,plain,( 2.60/0.74 (((^[Y0 : a]: ((~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y1 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (sK2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y2))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK4 @ Y0)))))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0)))))) @ sK5) = $false)), 2.60/0.74 inference(sigma_clausification,[],[f15])). 2.60/0.74 thf(f15,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: ((~ (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y5 @ Y7)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y1 @ Y2)))) & (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK3 @ Y6 @ Y5) | (sK2 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) | (sK3 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y5) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y7 @ Y6))))))))) => (Y4 @ Y3 @ Y2))))))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y1))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y2 @ Y1)))))))))) => (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK4 @ Y0)))))) | (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y3) & (Y1 @ Y3 @ Y4)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK3 @ Y2 @ Y3) | (sK2 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK4 @ Y0))))))) = $false)), 2.60/0.74 inference(beta_eta_normalization,[],[f14])). 2.60/0.74 thf(f14,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y2 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (sK2 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (sK3 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y4 @ Y3))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1)))))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))))))) @ sK4) = $false)), 2.60/0.74 inference(sigma_clausification,[],[f13])). 2.60/0.74 thf(f13,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((~ (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y6 @ Y8)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (sK3 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y2 @ Y3)))) & (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK3 @ Y7 @ Y6) | (sK2 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) | (sK3 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y6) & (Y5 @ Y6 @ Y7)) => (Y5 @ Y8 @ Y7))))))))) => (Y5 @ Y4 @ Y3))))))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7))))))))) => (Y4 @ Y3 @ Y2))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y5 @ Y6) | (sK3 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y3 @ Y2)))))))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1)))))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK3 @ Y3 @ Y4) | (sK2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1))))))))) = $false)), 2.60/0.74 inference(beta_eta_normalization,[],[f12])). 2.60/0.74 thf(f12,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y3 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (sK2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y0 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y5 @ Y4))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y8 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2)))))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))))))))) @ sK3) = $false)), 2.60/0.74 inference(sigma_clausification,[],[f11])). 2.60/0.74 thf(f11,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((~ (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y7 @ Y9)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y7 @ Y8) | (Y0 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y3 @ Y4)))) & (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) | (sK2 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((sK2 @ Y8 @ Y7) | (Y0 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y7) & (Y6 @ Y7 @ Y8)) => (Y6 @ Y9 @ Y8))))))))) => (Y6 @ Y5 @ Y4))))))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((Y0 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y7 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8))))))))) => (Y5 @ Y4 @ Y3))))) => (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y6 @ Y7) | (Y0 @ Y6 @ Y7)) => (Y5 @ Y6 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y8 @ Y7) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y8 @ Y6))))))))) => (Y5 @ Y4 @ Y3)))))))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2)))))) | (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y5) & (Y3 @ Y5 @ Y6)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y0 @ Y4 @ Y5) | (sK2 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2))))))))))) = $false)), 2.60/0.74 inference(beta_eta_normalization,[],[f10])). 2.60/0.74 thf(f10,plain,( 2.60/0.74 (((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y9) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y6 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y1 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y5))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3)))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))))))))))) @ sK2) = $false)), 2.60/0.74 inference(sigma_clausification,[],[f7])). 2.60/0.74 thf(f7,plain,( 2.60/0.74 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y9) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y6 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y1 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y5))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3)))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3))))))))))))))), 2.60/0.74 inference(not_proxy_clausification,[],[f6])). 2.60/0.74 thf(f6,plain,( 2.60/0.74 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y9) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y6 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y1 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y5))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3)))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))))))))))))) = $true)), 2.60/0.74 inference(cnf_transformation,[],[f5])). 2.60/0.74 thf(f5,plain,( 2.60/0.74 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((~ (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y9) & (Y7 @ Y8 @ Y10)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y8 @ Y9) | (Y1 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y4 @ Y5)))) & (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y1 @ Y9 @ Y8) | (Y0 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y9 @ Y10) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y8 @ Y10))))))))) => (Y7 @ Y6 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y0 @ Y9 @ Y8) | (Y1 @ Y9 @ Y8)) => (Y7 @ Y9 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y10 @ Y8) & (Y7 @ Y8 @ Y9)) => (Y7 @ Y10 @ Y9))))))))) => (Y7 @ Y6 @ Y5))))))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y1 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y8 @ Y9) & (Y6 @ Y9 @ Y7)) => (Y6 @ Y8 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9))))))))) => (Y6 @ Y5 @ Y4))))) => (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y7 @ Y8) | (Y1 @ Y7 @ Y8)) => (Y6 @ Y7 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y9 @ Y8) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y9 @ Y7))))))))) => (Y6 @ Y5 @ Y4)))))))))) => (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y2 @ Y3)))))) | (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y6) & (Y4 @ Y6 @ Y7)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y1 @ Y5 @ Y6) | (Y0 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y2 @ Y3)))))))))))))) = $true)), 2.60/0.74 inference(fool_elimination,[],[f4])). 2.60/0.74 thf(f4,plain,( 2.60/0.74 ~! [X0 : a,X1 : a,X2 : a > a > $o,X3 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : (((X3 @ X6 @ X5) | (X2 @ X6 @ X5)) => (X4 @ X6 @ X5)) & ! [X7 : a,X8 : a,X9 : a] : (((X4 @ X8 @ X7) & (X4 @ X9 @ X8)) => (X4 @ X9 @ X7))) => (X4 @ X1 @ X0)) | ~((! [X10 : a,X11 : a] : ((! [X12 : a > a > $o] : ((! [X13 : a,X14 : a,X15 : a] : (((X12 @ X14 @ X13) & (X12 @ X15 @ X14)) => (X12 @ X15 @ X13)) & ! [X16 : a,X17 : a] : ((X3 @ X16 @ X17) => (X12 @ X16 @ X17))) => (X12 @ X10 @ X11)) | ! [X18 : a > a > $o] : ((! [X19 : a,X20 : a,X21 : a] : (((X18 @ X19 @ X21) & (X18 @ X20 @ X19)) => (X18 @ X20 @ X21)) & ! [X22 : a,X23 : a] : ((X2 @ X23 @ X22) => (X18 @ X23 @ X22))) => (X18 @ X10 @ X11))) => ! [X24 : a > a > $o] : ((! [X25 : a,X26 : a,X27 : a] : (((X24 @ X26 @ X27) & (X24 @ X25 @ X26)) => (X24 @ X25 @ X27)) & ! [X28 : a,X29 : a] : (((X2 @ X29 @ X28) | (X3 @ X29 @ X28)) => (X24 @ X29 @ X28))) => (X24 @ X10 @ X11))) & ! [X30 : a,X31 : a,X32 : a] : ((! [X33 : a > a > $o] : ((! [X34 : a,X35 : a,X36 : a] : (((X33 @ X36 @ X35) & (X33 @ X35 @ X34)) => (X33 @ X36 @ X34)) & ! [X37 : a,X38 : a] : (((X3 @ X37 @ X38) | (X2 @ X37 @ X38)) => (X33 @ X37 @ X38))) => (X33 @ X30 @ X32)) & ! [X39 : a > a > $o] : ((! [X40 : a,X41 : a] : (((X2 @ X41 @ X40) | (X3 @ X41 @ X40)) => (X39 @ X41 @ X40)) & ! [X42 : a,X43 : a,X44 : a] : (((X39 @ X44 @ X42) & (X39 @ X42 @ X43)) => (X39 @ X44 @ X43))) => (X39 @ X32 @ X31))) => ! [X45 : a > a > $o] : ((! [X46 : a,X47 : a,X48 : a] : (((X45 @ X48 @ X47) & (X45 @ X46 @ X48)) => (X45 @ X46 @ X47)) & ! [X49 : a,X50 : a] : (((X2 @ X49 @ X50) | (X3 @ X49 @ X50)) => (X45 @ X49 @ X50))) => (X45 @ X30 @ X31)))) => ! [X51 : a > a > $o] : ((! [X52 : a,X53 : a,X54 : a] : (((X51 @ X53 @ X54) & (X51 @ X54 @ X52)) => (X51 @ X53 @ X52)) & ! [X55 : a,X56 : a] : (((X3 @ X55 @ X56) | (X2 @ X55 @ X56)) => (X51 @ X55 @ X56))) => (X51 @ X1 @ X0))))), 2.60/0.74 inference(rectify,[],[f2])). 2.60/0.74 thf(f2,negated_conjecture,( 2.60/0.74 ~! [X3 : a,X2 : a,X1 : a > a > $o,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)) | ~((! [X5 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X7 : a,X9 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X7 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ! [X5 : a,X7 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X10 : a,X9 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) & ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X9 : a,X10 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X6 @ X7))) => ! [X4 : a > a > $o] : ((! [X8 : a,X10 : a,X9 : a] : (((X4 @ X9 @ X10) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X7)))) => ! [X4 : a > a > $o] : ((! [X7 : a,X5 : a,X6 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))))), 2.60/0.74 inference(negated_conjecture,[],[f1])). 2.60/0.74 thf(f1,conjecture,( 2.60/0.74 ! [X3 : a,X2 : a,X1 : a > a > $o,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)) | ~((! [X5 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X7 : a,X9 : a,X8 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X8 : a,X9 : a] : ((X0 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) | ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : ((X1 @ X8 @ X9) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) => ! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X7 : a] : (((X4 @ X9 @ X7) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X7)) & ! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6))) & ! [X5 : a,X7 : a,X6 : a] : ((! [X4 : a > a > $o] : ((! [X10 : a,X9 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X6)) & ! [X4 : a > a > $o] : ((! [X9 : a,X8 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9)) & ! [X9 : a,X10 : a,X8 : a] : (((X4 @ X8 @ X9) & (X4 @ X9 @ X10)) => (X4 @ X8 @ X10))) => (X4 @ X6 @ X7))) => ! [X4 : a > a > $o] : ((! [X8 : a,X10 : a,X9 : a] : (((X4 @ X9 @ X10) & (X4 @ X8 @ X9)) => (X4 @ X8 @ X10)) & ! [X8 : a,X9 : a] : (((X1 @ X8 @ X9) | (X0 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X5 @ X7)))) => ! [X4 : a > a > $o] : ((! [X7 : a,X5 : a,X6 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3))))), 2.60/0.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250G_pme)). 2.60/0.74 thf(f202,plain,( 2.60/0.74 ~spl0_3), 2.60/0.74 inference(avatar_contradiction_clause,[],[f201])). 2.60/0.74 thf(f201,plain,( 2.60/0.74 $false | ~spl0_3), 2.60/0.74 inference(trivial_inequality_removal,[],[f200])). 2.60/0.74 thf(f200,plain,( 2.60/0.74 ($true = $false) | ~spl0_3), 2.60/0.74 inference(boolean_simplification,[],[f199])). 2.60/0.74 thf(f199,plain,( 2.60/0.74 ((~ $true) = $true) | ~spl0_3), 2.60/0.74 inference(forward_demodulation,[],[f187,f150])). 2.60/0.74 thf(f150,plain,( 2.60/0.74 ((sK6 @ sK7 @ sK9) = $true) | ~spl0_3), 2.60/0.74 inference(binary_proxy_clausification,[],[f136])). 2.60/0.74 thf(f136,plain,( 2.60/0.74 (((sK6 @ sK7 @ sK9) & (sK6 @ sK8 @ sK7)) = $true) | ~spl0_3), 2.60/0.74 inference(binary_proxy_clausification,[],[f134])). 2.60/0.74 thf(f134,plain,( 2.60/0.74 ((((sK6 @ sK7 @ sK9) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ sK9)) = $false) | ~spl0_3), 2.60/0.74 inference(beta_eta_normalization,[],[f133])). 2.60/0.74 thf(f133,plain,( 2.60/0.74 (((^[Y0 : a]: (((sK6 @ sK7 @ Y0) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ Y0))) @ sK9) = $false) | ~spl0_3), 2.60/0.74 inference(sigma_clausification,[],[f132])). 2.60/0.74 thf(f132,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (((sK6 @ sK7 @ Y0) & (sK6 @ sK8 @ sK7)) => (sK6 @ sK8 @ Y0)))) = $false) | ~spl0_3), 2.60/0.74 inference(beta_eta_normalization,[],[f131])). 2.60/0.74 thf(f131,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK7 @ Y1) & (sK6 @ Y0 @ sK7)) => (sK6 @ Y0 @ Y1))))) @ sK8) = $false) | ~spl0_3), 2.60/0.74 inference(sigma_clausification,[],[f128])). 2.60/0.74 thf(f128,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ sK7 @ Y1) & (sK6 @ Y0 @ sK7)) => (sK6 @ Y0 @ Y1)))))) = $false) | ~spl0_3), 2.60/0.74 inference(beta_eta_normalization,[],[f126])). 2.60/0.74 thf(f126,plain,( 2.60/0.74 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))) @ sK7) = $false) | ~spl0_3), 2.60/0.74 inference(sigma_clausification,[],[f119])). 2.60/0.74 thf(f119,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))) = $false) | ~spl0_3), 2.60/0.74 inference(avatar_component_clause,[],[f118])). 2.60/0.74 thf(f118,plain,( 2.60/0.74 spl0_3 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))) = $false)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 2.60/0.74 thf(f187,plain,( 2.60/0.74 ((~ (sK6 @ sK7 @ sK9)) = $true) | ~spl0_3), 2.60/0.74 inference(boolean_simplification,[],[f186])). 2.60/0.74 thf(f186,plain,( 2.60/0.74 ((~ ($true & (sK6 @ sK7 @ sK9))) = $true) | ~spl0_3), 2.60/0.74 inference(superposition,[],[f146,f152])). 2.60/0.74 thf(f152,plain,( 2.60/0.74 ((sK6 @ sK8 @ sK7) = $true) | ~spl0_3), 2.60/0.74 inference(boolean_simplification,[],[f151])). 2.60/0.74 thf(f151,plain,( 2.60/0.74 (($true & (sK6 @ sK8 @ sK7)) = $true) | ~spl0_3), 2.60/0.74 inference(backward_demodulation,[],[f136,f150])). 2.60/0.74 thf(f146,plain,( 2.60/0.74 ( ! [X0 : a] : (((~ ((sK6 @ sK8 @ X0) & (sK6 @ X0 @ sK9))) = $true)) ) | ~spl0_3), 2.60/0.74 inference(boolean_simplification,[],[f141])). 2.60/0.74 thf(f141,plain,( 2.60/0.74 ( ! [X0 : a] : (((((sK6 @ sK8 @ X0) & (sK6 @ X0 @ sK9)) => $false) = $true)) ) | ~spl0_3), 2.60/0.74 inference(superposition,[],[f85,f138])). 2.60/0.74 thf(f138,plain,( 2.60/0.74 ((sK6 @ sK8 @ sK9) = $false) | ~spl0_3), 2.60/0.74 inference(boolean_simplification,[],[f137])). 2.60/0.74 thf(f137,plain,( 2.60/0.74 (($true => (sK6 @ sK8 @ sK9)) = $false) | ~spl0_3), 2.60/0.74 inference(backward_demodulation,[],[f134,f136])). 2.60/0.74 thf(f85,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK6 @ X1 @ X2) & (sK6 @ X2 @ X3)) => (sK6 @ X1 @ X3)) = $true)) )), 2.60/0.74 inference(beta_eta_normalization,[],[f84])). 2.60/0.74 thf(f84,plain,( 2.60/0.74 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X1 @ X2) & (sK6 @ X2 @ Y0)) => (sK6 @ X1 @ Y0))) @ X3) = $true)) )), 2.60/0.74 inference(pi_clausification,[],[f83])). 2.60/0.74 thf(f83,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X1 @ X2) & (sK6 @ X2 @ Y0)) => (sK6 @ X1 @ Y0)))) = $true)) )), 2.60/0.74 inference(beta_eta_normalization,[],[f82])). 2.60/0.74 thf(f82,plain,( 2.60/0.74 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ X1 @ Y1))))) @ X2) = $true)) )), 2.60/0.74 inference(pi_clausification,[],[f81])). 2.60/0.74 thf(f81,plain,( 2.60/0.74 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ X1 @ Y0) & (sK6 @ Y0 @ Y1)) => (sK6 @ X1 @ Y1)))))) = $true)) )), 2.60/0.74 inference(beta_eta_normalization,[],[f80])). 2.60/0.74 thf(f80,plain,( 2.60/0.74 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ Y2)) => (sK6 @ Y0 @ Y2))))))) @ X1) = $true)) )), 2.60/0.74 inference(pi_clausification,[],[f31])). 2.60/0.74 thf(f123,plain,( 2.60/0.74 spl0_3 | spl0_4 | ~spl0_2), 2.60/0.74 inference(avatar_split_clause,[],[f114,f58,f121,f118])). 2.60/0.74 thf(f58,plain,( 2.60/0.74 spl0_2 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5)))) = $true)), 2.60/0.74 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 2.60/0.74 thf(f114,plain,( 2.60/0.74 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))) = $false) | ~spl0_2), 2.60/0.74 inference(binary_proxy_clausification,[],[f104])). 2.60/0.74 thf(f104,plain,( 2.60/0.74 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))))) = $false) | ~spl0_2), 2.60/0.74 inference(not_proxy_clausification,[],[f77])). 2.60/0.74 thf(f77,plain,( 2.60/0.74 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2)))))))))) = $true) | ~spl0_2), 2.60/0.74 inference(boolean_simplification,[],[f74])). 2.60/0.74 thf(f74,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y0 @ Y2) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y2))))))))) => $false) = $true) | ~spl0_2), 2.60/0.74 inference(superposition,[],[f68,f24])). 2.60/0.74 thf(f24,plain,( 2.60/0.74 ((sK6 @ sK4 @ sK5) = $false)), 2.60/0.74 inference(binary_proxy_clausification,[],[f23])). 2.60/0.74 thf(f68,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK3 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK4 @ sK5)) = $true)) ) | ~spl0_2), 2.60/0.74 inference(beta_eta_normalization,[],[f67])). 2.60/0.74 thf(f67,plain,( 2.60/0.74 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5))) @ X1) = $true)) ) | ~spl0_2), 2.60/0.74 inference(pi_clausification,[],[f59])). 2.60/0.74 thf(f59,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5)))) = $true) | ~spl0_2), 2.60/0.74 inference(avatar_component_clause,[],[f58])). 2.60/0.74 thf(f60,plain,( 2.60/0.74 spl0_1 | spl0_2), 2.60/0.74 inference(avatar_split_clause,[],[f53,f58,f55])). 2.60/0.74 thf(f53,plain,( 2.60/0.74 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5)))) = $true) | (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false)), 2.60/0.74 inference(binary_proxy_clausification,[],[f44])). 2.60/0.74 thf(f44,plain,( 2.60/0.74 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y4 @ Y6)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y4 @ Y5) | (sK3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y0 @ Y1)))) & (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK3 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6))))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (sK3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y4) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y6 @ Y5))))))))) => (Y3 @ Y2 @ Y1))))))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK3 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y4) & (Y2 @ Y4 @ Y5)) => (Y2 @ Y3 @ Y5))))))))) => (Y2 @ Y1 @ Y0))))) => (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y3 @ Y4) | (sK3 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y1 @ Y0)))))))))) => (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK3 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK4 @ sK5))))) = $true)), 2.60/0.74 inference(not_proxy_clausification,[],[f19])). 2.60/0.74 % SZS output end Proof for theBenchmark 2.60/0.74 % (18829)------------------------------ 2.60/0.74 % (18829)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.60/0.74 % (18829)Termination reason: Refutation 2.60/0.74 2.60/0.74 % (18829)Memory used [KB]: 7419 2.60/0.74 % (18829)Time elapsed: 0.302 s 2.60/0.74 % (18829)Instructions burned: 541 (million) 2.60/0.74 % (18829)------------------------------ 2.60/0.74 % (18829)------------------------------ 2.60/0.74 % (18810)Success in time 0.389 s 2.60/0.74 % Vampire---4.8 exiting 2.60/0.74 EOF