0.01/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.01/0.12 % 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 0.12/0.33 % Computer : n027.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 300 0.12/0.33 % WCLimit : 300 0.12/0.33 % DateTime : Fri Jul 5 04:28:39 EDT 2024 0.12/0.33 % CPUTime : 0.19/0.35 This is a THF_ problem 0.19/0.36 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 0.19/0.37 % (29350)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) 0.19/0.37 % (29343)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (3000ds/96Mi) 0.19/0.37 % (29344)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (3000ds/36Mi) 0.19/0.37 % (29345)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (3000ds/34Mi) 0.19/0.37 % (29347)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (3000ds/17Mi) 0.19/0.37 % (29346)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) 0.19/0.37 % (29348)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) 0.19/0.37 % (29349)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi) 0.19/0.38 % (29349)Instruction limit reached! 0.19/0.38 % (29349)------------------------------ 0.19/0.38 % (29349)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (29349)Termination reason: Unknown 0.19/0.38 % (29349)Termination phase: Property scanning 0.19/0.38 0.19/0.38 % (29349)Memory used [KB]: 1023 0.19/0.38 % (29349)Time elapsed: 0.004 s 0.19/0.38 % (29349)Instructions burned: 4 (million) 0.19/0.38 % (29349)------------------------------ 0.19/0.38 % (29349)------------------------------ 0.19/0.38 % (29344)Refutation not found, incomplete strategy 0.19/0.38 % (29344)------------------------------ 0.19/0.38 % (29344)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (29344)Termination reason: Refutation not found, incomplete strategy 0.19/0.38 0.19/0.38 0.19/0.38 % (29344)Memory used [KB]: 5500 0.19/0.38 % (29344)Time elapsed: 0.009 s 0.19/0.38 % (29344)Instructions burned: 13 (million) 0.19/0.38 % (29344)------------------------------ 0.19/0.38 % (29344)------------------------------ 0.19/0.38 % (29347)Instruction limit reached! 0.19/0.38 % (29347)------------------------------ 0.19/0.38 % (29347)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (29347)Termination reason: Unknown 0.19/0.38 % (29347)Termination phase: Saturation 0.19/0.38 0.19/0.38 % (29347)Memory used [KB]: 5756 0.19/0.38 % (29347)Time elapsed: 0.011 s 0.19/0.38 % (29347)Instructions burned: 17 (million) 0.19/0.38 % (29347)------------------------------ 0.19/0.38 % (29347)------------------------------ 0.19/0.39 % (29345)Instruction limit reached! 0.19/0.39 % (29345)------------------------------ 0.19/0.39 % (29345)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.39 % (29345)Termination reason: Unknown 0.19/0.39 % (29345)Termination phase: Saturation 0.19/0.39 0.19/0.39 % (29345)Memory used [KB]: 5628 0.19/0.39 % (29345)Time elapsed: 0.019 s 0.19/0.39 % (29345)Instructions burned: 34 (million) 0.19/0.39 % (29345)------------------------------ 0.19/0.39 % (29345)------------------------------ 0.19/0.39 % (29351)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) 0.19/0.40 % (29352)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.19/0.40 % (29354)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) 0.19/0.40 % (29352)Instruction limit reached! 0.19/0.40 % (29352)------------------------------ 0.19/0.40 % (29352)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.40 % (29352)Termination reason: Unknown 0.19/0.40 % (29352)Termination phase: Saturation 0.19/0.40 0.19/0.40 % (29352)Memory used [KB]: 5500 0.19/0.40 % (29352)Time elapsed: 0.006 s 0.19/0.40 % (29352)Instructions burned: 8 (million) 0.19/0.40 % (29352)------------------------------ 0.19/0.40 % (29352)------------------------------ 0.19/0.40 % (29351)Instruction limit reached! 0.19/0.40 % (29351)------------------------------ 0.19/0.40 % (29351)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.40 % (29351)Termination reason: Unknown 0.19/0.40 % (29351)Termination phase: Saturation 0.19/0.40 0.19/0.40 % (29351)Memory used [KB]: 5628 0.19/0.40 % (29351)Time elapsed: 0.016 s 0.19/0.40 % (29351)Instructions burned: 22 (million) 0.19/0.40 % (29351)------------------------------ 0.19/0.40 % (29351)------------------------------ 0.19/0.41 % (29359)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) 0.19/0.41 % (29365)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) 0.19/0.42 % (29348)Instruction limit reached! 0.19/0.42 % (29348)------------------------------ 0.19/0.42 % (29348)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.42 % (29348)Termination reason: Unknown 0.19/0.42 % (29348)Termination phase: Saturation 0.19/0.42 0.19/0.42 % (29348)Memory used [KB]: 5884 0.19/0.42 % (29348)Time elapsed: 0.045 s 0.19/0.42 % (29348)Instructions burned: 75 (million) 0.19/0.42 % (29348)------------------------------ 0.19/0.42 % (29348)------------------------------ 0.19/0.42 % (29368)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) 0.19/0.42 % (29365)Instruction limit reached! 0.19/0.42 % (29365)------------------------------ 0.19/0.42 % (29365)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.42 % (29365)Termination reason: Unknown 0.19/0.42 % (29365)Termination phase: Saturation 0.19/0.42 0.19/0.42 % (29365)Memory used [KB]: 5500 0.19/0.42 % (29365)Time elapsed: 0.007 s 0.19/0.42 % (29365)Instructions burned: 9 (million) 0.19/0.42 % (29365)------------------------------ 0.19/0.42 % (29365)------------------------------ 0.19/0.42 % (29343)Instruction limit reached! 0.19/0.42 % (29343)------------------------------ 0.19/0.42 % (29343)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.42 % (29343)Termination reason: Unknown 0.19/0.42 % (29343)Termination phase: Saturation 0.19/0.42 0.19/0.42 % (29343)Memory used [KB]: 6012 0.19/0.42 % (29343)Time elapsed: 0.051 s 0.19/0.42 % (29343)Instructions burned: 97 (million) 0.19/0.42 % (29343)------------------------------ 0.19/0.42 % (29343)------------------------------ 0.21/0.43 % (29376)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) 0.21/0.43 % (29378)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.21/0.44 % (29381)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.21/0.44 % (29381)Instruction limit reached! 0.21/0.44 % (29381)------------------------------ 0.21/0.44 % (29381)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.44 % (29381)Termination reason: Unknown 0.21/0.44 % (29381)Termination phase: Saturation 0.21/0.44 0.21/0.44 % (29381)Memory used [KB]: 5500 0.21/0.44 % (29381)Time elapsed: 0.009 s 0.21/0.44 % (29381)Instructions burned: 14 (million) 0.21/0.44 % (29381)------------------------------ 0.21/0.44 % (29381)------------------------------ 0.21/0.45 % (29359)Instruction limit reached! 0.21/0.45 % (29359)------------------------------ 0.21/0.45 % (29359)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.45 % (29359)Termination reason: Unknown 0.21/0.45 % (29359)Termination phase: Saturation 0.21/0.45 0.21/0.45 % (29359)Memory used [KB]: 5628 0.21/0.45 % (29359)Time elapsed: 0.047 s 0.21/0.45 % (29359)Instructions burned: 71 (million) 0.21/0.45 % (29359)------------------------------ 0.21/0.45 % (29359)------------------------------ 0.21/0.46 % (29394)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) 0.21/0.46 % (29394)Instruction limit reached! 0.21/0.46 % (29394)------------------------------ 0.21/0.46 % (29394)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.46 % (29394)Termination reason: Unknown 0.21/0.46 % (29394)Termination phase: shuffling 0.21/0.46 0.21/0.46 % (29394)Memory used [KB]: 1023 0.21/0.46 % (29394)Time elapsed: 0.003 s 0.21/0.46 % (29394)Instructions burned: 2 (million) 0.21/0.46 % (29394)------------------------------ 0.21/0.46 % (29394)------------------------------ 0.21/0.46 % (29378)Instruction limit reached! 0.21/0.46 % (29378)------------------------------ 0.21/0.46 % (29378)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.46 % (29378)Termination reason: Unknown 0.21/0.46 % (29378)Termination phase: Saturation 0.21/0.46 0.21/0.46 % (29378)Memory used [KB]: 5756 0.21/0.46 % (29378)Time elapsed: 0.033 s 0.21/0.46 % (29378)Instructions burned: 62 (million) 0.21/0.46 % (29378)------------------------------ 0.21/0.46 % (29378)------------------------------ 0.21/0.47 % (29400)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi) 0.21/0.48 % (29405)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) 0.21/0.48 % (29405)Instruction limit reached! 0.21/0.48 % (29405)------------------------------ 0.21/0.48 % (29405)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.48 % (29405)Termination reason: Unknown 0.21/0.48 % (29405)Termination phase: Saturation 0.21/0.48 0.21/0.48 % (29405)Memory used [KB]: 5500 0.21/0.48 % (29405)Time elapsed: 0.007 s 0.21/0.48 % (29405)Instructions burned: 11 (million) 0.21/0.48 % (29405)------------------------------ 0.21/0.48 % (29405)------------------------------ 0.21/0.48 % (29406)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) 0.21/0.48 % (29406)Refutation not found, incomplete strategy 0.21/0.48 % (29406)------------------------------ 0.21/0.48 % (29406)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.48 % (29406)Termination reason: Refutation not found, incomplete strategy 0.21/0.48 0.21/0.48 0.21/0.48 % (29406)Memory used [KB]: 5500 0.21/0.48 % (29406)Time elapsed: 0.027 s 0.21/0.48 % (29406)Instructions burned: 7 (million) 0.21/0.48 % (29406)------------------------------ 0.21/0.48 % (29406)------------------------------ 0.21/0.49 % (29413)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) 0.21/0.49 % (29376)Instruction limit reached! 0.21/0.49 % (29376)------------------------------ 0.21/0.49 % (29376)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.49 % (29376)Termination reason: Unknown 0.21/0.49 % (29376)Termination phase: Saturation 0.21/0.49 0.21/0.49 % (29376)Memory used [KB]: 6012 0.21/0.49 % (29376)Time elapsed: 0.065 s 0.21/0.49 % (29376)Instructions burned: 128 (million) 0.21/0.49 % (29376)------------------------------ 0.21/0.49 % (29376)------------------------------ 0.21/0.50 % (29417)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) 0.21/0.50 % (29413)Instruction limit reached! 0.21/0.50 % (29413)------------------------------ 0.21/0.50 % (29413)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.50 % (29413)Termination reason: Unknown 0.21/0.50 % (29413)Termination phase: Saturation 0.21/0.50 0.21/0.50 % (29413)Memory used [KB]: 5500 0.21/0.50 % (29413)Time elapsed: 0.030 s 0.21/0.50 % (29413)Instructions burned: 27 (million) 0.21/0.50 % (29413)------------------------------ 0.21/0.50 % (29413)------------------------------ 0.21/0.50 % (29422)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) 0.21/0.51 % (29425)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) 0.21/0.51 % (29425)Instruction limit reached! 0.21/0.51 % (29425)------------------------------ 0.21/0.51 % (29425)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.51 % (29425)Termination reason: Unknown 0.21/0.51 % (29425)Termination phase: Saturation 0.21/0.51 0.21/0.51 % (29425)Memory used [KB]: 5500 0.21/0.51 % (29425)Time elapsed: 0.003 s 0.21/0.51 % (29425)Instructions burned: 5 (million) 0.21/0.51 % (29425)------------------------------ 0.21/0.51 % (29425)------------------------------ 0.21/0.51 % (29417)Instruction limit reached! 0.21/0.51 % (29417)------------------------------ 0.21/0.51 % (29417)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.51 % (29417)Termination reason: Unknown 0.21/0.51 % (29417)Termination phase: Saturation 0.21/0.51 0.21/0.51 % (29417)Memory used [KB]: 1279 0.21/0.51 % (29417)Time elapsed: 0.017 s 0.21/0.51 % (29417)Instructions burned: 57 (million) 0.21/0.51 % (29417)------------------------------ 0.21/0.51 % (29417)------------------------------ 0.21/0.52 % (29428)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) 0.21/0.52 % (29430)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) 0.21/0.52 % (29428)Instruction limit reached! 0.21/0.52 % (29428)------------------------------ 0.21/0.52 % (29428)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.52 % (29428)Termination reason: Unknown 0.21/0.52 % (29428)Termination phase: Saturation 0.21/0.52 0.21/0.52 % (29428)Memory used [KB]: 5500 0.21/0.52 % (29428)Time elapsed: 0.007 s 0.21/0.52 % (29428)Instructions burned: 21 (million) 0.21/0.52 % (29428)------------------------------ 0.21/0.52 % (29428)------------------------------ 0.21/0.53 % (29437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on theBenchmark for (2998ds/191Mi) 0.21/0.53 % (29430)Instruction limit reached! 0.21/0.53 % (29430)------------------------------ 0.21/0.53 % (29430)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.53 % (29430)Termination reason: Unknown 0.21/0.53 % (29430)Termination phase: Saturation 0.21/0.53 0.21/0.53 % (29430)Memory used [KB]: 1151 0.21/0.53 % (29430)Time elapsed: 0.013 s 0.21/0.53 % (29430)Instructions burned: 44 (million) 0.21/0.53 % (29430)------------------------------ 0.21/0.53 % (29430)------------------------------ 0.21/0.54 % (29447)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) 0.21/0.55 % (29346)Instruction limit reached! 0.21/0.55 % (29346)------------------------------ 0.21/0.55 % (29346)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.55 % (29346)Termination reason: Unknown 0.21/0.55 % (29346)Termination phase: Saturation 0.21/0.55 0.21/0.55 % (29346)Memory used [KB]: 7419 0.21/0.55 % (29346)Time elapsed: 0.175 s 0.21/0.55 % (29346)Instructions burned: 387 (million) 0.21/0.55 % (29346)------------------------------ 0.21/0.55 % (29346)------------------------------ 0.21/0.55 % (29454)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) 0.21/0.56 % (29400)First to succeed. 0.21/0.56 % (29447)Instruction limit reached! 0.21/0.56 % (29447)------------------------------ 0.21/0.56 % (29447)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.21/0.56 % (29447)Termination reason: Unknown 0.21/0.56 % (29447)Termination phase: Saturation 0.21/0.56 0.21/0.56 % (29447)Memory used [KB]: 5884 0.21/0.56 % (29447)Time elapsed: 0.020 s 0.21/0.56 % (29447)Instructions burned: 63 (million) 0.21/0.56 % (29447)------------------------------ 0.21/0.56 % (29447)------------------------------ 1.75/0.57 % (29468)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi) 1.75/0.57 % (29468)Instruction limit reached! 1.75/0.57 % (29468)------------------------------ 1.75/0.57 % (29468)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.75/0.57 % (29468)Termination reason: Unknown 1.75/0.57 % (29468)Termination phase: shuffling 1.75/0.57 1.75/0.57 % (29468)Memory used [KB]: 1023 1.75/0.57 % (29468)Time elapsed: 0.002 s 1.75/0.57 % (29468)Instructions burned: 3 (million) 1.75/0.57 % (29468)------------------------------ 1.75/0.57 % (29468)------------------------------ 1.75/0.57 % (29400)Refutation found. Thanks to Tanya! 1.75/0.57 % SZS status Theorem for theBenchmark 1.75/0.57 % SZS output start Proof for theBenchmark 1.75/0.57 thf(type_def_5, type, a: $tType). 1.75/0.57 thf(func_def_0, type, a: $tType). 1.75/0.57 thf(func_def_20, type, ph1: !>[X0: $tType]:(X0)). 1.75/0.57 thf(func_def_21, type, sK2: a > a > $o). 1.75/0.57 thf(func_def_22, type, sK3: a > a > $o). 1.75/0.57 thf(func_def_23, type, sK4: a). 1.75/0.57 thf(func_def_24, type, sK5: a). 1.75/0.57 thf(func_def_25, type, sK6: a > a > $o). 1.75/0.57 thf(func_def_26, type, sK7: a). 1.75/0.57 thf(func_def_27, type, sK8: a). 1.75/0.57 thf(func_def_28, type, sK9: a > a > $o). 1.75/0.57 thf(func_def_29, type, sK10: a > a > $o). 1.75/0.57 thf(func_def_30, type, sK11: a > a > $o). 1.75/0.57 thf(func_def_31, type, sK12: a). 1.75/0.57 thf(func_def_32, type, sK13: a). 1.75/0.57 thf(func_def_33, type, sK14: a). 1.75/0.57 thf(func_def_34, type, sK15: a > a > $o). 1.75/0.57 thf(func_def_35, type, sK16: a). 1.75/0.57 thf(func_def_36, type, sK17: a). 1.75/0.57 thf(func_def_37, type, sK18: a). 1.75/0.57 thf(func_def_38, type, sK19: a). 1.75/0.57 thf(func_def_39, type, sK20: a). 1.75/0.57 thf(func_def_40, type, sK21: a). 1.75/0.57 thf(func_def_41, type, sK22: a). 1.75/0.57 thf(func_def_42, type, sK23: a). 1.75/0.57 thf(func_def_43, type, sK24: a). 1.75/0.57 thf(func_def_44, type, sK25: a). 1.75/0.57 thf(func_def_45, type, sK26: a). 1.75/0.57 thf(func_def_46, type, sK27: a). 1.75/0.57 thf(func_def_47, type, sK28: a). 1.75/0.57 thf(func_def_48, type, sK29: a). 1.75/0.57 thf(func_def_49, type, sK30: a). 1.75/0.57 thf(func_def_50, type, sK31: a). 1.75/0.57 thf(func_def_51, type, sK32: a). 1.75/0.57 thf(func_def_52, type, sK33: a). 1.75/0.57 thf(f972,plain,( 1.75/0.57 $false), 1.75/0.57 inference(avatar_sat_refutation,[],[f27,f34,f60,f63,f94,f226,f396,f480,f569,f642,f707,f766,f806,f851,f901,f935,f971])). 1.75/0.57 thf(f971,plain,( 1.75/0.57 ~spl0_4 | ~spl0_20), 1.75/0.57 inference(avatar_contradiction_clause,[],[f970])). 1.75/0.57 thf(f970,plain,( 1.75/0.57 $false | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(trivial_inequality_removal,[],[f969])). 1.75/0.57 thf(f969,plain,( 1.75/0.57 ($false = $true) | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(boolean_simplification,[],[f968])). 1.75/0.57 thf(f968,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(boolean_simplification,[],[f967])). 1.75/0.57 thf(f967,plain,( 1.75/0.57 ((~ ($true | (sK3 @ sK33 @ sK32))) = $true) | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(forward_demodulation,[],[f963,f952])). 1.75/0.57 thf(f952,plain,( 1.75/0.57 ((sK2 @ sK33 @ sK32) = $true) | ~spl0_20), 1.75/0.57 inference(binary_proxy_clausification,[],[f950])). 1.75/0.57 thf(f950,plain,( 1.75/0.57 ($false = ((sK2 @ sK33 @ sK32) => (sK15 @ sK33 @ sK32))) | ~spl0_20), 1.75/0.57 inference(beta_eta_normalization,[],[f949])). 1.75/0.57 thf(f949,plain,( 1.75/0.57 (((^[Y0 : a]: ((sK2 @ Y0 @ sK32) => (sK15 @ Y0 @ sK32))) @ sK33) = $false) | ~spl0_20), 1.75/0.57 inference(sigma_clausification,[],[f946])). 1.75/0.57 thf(f946,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ sK32) => (sK15 @ Y0 @ sK32)))) = $false) | ~spl0_20), 1.75/0.57 inference(beta_eta_normalization,[],[f944])). 1.75/0.57 thf(f944,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0))))) @ sK32)) | ~spl0_20), 1.75/0.57 inference(sigma_clausification,[],[f900])). 1.75/0.57 thf(f900,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0))))))) | ~spl0_20), 1.75/0.57 inference(avatar_component_clause,[],[f899])). 1.75/0.57 thf(f899,plain,( 1.75/0.57 spl0_20 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0)))))))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])). 1.75/0.57 thf(f963,plain,( 1.75/0.57 ((~ ((sK2 @ sK33 @ sK32) | (sK3 @ sK33 @ sK32))) = $true) | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(boolean_simplification,[],[f960])). 1.75/0.57 thf(f960,plain,( 1.75/0.57 ($true = (((sK2 @ sK33 @ sK32) | (sK3 @ sK33 @ sK32)) => $false)) | (~spl0_4 | ~spl0_20)), 1.75/0.57 inference(superposition,[],[f507,f951])). 1.75/0.57 thf(f951,plain,( 1.75/0.57 ($false = (sK15 @ sK33 @ sK32)) | ~spl0_20), 1.75/0.57 inference(binary_proxy_clausification,[],[f950])). 1.75/0.57 thf(f507,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : (((((sK2 @ X2 @ X1) | (sK3 @ X2 @ X1)) => (sK15 @ X2 @ X1)) = $true)) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f506])). 1.75/0.57 thf(f506,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK15 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f503])). 1.75/0.57 thf(f503,plain,( 1.75/0.57 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ X1) | (sK3 @ Y0 @ X1)) => (sK15 @ Y0 @ X1)))) = $true)) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f502])). 1.75/0.57 thf(f502,plain,( 1.75/0.57 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0))))) @ X1) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f499])). 1.75/0.57 thf(f499,plain,( 1.75/0.57 ($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK15 @ Y1 @ Y0))))))) | ~spl0_4), 1.75/0.57 inference(binary_proxy_clausification,[],[f488])). 1.75/0.57 thf(f488,plain,( 1.75/0.57 (((!! @ 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 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ Y2 @ Y0))))))))) = $true) | ~spl0_4), 1.75/0.57 inference(binary_proxy_clausification,[],[f485])). 1.75/0.57 thf(f485,plain,( 1.75/0.57 ($false = (((!! @ 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 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ Y2 @ Y0))))))))) => (sK15 @ sK4 @ sK5))) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f484])). 1.75/0.57 thf(f484,plain,( 1.75/0.57 (((^[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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5))) @ sK15) = $false) | ~spl0_4), 1.75/0.57 inference(sigma_clausification,[],[f33])). 1.75/0.57 thf(f33,plain,( 1.75/0.57 ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ~spl0_4), 1.75/0.57 inference(avatar_component_clause,[],[f32])). 1.75/0.57 thf(f32,plain,( 1.75/0.57 spl0_4 <=> ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 1.75/0.57 thf(f935,plain,( 1.75/0.57 ~spl0_4 | ~spl0_19), 1.75/0.57 inference(avatar_contradiction_clause,[],[f934])). 1.75/0.57 thf(f934,plain,( 1.75/0.57 $false | (~spl0_4 | ~spl0_19)), 1.75/0.57 inference(trivial_inequality_removal,[],[f930])). 1.75/0.57 thf(f930,plain,( 1.75/0.57 ($false = $true) | (~spl0_4 | ~spl0_19)), 1.75/0.57 inference(superposition,[],[f927,f517])). 1.75/0.57 thf(f517,plain,( 1.75/0.57 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK15 @ X3 @ X2) & (sK15 @ X2 @ X1)) => (sK15 @ X3 @ X1)) = $true)) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f516])). 1.75/0.57 thf(f516,plain,( 1.75/0.57 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK15 @ Y0 @ X2) & (sK15 @ X2 @ X1)) => (sK15 @ Y0 @ X1))) @ X3) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f509])). 1.75/0.57 thf(f509,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK15 @ Y0 @ X2) & (sK15 @ X2 @ X1)) => (sK15 @ Y0 @ X1)))) = $true)) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f508])). 1.75/0.57 thf(f508,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ Y0) & (sK15 @ Y0 @ X1)) => (sK15 @ Y1 @ X1))))) @ X2) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f505])). 1.75/0.57 thf(f505,plain,( 1.75/0.57 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y1 @ Y0) & (sK15 @ Y0 @ X1)) => (sK15 @ Y1 @ X1)))))))) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f504])). 1.75/0.57 thf(f504,plain,( 1.75/0.57 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ Y2 @ Y0))))))) @ X1) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f501])). 1.75/0.57 thf(f501,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ Y2 @ Y0)))))))) = $true) | ~spl0_4), 1.75/0.57 inference(boolean_simplification,[],[f500])). 1.75/0.57 thf(f500,plain,( 1.75/0.57 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y2 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ Y2 @ Y0))))))))) = $true) | ~spl0_4), 1.75/0.57 inference(backward_demodulation,[],[f488,f499])). 1.75/0.57 thf(f927,plain,( 1.75/0.57 ((((sK15 @ sK29 @ sK31) & (sK15 @ sK31 @ sK30)) => (sK15 @ sK29 @ sK30)) = $false) | ~spl0_19), 1.75/0.57 inference(beta_eta_normalization,[],[f926])). 1.75/0.57 thf(f926,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (((sK15 @ sK29 @ Y0) & (sK15 @ Y0 @ sK30)) => (sK15 @ sK29 @ sK30))) @ sK31)) | ~spl0_19), 1.75/0.57 inference(sigma_clausification,[],[f918])). 1.75/0.57 thf(f918,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (((sK15 @ sK29 @ Y0) & (sK15 @ Y0 @ sK30)) => (sK15 @ sK29 @ sK30)))) = $false) | ~spl0_19), 1.75/0.57 inference(beta_eta_normalization,[],[f917])). 1.75/0.57 thf(f917,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ sK29 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ sK29 @ Y0))))) @ sK30) = $false) | ~spl0_19), 1.75/0.57 inference(sigma_clausification,[],[f911])). 1.75/0.57 thf(f911,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ sK29 @ Y1) & (sK15 @ Y1 @ Y0)) => (sK15 @ sK29 @ Y0)))))) = $false) | ~spl0_19), 1.75/0.57 inference(beta_eta_normalization,[],[f909])). 1.75/0.57 thf(f909,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1))))))) @ sK29) = $false) | ~spl0_19), 1.75/0.57 inference(sigma_clausification,[],[f897])). 1.75/0.57 thf(f897,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) = $false) | ~spl0_19), 1.75/0.57 inference(avatar_component_clause,[],[f896])). 1.75/0.57 thf(f896,plain,( 1.75/0.57 spl0_19 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])). 1.75/0.57 thf(f901,plain,( 1.75/0.57 spl0_19 | spl0_20 | ~spl0_10 | ~spl0_12), 1.75/0.57 inference(avatar_split_clause,[],[f892,f705,f567,f899,f896])). 1.75/0.57 thf(f567,plain,( 1.75/0.57 spl0_10 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0)))))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])). 1.75/0.57 thf(f705,plain,( 1.75/0.57 spl0_12 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) = $true)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])). 1.75/0.57 thf(f892,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0))))))) | (~spl0_10 | ~spl0_12)), 1.75/0.57 inference(binary_proxy_clausification,[],[f884])). 1.75/0.57 thf(f884,plain,( 1.75/0.57 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0)))))))) | (~spl0_10 | ~spl0_12)), 1.75/0.57 inference(not_proxy_clausification,[],[f877])). 1.75/0.57 thf(f877,plain,( 1.75/0.57 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0)))))))) = $true) | (~spl0_10 | ~spl0_12)), 1.75/0.57 inference(boolean_simplification,[],[f874])). 1.75/0.57 thf(f874,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y2) & (sK15 @ Y2 @ Y1)) => (sK15 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK15 @ Y1 @ Y0))))))) => $false) = $true) | (~spl0_10 | ~spl0_12)), 1.75/0.57 inference(superposition,[],[f865,f655])). 1.75/0.57 thf(f655,plain,( 1.75/0.57 ((sK15 @ sK20 @ sK19) = $false) | ~spl0_10), 1.75/0.57 inference(boolean_simplification,[],[f654])). 1.75/0.57 thf(f654,plain,( 1.75/0.57 ($false = ($true => (sK15 @ sK20 @ sK19))) | ~spl0_10), 1.75/0.57 inference(backward_demodulation,[],[f651,f653])). 1.75/0.57 thf(f653,plain,( 1.75/0.57 ($true = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19)))))) | ~spl0_10), 1.75/0.57 inference(binary_proxy_clausification,[],[f651])). 1.75/0.57 thf(f651,plain,( 1.75/0.57 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19))))) => (sK15 @ sK20 @ sK19)) = $false) | ~spl0_10), 1.75/0.57 inference(beta_eta_normalization,[],[f650])). 1.75/0.57 thf(f650,plain,( 1.75/0.57 (((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK19)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK19))))) => (sK15 @ Y0 @ sK19))) @ sK20) = $false) | ~spl0_10), 1.75/0.57 inference(sigma_clausification,[],[f647])). 1.75/0.57 thf(f647,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK19)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK19))))) => (sK15 @ Y0 @ sK19)))) = $false) | ~spl0_10), 1.75/0.57 inference(beta_eta_normalization,[],[f645])). 1.75/0.57 thf(f645,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0))))) @ sK19)) | ~spl0_10), 1.75/0.57 inference(sigma_clausification,[],[f568])). 1.75/0.57 thf(f568,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0)))))) = $false) | ~spl0_10), 1.75/0.57 inference(avatar_component_clause,[],[f567])). 1.75/0.57 thf(f865,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y2) & (X1 @ Y2 @ Y1)) => (X1 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK20 @ sK19)) = $true)) ) | ~spl0_12), 1.75/0.57 inference(beta_eta_normalization,[],[f864])). 1.75/0.57 thf(f864,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (($true = ((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19))) @ X1))) ) | ~spl0_12), 1.75/0.57 inference(pi_clausification,[],[f706])). 1.75/0.57 thf(f706,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) = $true) | ~spl0_12), 1.75/0.57 inference(avatar_component_clause,[],[f705])). 1.75/0.57 thf(f851,plain,( 1.75/0.57 ~spl0_4 | ~spl0_16), 1.75/0.57 inference(avatar_contradiction_clause,[],[f850])). 1.75/0.57 thf(f850,plain,( 1.75/0.57 $false | (~spl0_4 | ~spl0_16)), 1.75/0.57 inference(trivial_inequality_removal,[],[f847])). 1.75/0.57 thf(f847,plain,( 1.75/0.57 ($false = $true) | (~spl0_4 | ~spl0_16)), 1.75/0.57 inference(superposition,[],[f517,f833])). 1.75/0.57 thf(f833,plain,( 1.75/0.57 ((((sK15 @ sK26 @ sK27) & (sK15 @ sK27 @ sK28)) => (sK15 @ sK26 @ sK28)) = $false) | ~spl0_16), 1.75/0.57 inference(beta_eta_normalization,[],[f832])). 1.75/0.57 thf(f832,plain,( 1.75/0.57 (((^[Y0 : a]: (((sK15 @ sK26 @ sK27) & (sK15 @ sK27 @ Y0)) => (sK15 @ sK26 @ Y0))) @ sK28) = $false) | ~spl0_16), 1.75/0.57 inference(sigma_clausification,[],[f823])). 1.75/0.57 thf(f823,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (((sK15 @ sK26 @ sK27) & (sK15 @ sK27 @ Y0)) => (sK15 @ sK26 @ Y0))))) | ~spl0_16), 1.75/0.57 inference(beta_eta_normalization,[],[f822])). 1.75/0.57 thf(f822,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ sK26 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ sK26 @ Y1))))) @ sK27)) | ~spl0_16), 1.75/0.57 inference(sigma_clausification,[],[f811])). 1.75/0.57 thf(f811,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ sK26 @ Y0) & (sK15 @ Y0 @ Y1)) => (sK15 @ sK26 @ Y1)))))) = $false) | ~spl0_16), 1.75/0.57 inference(beta_eta_normalization,[],[f809])). 1.75/0.57 thf(f809,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2))))))) @ sK26) = $false) | ~spl0_16), 1.75/0.57 inference(sigma_clausification,[],[f765])). 1.75/0.57 thf(f765,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) = $false) | ~spl0_16), 1.75/0.57 inference(avatar_component_clause,[],[f764])). 1.75/0.57 thf(f764,plain,( 1.75/0.57 spl0_16 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_16])])). 1.75/0.57 thf(f806,plain,( 1.75/0.57 ~spl0_4 | ~spl0_15), 1.75/0.57 inference(avatar_contradiction_clause,[],[f805])). 1.75/0.57 thf(f805,plain,( 1.75/0.57 $false | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(trivial_inequality_removal,[],[f804])). 1.75/0.57 thf(f804,plain,( 1.75/0.57 ($false = $true) | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(boolean_simplification,[],[f803])). 1.75/0.57 thf(f803,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(boolean_simplification,[],[f802])). 1.75/0.57 thf(f802,plain,( 1.75/0.57 ((~ ((sK2 @ sK24 @ sK25) | $true)) = $true) | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(forward_demodulation,[],[f801,f787])). 1.75/0.57 thf(f787,plain,( 1.75/0.57 ((sK3 @ sK24 @ sK25) = $true) | ~spl0_15), 1.75/0.57 inference(binary_proxy_clausification,[],[f782])). 1.75/0.57 thf(f782,plain,( 1.75/0.57 (((sK3 @ sK24 @ sK25) => (sK15 @ sK24 @ sK25)) = $false) | ~spl0_15), 1.75/0.57 inference(beta_eta_normalization,[],[f781])). 1.75/0.57 thf(f781,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: ((sK3 @ sK24 @ Y0) => (sK15 @ sK24 @ Y0))) @ sK25)) | ~spl0_15), 1.75/0.57 inference(sigma_clausification,[],[f777])). 1.75/0.57 thf(f777,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: ((sK3 @ sK24 @ Y0) => (sK15 @ sK24 @ Y0))))) | ~spl0_15), 1.75/0.57 inference(beta_eta_normalization,[],[f773])). 1.75/0.57 thf(f773,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1))))) @ sK24)) | ~spl0_15), 1.75/0.57 inference(sigma_clausification,[],[f762])). 1.75/0.57 thf(f762,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1))))))) | ~spl0_15), 1.75/0.57 inference(avatar_component_clause,[],[f761])). 1.75/0.57 thf(f761,plain,( 1.75/0.57 spl0_15 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1)))))))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_15])])). 1.75/0.57 thf(f801,plain,( 1.75/0.57 ($true = (~ ((sK2 @ sK24 @ sK25) | (sK3 @ sK24 @ sK25)))) | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(boolean_simplification,[],[f795])). 1.75/0.57 thf(f795,plain,( 1.75/0.57 ((((sK2 @ sK24 @ sK25) | (sK3 @ sK24 @ sK25)) => $false) = $true) | (~spl0_4 | ~spl0_15)), 1.75/0.57 inference(superposition,[],[f507,f786])). 1.75/0.57 thf(f786,plain,( 1.75/0.57 ((sK15 @ sK24 @ sK25) = $false) | ~spl0_15), 1.75/0.57 inference(binary_proxy_clausification,[],[f782])). 1.75/0.57 thf(f766,plain,( 1.75/0.57 spl0_15 | spl0_16 | ~spl0_10 | ~spl0_11), 1.75/0.57 inference(avatar_split_clause,[],[f757,f702,f567,f764,f761])). 1.75/0.57 thf(f702,plain,( 1.75/0.57 spl0_11 <=> ((!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19)))) = $true)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])). 1.75/0.57 thf(f757,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1))))))) | (~spl0_10 | ~spl0_11)), 1.75/0.57 inference(binary_proxy_clausification,[],[f752])). 1.75/0.57 thf(f752,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1))))))) = $false) | (~spl0_10 | ~spl0_11)), 1.75/0.57 inference(not_proxy_clausification,[],[f722])). 1.75/0.57 thf(f722,plain,( 1.75/0.57 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1)))))))) = $true) | (~spl0_10 | ~spl0_11)), 1.75/0.57 inference(boolean_simplification,[],[f717])). 1.75/0.57 thf(f717,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ Y1 @ Y2)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK15 @ Y0 @ Y1))))))) => $false) = $true) | (~spl0_10 | ~spl0_11)), 1.75/0.57 inference(superposition,[],[f715,f655])). 1.75/0.57 thf(f715,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y0 @ Y1) & (X1 @ Y1 @ Y2)) => (X1 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))) => (X1 @ sK20 @ sK19)) = $true)) ) | ~spl0_11), 1.75/0.57 inference(beta_eta_normalization,[],[f714])). 1.75/0.57 thf(f714,plain,( 1.75/0.57 ( ! [X1 : 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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19))) @ X1) = $true)) ) | ~spl0_11), 1.75/0.57 inference(pi_clausification,[],[f703])). 1.75/0.57 thf(f703,plain,( 1.75/0.57 ((!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19)))) = $true) | ~spl0_11), 1.75/0.57 inference(avatar_component_clause,[],[f702])). 1.75/0.57 thf(f707,plain,( 1.75/0.57 spl0_11 | spl0_12 | ~spl0_10), 1.75/0.57 inference(avatar_split_clause,[],[f700,f567,f705,f702])). 1.75/0.57 thf(f700,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK20 @ sK19)))) = $true) | ((!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK20 @ sK19)))) = $true) | ~spl0_10), 1.75/0.57 inference(binary_proxy_clausification,[],[f653])). 1.75/0.57 thf(f642,plain,( 1.75/0.57 ~spl0_4 | ~spl0_9), 1.75/0.57 inference(avatar_contradiction_clause,[],[f641])). 1.75/0.57 thf(f641,plain,( 1.75/0.57 $false | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(trivial_inequality_removal,[],[f640])). 1.75/0.57 thf(f640,plain,( 1.75/0.57 ($false = $true) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(boolean_simplification,[],[f639])). 1.75/0.57 thf(f639,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(forward_demodulation,[],[f636,f617])). 1.75/0.57 thf(f617,plain,( 1.75/0.57 ($true = (sK15 @ sK17 @ sK18)) | ~spl0_9), 1.75/0.57 inference(binary_proxy_clausification,[],[f603])). 1.75/0.57 thf(f603,plain,( 1.75/0.57 (((sK15 @ sK17 @ sK18) & (sK15 @ sK16 @ sK17)) = $true) | ~spl0_9), 1.75/0.57 inference(binary_proxy_clausification,[],[f595])). 1.75/0.57 thf(f595,plain,( 1.75/0.57 ((((sK15 @ sK17 @ sK18) & (sK15 @ sK16 @ sK17)) => (sK15 @ sK16 @ sK18)) = $false) | ~spl0_9), 1.75/0.57 inference(beta_eta_normalization,[],[f594])). 1.75/0.57 thf(f594,plain,( 1.75/0.57 (((^[Y0 : a]: (((sK15 @ sK17 @ Y0) & (sK15 @ sK16 @ sK17)) => (sK15 @ sK16 @ Y0))) @ sK18) = $false) | ~spl0_9), 1.75/0.57 inference(sigma_clausification,[],[f587])). 1.75/0.57 thf(f587,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (((sK15 @ sK17 @ Y0) & (sK15 @ sK16 @ sK17)) => (sK15 @ sK16 @ Y0)))) = $false) | ~spl0_9), 1.75/0.57 inference(beta_eta_normalization,[],[f586])). 1.75/0.57 thf(f586,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ sK16 @ Y0)) => (sK15 @ sK16 @ Y1))))) @ sK17)) | ~spl0_9), 1.75/0.57 inference(sigma_clausification,[],[f579])). 1.75/0.57 thf(f579,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK15 @ Y0 @ Y1) & (sK15 @ sK16 @ Y0)) => (sK15 @ sK16 @ Y1))))))) | ~spl0_9), 1.75/0.57 inference(beta_eta_normalization,[],[f575])). 1.75/0.57 thf(f575,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))) @ sK16)) | ~spl0_9), 1.75/0.57 inference(sigma_clausification,[],[f565])). 1.75/0.57 thf(f565,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))))) | ~spl0_9), 1.75/0.57 inference(avatar_component_clause,[],[f564])). 1.75/0.57 thf(f564,plain,( 1.75/0.57 spl0_9 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])). 1.75/0.57 thf(f636,plain,( 1.75/0.57 ($true = (~ (sK15 @ sK17 @ sK18))) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(boolean_simplification,[],[f630])). 1.75/0.57 thf(f630,plain,( 1.75/0.57 ((~ ($true & (sK15 @ sK17 @ sK18))) = $true) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(superposition,[],[f614,f619])). 1.75/0.57 thf(f619,plain,( 1.75/0.57 ((sK15 @ sK16 @ sK17) = $true) | ~spl0_9), 1.75/0.57 inference(boolean_simplification,[],[f618])). 1.75/0.57 thf(f618,plain,( 1.75/0.57 (($true & (sK15 @ sK16 @ sK17)) = $true) | ~spl0_9), 1.75/0.57 inference(backward_demodulation,[],[f603,f617])). 1.75/0.57 thf(f614,plain,( 1.75/0.57 ( ! [X0 : a] : (((~ ((sK15 @ sK16 @ X0) & (sK15 @ X0 @ sK18))) = $true)) ) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(boolean_simplification,[],[f608])). 1.75/0.57 thf(f608,plain,( 1.75/0.57 ( ! [X0 : a] : (((((sK15 @ sK16 @ X0) & (sK15 @ X0 @ sK18)) => $false) = $true)) ) | (~spl0_4 | ~spl0_9)), 1.75/0.57 inference(superposition,[],[f517,f605])). 1.75/0.57 thf(f605,plain,( 1.75/0.57 ($false = (sK15 @ sK16 @ sK18)) | ~spl0_9), 1.75/0.57 inference(boolean_simplification,[],[f604])). 1.75/0.57 thf(f604,plain,( 1.75/0.57 (($true => (sK15 @ sK16 @ sK18)) = $false) | ~spl0_9), 1.75/0.57 inference(backward_demodulation,[],[f595,f603])). 1.75/0.57 thf(f569,plain,( 1.75/0.57 spl0_9 | spl0_10 | ~spl0_4), 1.75/0.57 inference(avatar_split_clause,[],[f560,f32,f567,f564])). 1.75/0.57 thf(f560,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0)))))) = $false) | ~spl0_4), 1.75/0.57 inference(binary_proxy_clausification,[],[f554])). 1.75/0.57 thf(f554,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0))))))) = $false) | ~spl0_4), 1.75/0.57 inference(not_proxy_clausification,[],[f497])). 1.75/0.57 thf(f497,plain,( 1.75/0.57 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0)))))))) = $true) | ~spl0_4), 1.75/0.57 inference(boolean_simplification,[],[f496])). 1.75/0.57 thf(f496,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK15 @ Y1 @ Y2) & (sK15 @ Y0 @ Y1)) => (sK15 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK15 @ Y1 @ Y0))))))) => $false) = $true) | ~spl0_4), 1.75/0.57 inference(superposition,[],[f483,f487])). 1.75/0.57 thf(f487,plain,( 1.75/0.57 ($false = (sK15 @ sK4 @ sK5)) | ~spl0_4), 1.75/0.57 inference(binary_proxy_clausification,[],[f485])). 1.75/0.57 thf(f483,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y1 @ Y2) & (X1 @ Y0 @ Y1)) => (X1 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK4 @ sK5)) = $true)) ) | ~spl0_4), 1.75/0.57 inference(beta_eta_normalization,[],[f482])). 1.75/0.57 thf(f482,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : ((((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))) @ X1) = $true)) ) | ~spl0_4), 1.75/0.57 inference(pi_clausification,[],[f481])). 1.75/0.57 thf(f481,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) != $false) | ~spl0_4), 1.75/0.57 inference(forward_demodulation,[],[f18,f33])). 1.75/0.57 thf(f18,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) != (!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))))), 1.75/0.57 inference(beta_eta_normalization,[],[f17])). 1.75/0.57 thf(f17,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ (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 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK4 @ Y0))))) @ sK5) != ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (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]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0))))) @ sK5))), 1.75/0.57 inference(negative_extensionality,[],[f16])). 1.75/0.57 thf(f16,plain,( 1.75/0.57 ((^[Y0 : a]: (!! @ (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 @ Y3) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y4 @ Y2))))))))) => (Y1 @ sK4 @ Y0))))) != (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y2 @ Y3)) => (Y1 @ Y2 @ Y4)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y7 @ Y6)) => (Y4 @ Y5 @ Y6)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) | (!! @ (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]: ((sK3 @ Y5 @ Y6) => (Y4 @ Y5 @ Y6))))))) => (Y4 @ Y3 @ Y2))))) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0))))))), 1.75/0.57 inference(beta_eta_normalization,[],[f15])). 1.75/0.57 thf(f15,plain,( 1.75/0.57 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4) != ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (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 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))) @ sK4))), 1.75/0.57 inference(negative_extensionality,[],[f14])). 1.75/0.57 thf(f14,plain,( 1.75/0.57 ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) | (sK3 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y5 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))))), 1.75/0.57 inference(equality_proxy_clausification,[],[f13])). 1.75/0.57 thf(f13,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: ((^[Y1 : a]: (!! @ (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 @ Y4) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y5 @ Y3))))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y3 @ Y4)) => (Y2 @ Y3 @ Y5)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y8 @ Y7)) => (Y5 @ Y6 @ Y7)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))) => (Y5 @ Y4 @ Y3)))) | (!! @ (a > a > $o) @ (^[Y5 : a > a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y5 @ Y6 @ Y7) & (Y5 @ Y7 @ Y8)) => (Y5 @ Y6 @ Y8)))))))) & (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: ((sK3 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))) => (Y5 @ Y4 @ Y3))))) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))))))))), 1.75/0.57 inference(beta_eta_normalization,[],[f12])). 1.75/0.57 thf(f12,plain,( 1.75/0.57 ($false = ((^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (Y0 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))) @ sK3))), 1.75/0.57 inference(sigma_clausification,[],[f11])). 1.75/0.57 thf(f11,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) | (Y0 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y6 @ Y5) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y6 @ Y4))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : a]: ((^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y4 @ Y5)) => (Y3 @ Y4 @ Y6)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y9 @ Y8)) => (Y6 @ Y7 @ Y8)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((sK2 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))) => (Y6 @ Y5 @ Y4)))) | (!! @ (a > a > $o) @ (^[Y6 : a > a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y6 @ Y7 @ Y8) & (Y6 @ Y8 @ Y9)) => (Y6 @ Y7 @ Y9)))))))) & (!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: ((Y0 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))) => (Y6 @ Y5 @ Y4))))) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2)))))))))) = $false)), 1.75/0.57 inference(beta_eta_normalization,[],[f10])). 1.75/0.57 thf(f10,plain,( 1.75/0.57 (((^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))))))))) @ sK2) = $false)), 1.75/0.57 inference(sigma_clausification,[],[f7])). 1.75/0.57 thf(f7,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3)))))))))))) = $false)), 1.75/0.57 inference(not_proxy_clausification,[],[f6])). 1.75/0.57 thf(f6,plain,( 1.75/0.57 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))))))))))) = $true)), 1.75/0.57 inference(cnf_transformation,[],[f5])). 1.75/0.57 thf(f5,plain,( 1.75/0.57 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y0 @ Y6 @ Y5) | (Y1 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y7 @ Y6) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y7 @ Y5))))))))) => (Y4 @ Y2 @ Y3))))))) = (^[Y2 : a]: ((^[Y3 : a]: (!! @ (a > a > $o) @ (^[Y4 : a > a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y5 @ Y6)) => (Y4 @ Y5 @ Y7)))))))) & (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y10) & (Y7 @ Y10 @ Y9)) => (Y7 @ Y8 @ Y9)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y0 @ Y9 @ Y8) => (Y7 @ Y9 @ Y8))))))) => (Y7 @ Y6 @ Y5)))) | (!! @ (a > a > $o) @ (^[Y7 : a > a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (!! @ a @ (^[Y10 : a]: (((Y7 @ Y8 @ Y9) & (Y7 @ Y9 @ Y10)) => (Y7 @ Y8 @ Y10)))))))) & (!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: ((Y1 @ Y8 @ Y9) => (Y7 @ Y8 @ Y9))))))) => (Y7 @ Y6 @ Y5))))) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3))))))))))))) = $true)), 1.75/0.57 inference(fool_elimination,[],[f4])). 1.75/0.57 thf(f4,plain,( 1.75/0.57 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) | (X1 @ X8 @ X9)) => (X4 @ X8 @ X9))) => (X4 @ X2 @ X3)))) = (^[X10 : a, X11 : a] : (! [X12 : a > a > $o] : ((! [X13 : a,X14 : a] : ((! [X15 : a > a > $o] : ((! [X16 : a,X17 : a] : ((X0 @ X17 @ X16) => (X15 @ X17 @ X16)) & ! [X18 : a,X19 : a,X20 : a] : (((X15 @ X19 @ X18) & (X15 @ X20 @ X19)) => (X15 @ X20 @ X18))) => (X15 @ X13 @ X14)) | ! [X21 : a > a > $o] : ((! [X22 : a,X23 : a] : ((X1 @ X22 @ X23) => (X21 @ X22 @ X23)) & ! [X24 : a,X25 : a,X26 : a] : (((X21 @ X24 @ X25) & (X21 @ X26 @ X24)) => (X21 @ X26 @ X25))) => (X21 @ X13 @ X14))) => (X12 @ X13 @ X14)) & ! [X27 : a,X28 : a,X29 : a] : (((X12 @ X29 @ X28) & (X12 @ X28 @ X27)) => (X12 @ X29 @ X27))) => (X12 @ X10 @ X11)))))), 1.75/0.57 inference(rectify,[],[f2])). 1.75/0.57 thf(f2,negated_conjecture,( 1.75/0.57 ~! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X0 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X7 : a,X10 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X10 : a,X7 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))))), 1.75/0.57 inference(negated_conjecture,[],[f1])). 1.75/0.57 thf(f1,conjecture,( 1.75/0.57 ! [X0 : a > a > $o,X1 : a > a > $o] : ((^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7)) & ! [X5 : a,X6 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)))) = (^[X2 : a, X3 : a] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a] : ((! [X8 : a > a > $o] : ((! [X10 : a,X9 : a] : ((X0 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X7 : a,X10 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6)) | ! [X8 : a > a > $o] : ((! [X9 : a,X10 : a] : ((X1 @ X9 @ X10) => (X8 @ X9 @ X10)) & ! [X10 : a,X7 : a,X9 : a] : (((X8 @ X10 @ X7) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X7))) => (X8 @ X5 @ X6))) => (X4 @ X5 @ X6)) & ! [X7 : a,X6 : a,X5 : a] : (((X4 @ X5 @ X6) & (X4 @ X6 @ X7)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)))))), 1.75/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM250_pme)). 1.75/0.57 thf(f480,plain,( 1.75/0.57 ~spl0_3 | ~spl0_6), 1.75/0.57 inference(avatar_contradiction_clause,[],[f479])). 1.75/0.57 thf(f479,plain,( 1.75/0.57 $false | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(trivial_inequality_removal,[],[f478])). 1.75/0.57 thf(f478,plain,( 1.75/0.57 ($false = $true) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(boolean_simplification,[],[f477])). 1.75/0.57 thf(f477,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(forward_demodulation,[],[f471,f427])). 1.75/0.57 thf(f427,plain,( 1.75/0.57 ($true = (sK6 @ sK13 @ sK12)) | ~spl0_6), 1.75/0.57 inference(binary_proxy_clausification,[],[f410])). 1.75/0.57 thf(f410,plain,( 1.75/0.57 ($true = ((sK6 @ sK14 @ sK13) & (sK6 @ sK13 @ sK12))) | ~spl0_6), 1.75/0.57 inference(binary_proxy_clausification,[],[f408])). 1.75/0.57 thf(f408,plain,( 1.75/0.57 ((((sK6 @ sK14 @ sK13) & (sK6 @ sK13 @ sK12)) => (sK6 @ sK14 @ sK12)) = $false) | ~spl0_6), 1.75/0.57 inference(beta_eta_normalization,[],[f407])). 1.75/0.57 thf(f407,plain,( 1.75/0.57 (((^[Y0 : a]: (((sK6 @ Y0 @ sK13) & (sK6 @ sK13 @ sK12)) => (sK6 @ Y0 @ sK12))) @ sK14) = $false) | ~spl0_6), 1.75/0.57 inference(sigma_clausification,[],[f406])). 1.75/0.57 thf(f406,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0 @ sK13) & (sK6 @ sK13 @ sK12)) => (sK6 @ Y0 @ sK12)))) = $false) | ~spl0_6), 1.75/0.57 inference(beta_eta_normalization,[],[f405])). 1.75/0.57 thf(f405,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ sK12)) => (sK6 @ Y1 @ sK12))))) @ sK13) = $false) | ~spl0_6), 1.75/0.57 inference(sigma_clausification,[],[f404])). 1.75/0.57 thf(f404,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1 @ Y0) & (sK6 @ Y0 @ sK12)) => (sK6 @ Y1 @ sK12))))))) | ~spl0_6), 1.75/0.57 inference(beta_eta_normalization,[],[f400])). 1.75/0.57 thf(f400,plain,( 1.75/0.57 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))) @ sK12)) | ~spl0_6), 1.75/0.57 inference(sigma_clausification,[],[f59])). 1.75/0.57 thf(f59,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))))) | ~spl0_6), 1.75/0.57 inference(avatar_component_clause,[],[f58])). 1.75/0.57 thf(f58,plain,( 1.75/0.57 spl0_6 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])). 1.75/0.57 thf(f471,plain,( 1.75/0.57 ((~ (sK6 @ sK13 @ sK12)) = $true) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(boolean_simplification,[],[f468])). 1.75/0.57 thf(f468,plain,( 1.75/0.57 (((sK6 @ sK13 @ sK12) => $false) = $true) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(superposition,[],[f438,f412])). 1.75/0.57 thf(f412,plain,( 1.75/0.57 ((sK6 @ sK14 @ sK12) = $false) | ~spl0_6), 1.75/0.57 inference(boolean_simplification,[],[f411])). 1.75/0.57 thf(f411,plain,( 1.75/0.57 (($true => (sK6 @ sK14 @ sK12)) = $false) | ~spl0_6), 1.75/0.57 inference(backward_demodulation,[],[f408,f410])). 1.75/0.57 thf(f438,plain,( 1.75/0.57 ( ! [X0 : a] : (($true = ((sK6 @ sK13 @ X0) => (sK6 @ sK14 @ X0)))) ) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(boolean_simplification,[],[f434])). 1.75/0.57 thf(f434,plain,( 1.75/0.57 ( ! [X0 : a] : (((((sK6 @ sK13 @ X0) & $true) => (sK6 @ sK14 @ X0)) = $true)) ) | (~spl0_3 | ~spl0_6)), 1.75/0.57 inference(superposition,[],[f267,f430])). 1.75/0.57 thf(f430,plain,( 1.75/0.57 ((sK6 @ sK14 @ sK13) = $true) | ~spl0_6), 1.75/0.57 inference(boolean_simplification,[],[f429])). 1.75/0.57 thf(f429,plain,( 1.75/0.57 (((sK6 @ sK14 @ sK13) & $true) = $true) | ~spl0_6), 1.75/0.57 inference(backward_demodulation,[],[f410,f427])). 1.75/0.57 thf(f267,plain,( 1.75/0.57 ( ! [X2 : a,X3 : a,X1 : a] : (((((sK6 @ X2 @ X3) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ X3)) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f266])). 1.75/0.57 thf(f266,plain,( 1.75/0.57 ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ Y0))) @ X3) = $true)) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f263])). 1.75/0.57 thf(f263,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ X2 @ Y0) & (sK6 @ X1 @ X2)) => (sK6 @ X1 @ Y0)))) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f262])). 1.75/0.57 thf(f262,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ X1 @ Y0)) => (sK6 @ X1 @ Y1))))) @ X2) = $true)) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f259])). 1.75/0.57 thf(f259,plain,( 1.75/0.57 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0 @ Y1) & (sK6 @ X1 @ Y0)) => (sK6 @ X1 @ Y1)))))) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f258])). 1.75/0.57 thf(f258,plain,( 1.75/0.57 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2))))))) @ X1) = $true)) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f255])). 1.75/0.57 thf(f255,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $true) | ~spl0_3), 1.75/0.57 inference(binary_proxy_clausification,[],[f246])). 1.75/0.57 thf(f246,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) = $true) | ~spl0_3), 1.75/0.57 inference(binary_proxy_clausification,[],[f244])). 1.75/0.57 thf(f244,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) => (sK6 @ sK4 @ sK5)) = $false) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f243])). 1.75/0.57 thf(f243,plain,( 1.75/0.57 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))) @ sK6) = $false) | ~spl0_3), 1.75/0.57 inference(sigma_clausification,[],[f30])). 1.75/0.57 thf(f30,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ~spl0_3), 1.75/0.57 inference(avatar_component_clause,[],[f29])). 1.75/0.57 thf(f29,plain,( 1.75/0.57 spl0_3 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 1.75/0.57 thf(f396,plain,( 1.75/0.57 ~spl0_3 | ~spl0_5 | ~spl0_8), 1.75/0.57 inference(avatar_contradiction_clause,[],[f395])). 1.75/0.57 thf(f395,plain,( 1.75/0.57 $false | (~spl0_3 | ~spl0_5 | ~spl0_8)), 1.75/0.57 inference(trivial_inequality_removal,[],[f394])). 1.75/0.57 thf(f394,plain,( 1.75/0.57 ($false = $true) | (~spl0_3 | ~spl0_5 | ~spl0_8)), 1.75/0.57 inference(boolean_simplification,[],[f393])). 1.75/0.57 thf(f393,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_3 | ~spl0_5 | ~spl0_8)), 1.75/0.57 inference(forward_demodulation,[],[f388,f93])). 1.75/0.57 thf(f93,plain,( 1.75/0.57 ($true = (sK3 @ sK8 @ sK7)) | ~spl0_8), 1.75/0.57 inference(avatar_component_clause,[],[f92])). 1.75/0.57 thf(f92,plain,( 1.75/0.57 spl0_8 <=> ($true = (sK3 @ sK8 @ sK7))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 1.75/0.57 thf(f388,plain,( 1.75/0.57 ((~ (sK3 @ sK8 @ sK7)) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f386])). 1.75/0.57 thf(f386,plain,( 1.75/0.57 (((sK3 @ sK8 @ sK7) => $false) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(superposition,[],[f384,f348])). 1.75/0.57 thf(f348,plain,( 1.75/0.57 ((sK11 @ sK8 @ sK7) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f347])). 1.75/0.57 thf(f347,plain,( 1.75/0.57 (($true => (sK11 @ sK8 @ sK7)) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(backward_demodulation,[],[f331,f346])). 1.75/0.57 thf(f346,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK11 @ Y0 @ Y1))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f331])). 1.75/0.57 thf(f331,plain,( 1.75/0.57 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK11 @ Y0 @ Y1))))))) => (sK11 @ sK8 @ sK7))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f328])). 1.75/0.57 thf(f328,plain,( 1.75/0.57 (((^[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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))) @ sK11) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(sigma_clausification,[],[f320])). 1.75/0.57 thf(f320,plain,( 1.75/0.57 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f319])). 1.75/0.57 thf(f319,plain,( 1.75/0.57 ($false = ($false | (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK3 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7)))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(backward_demodulation,[],[f290,f316])). 1.75/0.57 thf(f316,plain,( 1.75/0.57 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f290])). 1.75/0.57 thf(f290,plain,( 1.75/0.57 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(not_proxy_clausification,[],[f271])). 1.75/0.57 thf(f271,plain,( 1.75/0.57 ($true = (~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f269])). 1.75/0.57 thf(f269,plain,( 1.75/0.57 ((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))) => $false) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(superposition,[],[f265,f86])). 1.75/0.57 thf(f86,plain,( 1.75/0.57 ($false = (sK6 @ sK8 @ sK7)) | ~spl0_5), 1.75/0.57 inference(boolean_simplification,[],[f85])). 1.75/0.57 thf(f85,plain,( 1.75/0.57 (($true => (sK6 @ sK8 @ sK7)) = $false) | ~spl0_5), 1.75/0.57 inference(backward_demodulation,[],[f79,f84])). 1.75/0.57 thf(f84,plain,( 1.75/0.57 (((sK2 @ sK8 @ sK7) | (sK3 @ sK8 @ sK7)) = $true) | ~spl0_5), 1.75/0.57 inference(binary_proxy_clausification,[],[f79])). 1.75/0.57 thf(f79,plain,( 1.75/0.57 ($false = (((sK2 @ sK8 @ sK7) | (sK3 @ sK8 @ sK7)) => (sK6 @ sK8 @ sK7))) | ~spl0_5), 1.75/0.57 inference(beta_eta_normalization,[],[f78])). 1.75/0.57 thf(f78,plain,( 1.75/0.57 (((^[Y0 : a]: (((sK2 @ Y0 @ sK7) | (sK3 @ Y0 @ sK7)) => (sK6 @ Y0 @ sK7))) @ sK8) = $false) | ~spl0_5), 1.75/0.57 inference(sigma_clausification,[],[f68])). 1.75/0.57 thf(f68,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK7) | (sK3 @ Y0 @ sK7)) => (sK6 @ Y0 @ sK7))))) | ~spl0_5), 1.75/0.57 inference(beta_eta_normalization,[],[f67])). 1.75/0.57 thf(f67,plain,( 1.75/0.57 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0))))) @ sK7) = $false) | ~spl0_5), 1.75/0.57 inference(sigma_clausification,[],[f56])). 1.75/0.57 thf(f56,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | ~spl0_5), 1.75/0.57 inference(avatar_component_clause,[],[f55])). 1.75/0.57 thf(f55,plain,( 1.75/0.57 spl0_5 <=> ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 1.75/0.57 thf(f265,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : (((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X2 @ X1)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X2 @ X1))))) => (sK6 @ X2 @ X1)) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f264])). 1.75/0.57 thf(f264,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ X1))))) => (sK6 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f261])). 1.75/0.57 thf(f261,plain,( 1.75/0.57 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ X1))))) => (sK6 @ Y0 @ X1)))) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f260])). 1.75/0.57 thf(f260,plain,( 1.75/0.57 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f257])). 1.75/0.57 thf(f257,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))) = $true) | ~spl0_3), 1.75/0.57 inference(boolean_simplification,[],[f256])). 1.75/0.57 thf(f256,plain,( 1.75/0.57 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))))) | ~spl0_3), 1.75/0.57 inference(backward_demodulation,[],[f246,f255])). 1.75/0.57 thf(f384,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((sK3 @ X1 @ X2) => (sK11 @ X1 @ X2)) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f383])). 1.75/0.57 thf(f383,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK11 @ X1 @ Y0))) @ X2) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(pi_clausification,[],[f376])). 1.75/0.57 thf(f376,plain,( 1.75/0.57 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK3 @ X1 @ Y0) => (sK11 @ X1 @ Y0)))) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f375])). 1.75/0.57 thf(f375,plain,( 1.75/0.57 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK11 @ Y0 @ Y1))))) @ X1) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(pi_clausification,[],[f368])). 1.75/0.57 thf(f368,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK11 @ Y0 @ Y1)))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f367])). 1.75/0.57 thf(f367,plain,( 1.75/0.57 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK3 @ Y0 @ Y1) => (sK11 @ Y0 @ Y1))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(backward_demodulation,[],[f346,f366])). 1.75/0.57 thf(f366,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK11 @ Y0 @ Y1) & (sK11 @ Y1 @ Y2)) => (sK11 @ Y0 @ Y2)))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f346])). 1.75/0.57 thf(f226,plain,( 1.75/0.57 ~spl0_3 | ~spl0_5 | ~spl0_7), 1.75/0.57 inference(avatar_contradiction_clause,[],[f225])). 1.75/0.57 thf(f225,plain,( 1.75/0.57 $false | (~spl0_3 | ~spl0_5 | ~spl0_7)), 1.75/0.57 inference(trivial_inequality_removal,[],[f224])). 1.75/0.57 thf(f224,plain,( 1.75/0.57 ($false = $true) | (~spl0_3 | ~spl0_5 | ~spl0_7)), 1.75/0.57 inference(boolean_simplification,[],[f223])). 1.75/0.57 thf(f223,plain,( 1.75/0.57 ((~ $true) = $true) | (~spl0_3 | ~spl0_5 | ~spl0_7)), 1.75/0.57 inference(forward_demodulation,[],[f218,f90])). 1.75/0.57 thf(f90,plain,( 1.75/0.57 ($true = (sK2 @ sK8 @ sK7)) | ~spl0_7), 1.75/0.57 inference(avatar_component_clause,[],[f89])). 1.75/0.57 thf(f89,plain,( 1.75/0.57 spl0_7 <=> ($true = (sK2 @ sK8 @ sK7))), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])). 1.75/0.57 thf(f218,plain,( 1.75/0.57 ($true = (~ (sK2 @ sK8 @ sK7))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f216])). 1.75/0.57 thf(f216,plain,( 1.75/0.57 ($true = ((sK2 @ sK8 @ sK7) => $false)) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(superposition,[],[f208,f180])). 1.75/0.57 thf(f180,plain,( 1.75/0.57 ($false = (sK9 @ sK8 @ sK7)) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f170])). 1.75/0.57 thf(f170,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y2) & (sK9 @ Y2 @ Y1)) => (sK9 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) => (sK9 @ sK8 @ sK7)) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f167])). 1.75/0.57 thf(f167,plain,( 1.75/0.57 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))) @ sK9) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(sigma_clausification,[],[f157])). 1.75/0.57 thf(f157,plain,( 1.75/0.57 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f156])). 1.75/0.57 thf(f156,plain,( 1.75/0.57 ($false = ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | $false)) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(backward_demodulation,[],[f142,f152])). 1.75/0.57 thf(f152,plain,( 1.75/0.57 ($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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f142])). 1.75/0.57 thf(f142,plain,( 1.75/0.57 (((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))) = $false) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(not_proxy_clausification,[],[f112])). 1.75/0.57 thf(f112,plain,( 1.75/0.57 ($true = (~ ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK8 @ sK7)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK8 @ sK7))))))) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f111])). 1.75/0.57 thf(f111,plain,( 1.75/0.57 ((((!! 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[X2 : a,X1 : a] : (((((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ X2 @ X1)))) | (!! @ (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) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ X2 @ X1))))) => (sK6 @ X2 @ X1)) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f105])). 1.75/0.57 thf(f105,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ X1))))) => (sK6 @ Y0 @ X1))) @ X2) = $true)) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f102])). 1.75/0.57 thf(f102,plain,( 1.75/0.57 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y2 @ Y3)))))))) & (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ X1)))) | (!! @ (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) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ X1))))) => (sK6 @ Y0 @ X1)))) = $true)) ) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f101])). 1.75/0.57 thf(f101,plain,( 1.75/0.57 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_3), 1.75/0.57 inference(pi_clausification,[],[f100])). 1.75/0.57 thf(f100,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))) = $true) | ~spl0_3), 1.75/0.57 inference(boolean_simplification,[],[f99])). 1.75/0.57 thf(f99,plain,( 1.75/0.57 ($true = ($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0)))))))) | ~spl0_3), 1.75/0.57 inference(backward_demodulation,[],[f43,f98])). 1.75/0.57 thf(f98,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) = $true) | ~spl0_3), 1.75/0.57 inference(binary_proxy_clausification,[],[f43])). 1.75/0.57 thf(f43,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) = $true) | ~spl0_3), 1.75/0.57 inference(binary_proxy_clausification,[],[f41])). 1.75/0.57 thf(f41,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y0 @ Y1)) => (sK6 @ Y0 @ Y2)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y5 @ Y4)) => (Y2 @ Y3 @ Y4)))))))) & (!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) | (!! @ (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) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0))))) => (sK6 @ Y1 @ Y0))))))) => (sK6 @ sK4 @ sK5)) = $false) | ~spl0_3), 1.75/0.57 inference(beta_eta_normalization,[],[f40])). 1.75/0.57 thf(f40,plain,( 1.75/0.57 (((^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5))) @ sK6) = $false) | ~spl0_3), 1.75/0.57 inference(sigma_clausification,[],[f30])). 1.75/0.57 thf(f208,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((sK2 @ X2 @ X1) => (sK9 @ X2 @ X1)) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f207])). 1.75/0.57 thf(f207,plain,( 1.75/0.57 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK9 @ Y0 @ X1))) @ X2) = $true)) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(pi_clausification,[],[f200])). 1.75/0.57 thf(f200,plain,( 1.75/0.57 ( ! [X1 : a] : (($true = (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0 @ X1) => (sK9 @ Y0 @ X1)))))) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(beta_eta_normalization,[],[f199])). 1.75/0.57 thf(f199,plain,( 1.75/0.57 ( ! [X1 : a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))) @ X1))) ) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(pi_clausification,[],[f192])). 1.75/0.57 thf(f192,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0)))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(boolean_simplification,[],[f191])). 1.75/0.57 thf(f191,plain,( 1.75/0.57 (($true & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(backward_demodulation,[],[f181,f190])). 1.75/0.57 thf(f190,plain,( 1.75/0.57 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y2) & (sK9 @ Y2 @ Y1)) => (sK9 @ Y0 @ Y1)))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f181])). 1.75/0.57 thf(f181,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK9 @ Y0 @ Y2) & (sK9 @ Y2 @ Y1)) => (sK9 @ Y0 @ Y1)))))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((sK2 @ Y1 @ Y0) => (sK9 @ Y1 @ Y0))))))) = $true) | (~spl0_3 | ~spl0_5)), 1.75/0.57 inference(binary_proxy_clausification,[],[f170])). 1.75/0.57 thf(f94,plain,( 1.75/0.57 spl0_7 | spl0_8 | ~spl0_5), 1.75/0.57 inference(avatar_split_clause,[],[f87,f55,f92,f89])). 1.75/0.57 thf(f87,plain,( 1.75/0.57 ($true = (sK3 @ sK8 @ sK7)) | ($true = (sK2 @ sK8 @ sK7)) | ~spl0_5), 1.75/0.57 inference(binary_proxy_clausification,[],[f84])). 1.75/0.57 thf(f63,plain,( 1.75/0.57 ~spl0_1 | ~spl0_3), 1.75/0.57 inference(avatar_contradiction_clause,[],[f62])). 1.75/0.57 thf(f62,plain,( 1.75/0.57 $false | (~spl0_1 | ~spl0_3)), 1.75/0.57 inference(trivial_inequality_removal,[],[f61])). 1.75/0.57 thf(f61,plain,( 1.75/0.57 ($false = $true) | (~spl0_1 | ~spl0_3)), 1.75/0.57 inference(forward_demodulation,[],[f23,f30])). 1.75/0.57 thf(f23,plain,( 1.75/0.57 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $true) | ~spl0_1), 1.75/0.57 inference(avatar_component_clause,[],[f22])). 1.75/0.57 thf(f22,plain,( 1.75/0.57 spl0_1 <=> ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $true)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 1.75/0.57 thf(f60,plain,( 1.75/0.57 spl0_5 | spl0_6 | ~spl0_2 | ~spl0_3), 1.75/0.57 inference(avatar_split_clause,[],[f51,f29,f25,f58,f55])). 1.75/0.57 thf(f25,plain,( 1.75/0.57 spl0_2 <=> ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $true)), 1.75/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 1.75/0.57 thf(f51,plain,( 1.75/0.57 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))))) | ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) = $false) | (~spl0_2 | ~spl0_3)), 1.75/0.57 inference(binary_proxy_clausification,[],[f48])). 1.75/0.57 thf(f48,plain,( 1.75/0.57 (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))))) = $false) | (~spl0_2 | ~spl0_3)), 1.75/0.57 inference(not_proxy_clausification,[],[f47])). 1.75/0.57 thf(f47,plain,( 1.75/0.57 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0)))))))))) = $true) | (~spl0_2 | ~spl0_3)), 1.75/0.57 inference(boolean_simplification,[],[f46])). 1.75/0.57 thf(f46,plain,( 1.75/0.57 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (sK6 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK6 @ Y2 @ Y1) & (sK6 @ Y1 @ Y0)) => (sK6 @ Y2 @ Y0))))))))) => $false) = $true) | (~spl0_2 | ~spl0_3)), 1.75/0.57 inference(superposition,[],[f38,f45])). 1.75/0.57 thf(f45,plain,( 1.75/0.57 ((sK6 @ sK4 @ sK5) = $false) | ~spl0_3), 1.75/0.57 inference(boolean_simplification,[],[f44])). 1.75/0.57 thf(f44,plain,( 1.75/0.57 ($false = ($true => (sK6 @ sK4 @ sK5))) | ~spl0_3), 1.75/0.57 inference(backward_demodulation,[],[f41,f43])). 1.75/0.57 thf(f38,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) | (sK3 @ Y1 @ Y0)) => (X1 @ Y1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((X1 @ Y2 @ Y1) & (X1 @ Y1 @ Y0)) => (X1 @ Y2 @ Y0))))))))) => (X1 @ sK4 @ sK5)) = $true)) ) | ~spl0_2), 1.75/0.57 inference(beta_eta_normalization,[],[f37])). 1.75/0.57 thf(f37,plain,( 1.75/0.57 ( ! [X1 : a > a > $o] : (($true = ((^[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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5))) @ X1))) ) | ~spl0_2), 1.75/0.57 inference(pi_clausification,[],[f26])). 1.75/0.57 thf(f26,plain,( 1.75/0.57 ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $true) | ~spl0_2), 1.75/0.57 inference(avatar_component_clause,[],[f25])). 1.75/0.57 thf(f34,plain,( 1.75/0.57 spl0_3 | spl0_4), 1.75/0.57 inference(avatar_split_clause,[],[f20,f32,f29])). 1.75/0.57 thf(f20,plain,( 1.75/0.57 ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $false) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $false)), 1.75/0.57 inference(binary_proxy_clausification,[],[f18])). 1.75/0.57 thf(f27,plain,( 1.75/0.57 spl0_1 | spl0_2), 1.75/0.57 inference(avatar_split_clause,[],[f19,f25,f22])). 1.75/0.57 thf(f19,plain,( 1.75/0.57 ((!! @ (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 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) => (Y0 @ sK4 @ sK5)))) = $true) | ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3)))))))) & (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y6 @ Y5)) => (Y3 @ Y4 @ Y5)))))))) & (!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) | (!! @ (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]: ((sK3 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1))))) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) = $true)), 1.75/0.57 inference(binary_proxy_clausification,[],[f18])). 1.75/0.57 % SZS output end Proof for theBenchmark 1.75/0.57 % (29400)------------------------------ 1.75/0.57 % (29400)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.75/0.57 % (29400)Termination reason: Refutation 1.75/0.57 1.75/0.57 % (29400)Memory used [KB]: 6396 1.75/0.57 % (29400)Time elapsed: 0.108 s 1.75/0.57 % (29400)Instructions burned: 233 (million) 1.75/0.57 % (29400)------------------------------ 1.75/0.57 % (29400)------------------------------ 1.75/0.57 % (29342)Success in time 0.218 s 1.75/0.57 % Vampire---4.8 exiting 1.75/0.57 EOF