TSTP Solution File: SYN397^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% 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
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:22:15 EDT 2024
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN397^7 : TPTP v8.2.0. Released v5.5.0.
% 0.12/0.14 % 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
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 14:59:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (5165)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (5159)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (5161)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (5160)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (5162)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (5163)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (5164)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 (2999ds/275Mi)
% 0.14/0.37 % (5166)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (5162)Instruction limit reached!
% 0.14/0.37 % (5162)------------------------------
% 0.14/0.37 % (5162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (5162)Termination reason: Unknown
% 0.14/0.37 % (5162)Termination phase: shuffling
% 0.14/0.37 % (5163)Instruction limit reached!
% 0.14/0.37 % (5163)------------------------------
% 0.14/0.37 % (5163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (5163)Termination reason: Unknown
% 0.14/0.37 % (5163)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (5163)Memory used [KB]: 1023
% 0.14/0.37 % (5163)Time elapsed: 0.003 s
% 0.14/0.37 % (5163)Instructions burned: 2 (million)
% 0.14/0.37 % (5163)------------------------------
% 0.14/0.37 % (5163)------------------------------
% 0.14/0.37
% 0.14/0.37 % (5162)Memory used [KB]: 1023
% 0.14/0.37 % (5162)Time elapsed: 0.003 s
% 0.14/0.37 % (5162)Instructions burned: 2 (million)
% 0.14/0.37 % (5162)------------------------------
% 0.14/0.37 % (5162)------------------------------
% 0.14/0.37 % (5160)Instruction limit reached!
% 0.14/0.37 % (5160)------------------------------
% 0.14/0.37 % (5160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (5160)Termination reason: Unknown
% 0.14/0.37 % (5160)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (5160)Memory used [KB]: 1023
% 0.14/0.37 % (5160)Time elapsed: 0.004 s
% 0.14/0.37 % (5160)Instructions burned: 4 (million)
% 0.14/0.37 % (5160)------------------------------
% 0.14/0.37 % (5160)------------------------------
% 0.14/0.37 % (5166)Instruction limit reached!
% 0.14/0.37 % (5166)------------------------------
% 0.14/0.37 % (5166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (5166)Termination reason: Unknown
% 0.14/0.37 % (5166)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (5166)Memory used [KB]: 1023
% 0.14/0.37 % (5166)Time elapsed: 0.004 s
% 0.14/0.37 % (5166)Instructions burned: 3 (million)
% 0.14/0.37 % (5166)------------------------------
% 0.14/0.37 % (5166)------------------------------
% 0.14/0.37 % (5165)Instruction limit reached!
% 0.14/0.37 % (5165)------------------------------
% 0.14/0.37 % (5165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (5165)Termination reason: Unknown
% 0.14/0.37 % (5165)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (5165)Memory used [KB]: 5628
% 0.14/0.37 % (5165)Time elapsed: 0.010 s
% 0.14/0.37 % (5165)Instructions burned: 19 (million)
% 0.14/0.37 % (5165)------------------------------
% 0.14/0.37 % (5165)------------------------------
% 0.14/0.38 % (5161)Instruction limit reached!
% 0.14/0.38 % (5161)------------------------------
% 0.14/0.38 % (5161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (5161)Termination reason: Unknown
% 0.14/0.38 % (5161)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (5161)Memory used [KB]: 5628
% 0.14/0.38 % (5161)Time elapsed: 0.015 s
% 0.14/0.38 % (5161)Instructions burned: 27 (million)
% 0.14/0.38 % (5161)------------------------------
% 0.14/0.38 % (5161)------------------------------
% 0.14/0.38 % (5167)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38 % (5168)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.38 % (5170)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.14/0.39 % (5169)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39 % (5171)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.39 % (5169)Instruction limit reached!
% 0.14/0.39 % (5169)------------------------------
% 0.14/0.39 % (5169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (5169)Termination reason: Unknown
% 0.14/0.39 % (5169)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (5169)Memory used [KB]: 1023
% 0.14/0.39 % (5169)Time elapsed: 0.004 s
% 0.14/0.39 % (5169)Instructions burned: 4 (million)
% 0.14/0.39 % (5169)------------------------------
% 0.14/0.39 % (5169)------------------------------
% 0.14/0.39 % (5168)Instruction limit reached!
% 0.14/0.39 % (5168)------------------------------
% 0.14/0.39 % (5168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (5168)Termination reason: Unknown
% 0.14/0.39 % (5168)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (5168)Memory used [KB]: 5628
% 0.14/0.39 % (5168)Time elapsed: 0.009 s
% 0.14/0.39 % (5168)Instructions burned: 15 (million)
% 0.14/0.39 % (5168)------------------------------
% 0.14/0.39 % (5168)------------------------------
% 0.14/0.39 % (5171)Instruction limit reached!
% 0.14/0.39 % (5171)------------------------------
% 0.14/0.39 % (5171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (5171)Termination reason: Unknown
% 0.14/0.39 % (5171)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (5171)Memory used [KB]: 1023
% 0.14/0.39 % (5171)Time elapsed: 0.005 s
% 0.14/0.39 % (5171)Instructions burned: 8 (million)
% 0.14/0.39 % (5171)------------------------------
% 0.14/0.39 % (5171)------------------------------
% 0.14/0.39 % (5172)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40 % (5173)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.40 % (5167)Instruction limit reached!
% 0.14/0.40 % (5167)------------------------------
% 0.14/0.40 % (5167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (5167)Termination reason: Unknown
% 0.14/0.40 % (5167)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (5167)Memory used [KB]: 5756
% 0.14/0.40 % (5167)Time elapsed: 0.022 s
% 0.14/0.40 % (5167)Instructions burned: 39 (million)
% 0.14/0.40 % (5167)------------------------------
% 0.14/0.40 % (5167)------------------------------
% 0.14/0.40 % (5172)Instruction limit reached!
% 0.14/0.40 % (5172)------------------------------
% 0.14/0.40 % (5172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (5172)Termination reason: Unknown
% 0.14/0.40 % (5172)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (5172)Memory used [KB]: 5756
% 0.14/0.40 % (5172)Time elapsed: 0.011 s
% 0.14/0.40 % (5172)Instructions burned: 16 (million)
% 0.14/0.40 % (5172)------------------------------
% 0.14/0.40 % (5172)------------------------------
% 0.14/0.40 % (5175)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (5174)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.40 % (5173)Instruction limit reached!
% 0.14/0.40 % (5173)------------------------------
% 0.14/0.40 % (5173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (5173)Termination reason: Unknown
% 0.14/0.40 % (5173)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.41 % (5173)Memory used [KB]: 1023
% 0.14/0.41 % (5173)Time elapsed: 0.004 s
% 0.14/0.41 % (5173)Instructions burned: 4 (million)
% 0.14/0.41 % (5173)------------------------------
% 0.14/0.41 % (5173)------------------------------
% 0.14/0.41 % (5174)Instruction limit reached!
% 0.14/0.41 % (5174)------------------------------
% 0.14/0.41 % (5174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (5174)Termination reason: Unknown
% 0.14/0.41 % (5174)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (5174)Memory used [KB]: 1023
% 0.14/0.41 % (5174)Time elapsed: 0.003 s
% 0.14/0.41 % (5174)Instructions burned: 3 (million)
% 0.14/0.41 % (5174)------------------------------
% 0.14/0.41 % (5174)------------------------------
% 0.14/0.41 % (5175)Instruction limit reached!
% 0.14/0.41 % (5175)------------------------------
% 0.14/0.41 % (5175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (5175)Termination reason: Unknown
% 0.14/0.41 % (5175)Termination phase: Property scanning
% 0.14/0.41
% 0.14/0.41 % (5175)Memory used [KB]: 1023
% 0.14/0.41 % (5175)Time elapsed: 0.005 s
% 0.14/0.41 % (5175)Instructions burned: 7 (million)
% 0.14/0.41 % (5175)------------------------------
% 0.14/0.41 % (5175)------------------------------
% 0.14/0.42 % (5176)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.42 % (5177)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.42 % (5176)Instruction limit reached!
% 0.14/0.42 % (5176)------------------------------
% 0.14/0.42 % (5176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (5176)Termination reason: Unknown
% 0.14/0.42 % (5176)Termination phase: shuffling
% 0.14/0.42
% 0.14/0.42 % (5176)Memory used [KB]: 1023
% 0.14/0.42 % (5176)Time elapsed: 0.003 s
% 0.14/0.42 % (5176)Instructions burned: 3 (million)
% 0.14/0.42 % (5176)------------------------------
% 0.14/0.42 % (5176)------------------------------
% 0.14/0.42 % (5180)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.42 % (5178)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.42 % (5179)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.42 % (5177)Instruction limit reached!
% 0.14/0.42 % (5177)------------------------------
% 0.14/0.42 % (5177)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (5177)Termination reason: Unknown
% 0.14/0.42 % (5177)Termination phase: shuffling
% 0.14/0.42
% 0.14/0.42 % (5177)Memory used [KB]: 1023
% 0.14/0.42 % (5177)Time elapsed: 0.004 s
% 0.14/0.42 % (5177)Instructions burned: 5 (million)
% 0.14/0.42 % (5177)------------------------------
% 0.14/0.42 % (5177)------------------------------
% 0.14/0.42 % (5180)Instruction limit reached!
% 0.14/0.42 % (5180)------------------------------
% 0.14/0.42 % (5180)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (5180)Termination reason: Unknown
% 0.14/0.42 % (5180)Termination phase: Function definition elimination
% 0.14/0.42
% 0.14/0.42 % (5180)Memory used [KB]: 1151
% 0.14/0.42 % (5180)Time elapsed: 0.003 s
% 0.14/0.42 % (5180)Instructions burned: 8 (million)
% 0.14/0.42 % (5180)------------------------------
% 0.14/0.42 % (5180)------------------------------
% 0.20/0.43 % (5179)Refutation not found, incomplete strategy
% 0.20/0.43 % (5179)------------------------------
% 0.20/0.43 % (5179)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (5179)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 % (5179)Memory used [KB]: 5628
% 0.20/0.43 % (5179)Time elapsed: 0.010 s
% 0.20/0.43 % (5179)Instructions burned: 13 (million)
% 0.20/0.43 % (5179)------------------------------
% 0.20/0.43 % (5179)------------------------------
% 0.20/0.43 % (5178)Instruction limit reached!
% 0.20/0.43 % (5178)------------------------------
% 0.20/0.43 % (5178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (5178)Termination reason: Unknown
% 0.20/0.43 % (5178)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (5178)Memory used [KB]: 5628
% 0.20/0.43 % (5178)Time elapsed: 0.013 s
% 0.20/0.43 % (5178)Instructions burned: 18 (million)
% 0.20/0.43 % (5178)------------------------------
% 0.20/0.43 % (5178)------------------------------
% 0.20/0.43 % (5183)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.43 % (5183)Instruction limit reached!
% 0.20/0.43 % (5183)------------------------------
% 0.20/0.43 % (5183)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (5183)Termination reason: Unknown
% 0.20/0.43 % (5183)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (5183)Memory used [KB]: 1023
% 0.20/0.43 % (5183)Time elapsed: 0.003 s
% 0.20/0.43 % (5183)Instructions burned: 6 (million)
% 0.20/0.43 % (5183)------------------------------
% 0.20/0.43 % (5183)------------------------------
% 0.20/0.43 % (5181)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.20/0.44 % (5182)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)
% 0.20/0.44 % (5181)Refutation not found, incomplete strategy
% 0.20/0.44 % (5181)------------------------------
% 0.20/0.44 % (5181)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (5181)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 % (5181)Memory used [KB]: 5628
% 0.20/0.44 % (5181)Time elapsed: 0.008 s
% 0.20/0.44 % (5181)Instructions burned: 10 (million)
% 0.20/0.44 % (5181)------------------------------
% 0.20/0.44 % (5181)------------------------------
% 0.20/0.44 % (5184)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.45 % (5185)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.45 % (5184)Instruction limit reached!
% 0.20/0.45 % (5184)------------------------------
% 0.20/0.45 % (5184)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (5184)Termination reason: Unknown
% 0.20/0.45 % (5184)Termination phase: SInE selection
% 0.20/0.45
% 0.20/0.45 % (5184)Memory used [KB]: 1023
% 0.20/0.45 % (5184)Time elapsed: 0.005 s
% 0.20/0.45 % (5184)Instructions burned: 6 (million)
% 0.20/0.45 % (5184)------------------------------
% 0.20/0.45 % (5184)------------------------------
% 0.20/0.45 % (5182)Instruction limit reached!
% 0.20/0.45 % (5182)------------------------------
% 0.20/0.45 % (5182)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (5182)Termination reason: Unknown
% 0.20/0.45 % (5182)Termination phase: Saturation
% 0.20/0.45
% 0.20/0.45 % (5186)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.45 % (5182)Memory used [KB]: 5756
% 0.20/0.45 % (5182)Time elapsed: 0.035 s
% 0.20/0.45 % (5182)Instructions burned: 21 (million)
% 0.20/0.45 % (5182)------------------------------
% 0.20/0.45 % (5182)------------------------------
% 0.20/0.45 % (5187)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 (2999ds/19Mi)
% 0.20/0.46 % (5188)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.20/0.46 % (5189)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.20/0.46 % (5187)Instruction limit reached!
% 0.20/0.46 % (5187)------------------------------
% 0.20/0.46 % (5187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (5187)Termination reason: Unknown
% 0.20/0.46 % (5187)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (5187)Memory used [KB]: 5628
% 0.20/0.46 % (5187)Time elapsed: 0.036 s
% 0.20/0.46 % (5187)Instructions burned: 20 (million)
% 0.20/0.46 % (5187)------------------------------
% 0.20/0.46 % (5187)------------------------------
% 0.20/0.47 % (5189)Instruction limit reached!
% 0.20/0.47 % (5189)------------------------------
% 0.20/0.47 % (5189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (5189)Termination reason: Unknown
% 0.20/0.47 % (5189)Termination phase: Saturation
% 0.20/0.47
% 0.20/0.47 % (5189)Memory used [KB]: 5628
% 0.20/0.47 % (5189)Time elapsed: 0.011 s
% 0.20/0.47 % (5189)Instructions burned: 18 (million)
% 0.20/0.47 % (5189)------------------------------
% 0.20/0.47 % (5189)------------------------------
% 0.20/0.48 % (5190)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.48 % (5190)Instruction limit reached!
% 0.20/0.48 % (5190)------------------------------
% 0.20/0.48 % (5190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (5190)Termination reason: Unknown
% 0.20/0.48 % (5190)Termination phase: shuffling
% 0.20/0.48
% 0.20/0.48 % (5190)Memory used [KB]: 1023
% 0.20/0.48 % (5190)Time elapsed: 0.004 s
% 0.20/0.48 % (5190)Instructions burned: 5 (million)
% 0.20/0.48 % (5190)------------------------------
% 0.20/0.48 % (5190)------------------------------
% 0.20/0.49 % (5186)First to succeed.
% 0.20/0.49 % (5191)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.20/0.49 % (5159)Instruction limit reached!
% 0.20/0.49 % (5159)------------------------------
% 0.20/0.49 % (5159)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.49 % (5159)Termination reason: Unknown
% 0.20/0.49 % (5159)Termination phase: Saturation
% 0.20/0.49
% 0.20/0.49 % (5159)Memory used [KB]: 6780
% 0.20/0.49 % (5159)Time elapsed: 0.126 s
% 0.20/0.49 % (5159)Instructions burned: 184 (million)
% 0.20/0.49 % (5159)------------------------------
% 0.20/0.49 % (5159)------------------------------
% 0.20/0.49 % (5192)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.20/0.50 % (5191)Instruction limit reached!
% 0.20/0.50 % (5191)------------------------------
% 0.20/0.50 % (5191)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (5191)Termination reason: Unknown
% 0.20/0.50 % (5191)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (5191)Memory used [KB]: 5756
% 0.20/0.50 % (5191)Time elapsed: 0.010 s
% 0.20/0.50 % (5191)Instructions burned: 31 (million)
% 0.20/0.50 % (5191)------------------------------
% 0.20/0.50 % (5191)------------------------------
% 0.20/0.50 % (5193)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.20/0.50 % (5186)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% 0.20/0.50 thf(type_def_5, type, mu: $tType).
% 0.20/0.50 thf(func_def_0, type, mu: $tType).
% 0.20/0.50 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.20/0.50 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_8, type, mtrue: $i > $o).
% 0.20/0.50 thf(func_def_9, type, mfalse: $i > $o).
% 0.20/0.50 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.20/0.50 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.50 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.20/0.50 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.50 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.50 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.20/0.50 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.20/0.50 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.20/0.50 thf(func_def_37, type, f: mu > $i > $o).
% 0.20/0.50 thf(func_def_54, type, sK1: $i > mu).
% 0.20/0.50 thf(func_def_59, type, sK6: mu).
% 0.20/0.50 thf(func_def_60, type, sK7: $i > mu > $i).
% 0.20/0.50 thf(func_def_62, type, sK9: mu).
% 0.20/0.50 thf(f785,plain,(
% 0.20/0.50 $false),
% 0.20/0.50 inference(avatar_sat_refutation,[],[f215,f221,f234,f235,f254,f256,f292,f297,f308,f309,f372,f379,f391,f393,f405,f406,f429,f431,f443,f449,f451,f464,f470,f471,f480,f490,f492,f507,f517,f522,f642,f666,f715,f756,f782])).
% 0.20/0.50 thf(f782,plain,(
% 0.20/0.50 ~spl0_10 | ~spl0_11 | ~spl0_17),
% 0.20/0.50 inference(avatar_contradiction_clause,[],[f781])).
% 0.20/0.50 thf(f781,plain,(
% 0.20/0.50 $false | (~spl0_10 | ~spl0_11 | ~spl0_17)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f776])).
% 0.20/0.50 thf(f776,plain,(
% 0.20/0.50 ($true = $false) | (~spl0_10 | ~spl0_11 | ~spl0_17)),
% 0.20/0.50 inference(backward_demodulation,[],[f378,f772])).
% 0.20/0.50 thf(f772,plain,(
% 0.20/0.50 ((rel_s4 @ sK8 @ sK10) = $false) | (~spl0_11 | ~spl0_17)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f768])).
% 0.20/0.50 thf(f768,plain,(
% 0.20/0.50 ($true = $false) | ((rel_s4 @ sK8 @ sK10) = $false) | (~spl0_11 | ~spl0_17)),
% 0.20/0.50 inference(superposition,[],[f763,f404])).
% 0.20/0.50 thf(f404,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK9 @ sK8)) | ~spl0_11),
% 0.20/0.50 inference(avatar_component_clause,[],[f402])).
% 0.20/0.50 thf(f402,plain,(
% 0.20/0.50 spl0_11 <=> ($true = (exists_in_world @ sK9 @ sK8))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.20/0.50 thf(f763,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (($false = (exists_in_world @ sK9 @ X0)) | ((rel_s4 @ X0 @ sK10) = $false)) ) | ~spl0_17),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f761])).
% 0.20/0.50 thf(f761,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (((rel_s4 @ X0 @ sK10) = $false) | ($false = (exists_in_world @ sK9 @ X0)) | ($true = $false)) ) | ~spl0_17),
% 0.20/0.50 inference(superposition,[],[f711,f608])).
% 0.20/0.50 thf(f608,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (exists_in_world @ X2 @ X3)) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f607])).
% 0.20/0.50 thf(f607,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (exists_in_world @ X2 @ X3)) | (((exists_in_world @ X2 @ X1) & (rel_s4 @ X1 @ X3)) = $false)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f606])).
% 0.20/0.50 thf(f606,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (((exists_in_world @ X2 @ X1) & (rel_s4 @ X1 @ X3)) => (exists_in_world @ X2 @ X3)))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f605])).
% 0.20/0.50 thf(f605,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((exists_in_world @ X2 @ X1) & (rel_s4 @ X1 @ Y0)) => (exists_in_world @ X2 @ Y0))) @ X3))) )),
% 0.20/0.50 inference(pi_clausification,[],[f604])).
% 0.20/0.50 thf(f604,plain,(
% 0.20/0.50 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((exists_in_world @ X2 @ X1) & (rel_s4 @ X1 @ Y0)) => (exists_in_world @ X2 @ Y0)))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f603])).
% 0.20/0.50 thf(f603,plain,(
% 0.20/0.50 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ Y0 @ X1) & (rel_s4 @ X1 @ Y1)) => (exists_in_world @ Y0 @ Y1))))) @ X2) = $true)) )),
% 0.20/0.50 inference(pi_clausification,[],[f602])).
% 0.20/0.50 thf(f602,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ Y0 @ X1) & (rel_s4 @ X1 @ Y1)) => (exists_in_world @ Y0 @ Y1)))))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f601])).
% 0.20/0.50 thf(f601,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y0) & (rel_s4 @ Y0 @ Y2)) => (exists_in_world @ Y1 @ Y2))))))) @ X1))) )),
% 0.20/0.50 inference(pi_clausification,[],[f118])).
% 0.20/0.50 thf(f118,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y0) & (rel_s4 @ Y0 @ Y2)) => (exists_in_world @ Y1 @ Y2)))))))) = $true)),
% 0.20/0.50 inference(cnf_transformation,[],[f104])).
% 0.20/0.50 thf(f104,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y0) & (rel_s4 @ Y0 @ Y2)) => (exists_in_world @ Y1 @ Y2)))))))) = $true)),
% 0.20/0.50 inference(fool_elimination,[],[f103])).
% 0.20/0.50 thf(f103,plain,(
% 0.20/0.50 ! [X0,X1 : mu,X2] : (((rel_s4 @ X2 @ X0) & (exists_in_world @ X1 @ X2)) => (exists_in_world @ X1 @ X0))),
% 0.20/0.50 inference(rectify,[],[f36])).
% 0.20/0.50 thf(f36,axiom,(
% 0.20/0.50 ! [X2,X0 : mu,X6] : (((rel_s4 @ X6 @ X2) & (exists_in_world @ X0 @ X6)) => (exists_in_world @ X0 @ X2))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)).
% 0.20/0.50 thf(f711,plain,(
% 0.20/0.50 ((exists_in_world @ sK9 @ sK10) = $false) | ~spl0_17),
% 0.20/0.50 inference(avatar_component_clause,[],[f709])).
% 0.20/0.50 thf(f709,plain,(
% 0.20/0.50 spl0_17 <=> ((exists_in_world @ sK9 @ sK10) = $false)),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_17])])).
% 0.20/0.50 thf(f378,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK8 @ sK10)) | ~spl0_10),
% 0.20/0.50 inference(avatar_component_clause,[],[f376])).
% 0.20/0.50 thf(f376,plain,(
% 0.20/0.50 spl0_10 <=> ($true = (rel_s4 @ sK8 @ sK10))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.20/0.50 thf(f756,plain,(
% 0.20/0.50 ~spl0_10 | ~spl0_12 | ~spl0_16),
% 0.20/0.50 inference(avatar_contradiction_clause,[],[f755])).
% 0.20/0.50 thf(f755,plain,(
% 0.20/0.50 $false | (~spl0_10 | ~spl0_12 | ~spl0_16)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f748])).
% 0.20/0.50 thf(f748,plain,(
% 0.20/0.50 ($true = $false) | (~spl0_10 | ~spl0_12 | ~spl0_16)),
% 0.20/0.50 inference(backward_demodulation,[],[f378,f736])).
% 0.20/0.50 thf(f736,plain,(
% 0.20/0.50 ((rel_s4 @ sK8 @ sK10) = $false) | (~spl0_12 | ~spl0_16)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f732])).
% 0.20/0.50 thf(f732,plain,(
% 0.20/0.50 ((rel_s4 @ sK8 @ sK10) = $false) | ($true = $false) | (~spl0_12 | ~spl0_16)),
% 0.20/0.50 inference(superposition,[],[f428,f720])).
% 0.20/0.50 thf(f720,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ((rel_s4 @ X0 @ sK10) = $false)) ) | ~spl0_16),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f718])).
% 0.20/0.50 thf(f718,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (($true = $false) | ((rel_s4 @ sK3 @ X0) = $false) | ((rel_s4 @ X0 @ sK10) = $false)) ) | ~spl0_16),
% 0.20/0.50 inference(superposition,[],[f159,f707])).
% 0.20/0.50 thf(f707,plain,(
% 0.20/0.50 ((rel_s4 @ sK3 @ sK10) = $false) | ~spl0_16),
% 0.20/0.50 inference(avatar_component_clause,[],[f705])).
% 0.20/0.50 thf(f705,plain,(
% 0.20/0.50 spl0_16 <=> ((rel_s4 @ sK3 @ sK10) = $false)),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_16])])).
% 0.20/0.50 thf(f159,plain,(
% 0.20/0.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X3)) | ((rel_s4 @ X2 @ X3) = $false) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f158])).
% 0.20/0.50 thf(f158,plain,(
% 0.20/0.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X3)) | ($false = ((rel_s4 @ X2 @ X3) & (rel_s4 @ X1 @ X2)))) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f157])).
% 0.20/0.50 thf(f157,plain,(
% 0.20/0.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s4 @ X2 @ X3) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ X1 @ X3)) = $true)) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f156])).
% 0.20/0.50 thf(f156,plain,(
% 0.20/0.50 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s4 @ X2 @ Y0) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ X1 @ Y0))) @ X3) = $true)) )),
% 0.20/0.50 inference(pi_clausification,[],[f155])).
% 0.20/0.50 thf(f155,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X2 @ Y0) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ X1 @ Y0)))) = $true)) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f154])).
% 0.20/0.50 thf(f154,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ Y1))))) @ X2))) )),
% 0.20/0.50 inference(pi_clausification,[],[f153])).
% 0.20/0.50 thf(f153,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ Y1)))))) = $true)) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f152])).
% 0.20/0.50 thf(f152,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y1 @ Y2) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ Y2))))))) @ X1))) )),
% 0.20/0.50 inference(pi_clausification,[],[f151])).
% 0.20/0.50 thf(f151,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y1 @ Y2) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ Y2)))))))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f147])).
% 0.20/0.50 thf(f147,plain,(
% 0.20/0.50 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) @ rel_s4))),
% 0.20/0.50 inference(definition_unfolding,[],[f134,f122])).
% 0.20/0.50 thf(f122,plain,(
% 0.20/0.50 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f45])).
% 0.20/0.50 thf(f45,plain,(
% 0.20/0.50 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.20/0.50 inference(fool_elimination,[],[f44])).
% 0.20/0.50 thf(f44,plain,(
% 0.20/0.50 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X2 @ X1)) => (X0 @ X3 @ X1)))))),
% 0.20/0.50 inference(rectify,[],[f21])).
% 0.20/0.50 thf(f21,axiom,(
% 0.20/0.50 (mtransitive = (^[X5 : $i > $i > $o] : (! [X10,X9,X8] : (((X5 @ X8 @ X9) & (X5 @ X9 @ X10)) => (X5 @ X8 @ X10)))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.50 thf(f134,plain,(
% 0.20/0.50 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.50 inference(cnf_transformation,[],[f102])).
% 0.20/0.50 thf(f102,plain,(
% 0.20/0.50 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.50 inference(fool_elimination,[],[f101])).
% 0.20/0.50 thf(f101,plain,(
% 0.20/0.50 (mtransitive @ rel_s4)),
% 0.20/0.50 inference(rectify,[],[f35])).
% 0.20/0.50 thf(f35,axiom,(
% 0.20/0.50 (mtransitive @ rel_s4)),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.20/0.50 thf(f428,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | ~spl0_12),
% 0.20/0.50 inference(avatar_component_clause,[],[f426])).
% 0.20/0.50 thf(f426,plain,(
% 0.20/0.50 spl0_12 <=> ($true = (rel_s4 @ sK3 @ sK8))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.20/0.50 thf(f715,plain,(
% 0.20/0.50 spl0_16 | spl0_17 | ~spl0_1 | ~spl0_3 | ~spl0_9),
% 0.20/0.50 inference(avatar_split_clause,[],[f693,f370,f219,f210,f709,f705])).
% 0.20/0.50 thf(f210,plain,(
% 0.20/0.50 spl0_1 <=> ! [X2 : mu,X1] : (((exists_in_world @ X2 @ X1) = $false) | ($false = (f @ X2 @ (sK7 @ X1 @ X2))) | ((rel_s4 @ sK3 @ X1) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.50 thf(f219,plain,(
% 0.20/0.50 spl0_3 <=> ! [X2 : mu,X1] : (($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.50 thf(f370,plain,(
% 0.20/0.50 spl0_9 <=> ! [X4] : (($true = (f @ sK9 @ X4)) | ($false = (rel_s4 @ sK10 @ X4)))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.20/0.50 thf(f693,plain,(
% 0.20/0.50 ((rel_s4 @ sK3 @ sK10) = $false) | ((exists_in_world @ sK9 @ sK10) = $false) | (~spl0_1 | ~spl0_3 | ~spl0_9)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f692])).
% 0.20/0.50 thf(f692,plain,(
% 0.20/0.50 ($true = $false) | ((rel_s4 @ sK3 @ sK10) = $false) | ((exists_in_world @ sK9 @ sK10) = $false) | (~spl0_1 | ~spl0_3 | ~spl0_9)),
% 0.20/0.50 inference(duplicate_literal_removal,[],[f689])).
% 0.20/0.50 thf(f689,plain,(
% 0.20/0.50 ((rel_s4 @ sK3 @ sK10) = $false) | ((rel_s4 @ sK3 @ sK10) = $false) | ((exists_in_world @ sK9 @ sK10) = $false) | ((exists_in_world @ sK9 @ sK10) = $false) | ($true = $false) | (~spl0_1 | ~spl0_3 | ~spl0_9)),
% 0.20/0.50 inference(superposition,[],[f220,f681])).
% 0.20/0.50 thf(f681,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (($false = (rel_s4 @ sK10 @ (sK7 @ X0 @ sK9))) | ((rel_s4 @ sK3 @ X0) = $false) | ($false = (exists_in_world @ sK9 @ X0))) ) | (~spl0_1 | ~spl0_9)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f679])).
% 0.20/0.50 thf(f679,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (($false = (exists_in_world @ sK9 @ X0)) | ($true = $false) | ($false = (rel_s4 @ sK10 @ (sK7 @ X0 @ sK9))) | ((rel_s4 @ sK3 @ X0) = $false)) ) | (~spl0_1 | ~spl0_9)),
% 0.20/0.50 inference(superposition,[],[f211,f371])).
% 0.20/0.50 thf(f371,plain,(
% 0.20/0.50 ( ! [X4 : $i] : (($true = (f @ sK9 @ X4)) | ($false = (rel_s4 @ sK10 @ X4))) ) | ~spl0_9),
% 0.20/0.50 inference(avatar_component_clause,[],[f370])).
% 0.20/0.50 thf(f211,plain,(
% 0.20/0.50 ( ! [X2 : mu,X1 : $i] : (($false = (f @ X2 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) ) | ~spl0_1),
% 0.20/0.50 inference(avatar_component_clause,[],[f210])).
% 0.20/0.50 thf(f220,plain,(
% 0.20/0.50 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) ) | ~spl0_3),
% 0.20/0.50 inference(avatar_component_clause,[],[f219])).
% 0.20/0.50 thf(f666,plain,(
% 0.20/0.50 ~spl0_4 | ~spl0_5 | ~spl0_14),
% 0.20/0.50 inference(avatar_contradiction_clause,[],[f665])).
% 0.20/0.50 thf(f665,plain,(
% 0.20/0.50 $false | (~spl0_4 | ~spl0_5 | ~spl0_14)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f658])).
% 0.20/0.50 thf(f658,plain,(
% 0.20/0.50 ($true = $false) | (~spl0_4 | ~spl0_5 | ~spl0_14)),
% 0.20/0.50 inference(superposition,[],[f654,f600])).
% 0.20/0.50 thf(f600,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f599])).
% 0.20/0.50 thf(f599,plain,(
% 0.20/0.50 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.20/0.50 inference(pi_clausification,[],[f148])).
% 0.20/0.50 thf(f148,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f145])).
% 0.20/0.50 thf(f145,plain,(
% 0.20/0.50 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.20/0.50 inference(definition_unfolding,[],[f114,f129])).
% 0.20/0.50 thf(f129,plain,(
% 0.20/0.50 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.50 inference(cnf_transformation,[],[f68])).
% 0.20/0.50 thf(f68,plain,(
% 0.20/0.50 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.50 inference(fool_elimination,[],[f67])).
% 0.20/0.50 thf(f67,plain,(
% 0.20/0.50 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.20/0.50 inference(rectify,[],[f18])).
% 0.20/0.50 thf(f18,axiom,(
% 0.20/0.50 ((^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))) = mreflexive)),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.20/0.50 thf(f114,plain,(
% 0.20/0.50 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.50 inference(cnf_transformation,[],[f98])).
% 0.20/0.50 thf(f98,plain,(
% 0.20/0.50 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.50 inference(fool_elimination,[],[f97])).
% 0.20/0.50 thf(f97,plain,(
% 0.20/0.50 (mreflexive @ rel_s4)),
% 0.20/0.50 inference(rectify,[],[f34])).
% 0.20/0.50 thf(f34,axiom,(
% 0.20/0.50 (mreflexive @ rel_s4)),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.20/0.50 thf(f654,plain,(
% 0.20/0.50 ((rel_s4 @ sK5 @ sK5) = $false) | (~spl0_4 | ~spl0_5 | ~spl0_14)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f653])).
% 0.20/0.50 thf(f653,plain,(
% 0.20/0.50 ((rel_s4 @ sK5 @ sK5) = $false) | ($true = $false) | (~spl0_4 | ~spl0_5 | ~spl0_14)),
% 0.20/0.50 inference(forward_demodulation,[],[f651,f253])).
% 0.20/0.50 thf(f253,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | ~spl0_5),
% 0.20/0.50 inference(avatar_component_clause,[],[f251])).
% 0.20/0.50 thf(f251,plain,(
% 0.20/0.50 spl0_5 <=> ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.20/0.50 thf(f651,plain,(
% 0.20/0.50 ((rel_s4 @ sK5 @ sK5) = $false) | ($false = (rel_s4 @ sK4 @ sK5)) | (~spl0_4 | ~spl0_14)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f647])).
% 0.20/0.50 thf(f647,plain,(
% 0.20/0.50 ($false = (rel_s4 @ sK4 @ sK5)) | ((rel_s4 @ sK5 @ sK5) = $false) | ($true = $false) | (~spl0_4 | ~spl0_14)),
% 0.20/0.50 inference(superposition,[],[f233,f640])).
% 0.20/0.50 thf(f640,plain,(
% 0.20/0.50 ( ! [X0 : $i] : (((exists_in_world @ sK6 @ X0) = $false) | ((rel_s4 @ sK4 @ X0) = $false) | ((rel_s4 @ X0 @ sK5) = $false)) ) | ~spl0_14),
% 0.20/0.50 inference(avatar_component_clause,[],[f639])).
% 0.20/0.50 thf(f639,plain,(
% 0.20/0.50 spl0_14 <=> ! [X0] : (((rel_s4 @ sK4 @ X0) = $false) | ((exists_in_world @ sK6 @ X0) = $false) | ((rel_s4 @ X0 @ sK5) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_14])])).
% 0.20/0.50 thf(f233,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK6 @ sK5)) | ~spl0_4),
% 0.20/0.50 inference(avatar_component_clause,[],[f231])).
% 0.20/0.50 thf(f231,plain,(
% 0.20/0.50 spl0_4 <=> ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.50 thf(f642,plain,(
% 0.20/0.50 spl0_14 | spl0_14 | ~spl0_2 | ~spl0_6 | ~spl0_7),
% 0.20/0.50 inference(avatar_split_clause,[],[f634,f295,f290,f213,f639,f639])).
% 0.20/0.50 thf(f213,plain,(
% 0.20/0.50 spl0_2 <=> ! [X3] : (($true = (f @ sK6 @ X3)) | ((rel_s4 @ sK5 @ X3) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.50 thf(f290,plain,(
% 0.20/0.50 spl0_6 <=> ! [X4 : mu,X5,X2] : (($true = (rel_s4 @ X5 @ (sK7 @ X5 @ X4))) | ((rel_s4 @ sK4 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X2 @ X5) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.50 thf(f295,plain,(
% 0.20/0.50 spl0_7 <=> ! [X2,X5,X4 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X2 @ X5) = $false) | ((f @ X4 @ (sK7 @ X5 @ X4)) = $false) | ((rel_s4 @ sK4 @ X2) = $false))),
% 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.20/0.50 thf(f634,plain,(
% 0.20/0.50 ( ! [X0 : $i,X1 : $i] : (((exists_in_world @ sK6 @ X0) = $false) | ((rel_s4 @ X0 @ sK5) = $false) | ((rel_s4 @ sK4 @ X0) = $false) | ((exists_in_world @ sK6 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($false = (rel_s4 @ X1 @ sK5))) ) | (~spl0_2 | ~spl0_6 | ~spl0_7)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f629])).
% 0.20/0.50 thf(f629,plain,(
% 0.20/0.50 ( ! [X0 : $i,X1 : $i] : (((exists_in_world @ sK6 @ X1) = $false) | ((rel_s4 @ sK4 @ X0) = $false) | ($false = (rel_s4 @ X1 @ sK5)) | ((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X0 @ sK5) = $false) | ((exists_in_world @ sK6 @ X0) = $false) | ($true = $false)) ) | (~spl0_2 | ~spl0_6 | ~spl0_7)),
% 0.20/0.50 inference(superposition,[],[f625,f291])).
% 0.20/0.50 thf(f291,plain,(
% 0.20/0.50 ( ! [X2 : $i,X4 : mu,X5 : $i] : (($true = (rel_s4 @ X5 @ (sK7 @ X5 @ X4))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ X2 @ X5) = $false)) ) | ~spl0_6),
% 0.20/0.50 inference(avatar_component_clause,[],[f290])).
% 0.20/0.50 thf(f625,plain,(
% 0.20/0.50 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ sK5 @ (sK7 @ X0 @ sK6)) = $false) | ((rel_s4 @ X1 @ X0) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ sK6 @ X1) = $false)) ) | (~spl0_2 | ~spl0_7)),
% 0.20/0.50 inference(trivial_inequality_removal,[],[f623])).
% 0.20/0.50 thf(f623,plain,(
% 0.20/0.50 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ sK5 @ (sK7 @ X0 @ sK6)) = $false) | ((rel_s4 @ X1 @ X0) = $false) | ($true = $false) | ((exists_in_world @ sK6 @ X1) = $false)) ) | (~spl0_2 | ~spl0_7)),
% 0.20/0.50 inference(superposition,[],[f296,f214])).
% 0.20/0.50 thf(f214,plain,(
% 0.20/0.50 ( ! [X3 : $i] : (($true = (f @ sK6 @ X3)) | ((rel_s4 @ sK5 @ X3) = $false)) ) | ~spl0_2),
% 0.20/0.50 inference(avatar_component_clause,[],[f213])).
% 0.20/0.50 thf(f296,plain,(
% 0.20/0.50 ( ! [X2 : $i,X4 : mu,X5 : $i] : (((f @ X4 @ (sK7 @ X5 @ X4)) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X2 @ X5) = $false) | ((rel_s4 @ sK4 @ X2) = $false)) ) | ~spl0_7),
% 0.20/0.50 inference(avatar_component_clause,[],[f295])).
% 0.20/0.50 thf(f522,plain,(
% 0.20/0.50 spl0_2 | spl0_11),
% 0.20/0.50 inference(avatar_split_clause,[],[f521,f402,f213])).
% 0.20/0.50 thf(f521,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (f @ sK6 @ X1)) | ($true = (exists_in_world @ sK9 @ sK8)) | ((rel_s4 @ sK5 @ X1) = $false)) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f520])).
% 0.20/0.50 thf(f520,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((~ (rel_s4 @ sK5 @ X1)) = $true) | ($true = (exists_in_world @ sK9 @ sK8)) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f519])).
% 0.20/0.50 thf(f519,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (exists_in_world @ sK9 @ sK8)) | ($true = ((f @ sK6 @ X1) | (~ (rel_s4 @ sK5 @ X1))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f518])).
% 0.20/0.50 thf(f518,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))) @ X1)) | ($true = (exists_in_world @ sK9 @ sK8))) )),
% 0.20/0.50 inference(pi_clausification,[],[f497])).
% 0.20/0.50 thf(f497,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) | ($true = (exists_in_world @ sK9 @ sK8))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f495])).
% 0.20/0.50 thf(f495,plain,(
% 0.20/0.50 (((exists_in_world @ sK9 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f494])).
% 0.20/0.50 thf(f494,plain,(
% 0.20/0.50 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1))))))) @ sK9) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(sigma_clausification,[],[f493])).
% 0.20/0.50 thf(f493,plain,(
% 0.20/0.50 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f474])).
% 0.20/0.50 thf(f474,plain,(
% 0.20/0.50 ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f473])).
% 0.20/0.50 thf(f473,plain,(
% 0.20/0.50 ($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.50 inference(beta_eta_normalization,[],[f472])).
% 0.20/0.50 thf(f472,plain,(
% 0.20/0.50 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))) @ sK6) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f453])).
% 0.20/0.50 thf(f453,plain,(
% 0.20/0.50 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f435])).
% 0.20/0.50 thf(f435,plain,(
% 0.20/0.50 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))) | (~ (rel_s4 @ sK4 @ sK5))) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f433])).
% 0.20/0.50 thf(f433,plain,(
% 0.20/0.50 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK8))) = $false) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))) | (~ (rel_s4 @ sK4 @ sK5))) = $false)),
% 0.20/0.50 inference(beta_eta_normalization,[],[f432])).
% 0.20/0.50 thf(f432,plain,(
% 0.20/0.50 ($false = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ sK5)) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK8))) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f335])).
% 0.20/0.50 thf(f335,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0))))) = $false) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK8))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f334])).
% 0.20/0.50 thf(f334,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) = $false) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK8))) = $false)),
% 0.20/0.50 inference(beta_eta_normalization,[],[f333])).
% 0.20/0.50 thf(f333,plain,(
% 0.20/0.50 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ sK8) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f332])).
% 0.20/0.50 thf(f332,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f177])).
% 0.20/0.50 thf(f177,plain,(
% 0.20/0.50 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (~ (rel_s4 @ sK2 @ sK4)))) | ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f176])).
% 0.20/0.50 thf(f176,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (~ (rel_s4 @ sK2 @ sK4))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f175])).
% 0.20/0.50 thf(f175,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) = $false) | ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK4))),
% 0.20/0.50 inference(sigma_clausification,[],[f174])).
% 0.20/0.50 thf(f174,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) = $false)),
% 0.20/0.50 inference(not_proxy_clausification,[],[f173])).
% 0.20/0.50 thf(f173,plain,(
% 0.20/0.50 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0))))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f171])).
% 0.20/0.50 thf(f171,plain,(
% 0.20/0.50 ((((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | (~ (rel_s4 @ sK2 @ sK3))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f170])).
% 0.20/0.50 thf(f170,plain,(
% 0.20/0.50 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))))),
% 0.20/0.50 inference(sigma_clausification,[],[f169])).
% 0.20/0.50 thf(f169,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f168])).
% 0.20/0.50 thf(f168,plain,(
% 0.20/0.50 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f167])).
% 0.20/0.50 thf(f167,plain,(
% 0.20/0.50 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0))))))))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f166])).
% 0.20/0.50 thf(f166,plain,(
% 0.20/0.50 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y1 @ Y3)))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y2 @ Y3) | (~ (rel_s4 @ Y1 @ Y3))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK2 @ Y0)))))))) = $false)),
% 0.20/0.50 inference(beta_eta_normalization,[],[f165])).
% 0.20/0.50 thf(f165,plain,(
% 0.20/0.50 (((^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1))))))))) @ sK2) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f164])).
% 0.20/0.50 thf(f164,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))))))) = $false)),
% 0.20/0.50 inference(not_proxy_clausification,[],[f150])).
% 0.20/0.50 thf(f150,plain,(
% 0.20/0.50 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1))))))))))))),
% 0.20/0.50 inference(boolean_simplification,[],[f149])).
% 0.20/0.50 thf(f149,plain,(
% 0.20/0.50 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ $i @ (^[Y5 : $i]: ((f @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y2 @ Y4)))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ (!! @ $i @ (^[Y4 : $i]: ((f @ Y3 @ Y4) | (~ (rel_s4 @ Y2 @ Y4))))))))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1))))))))))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f146])).
% 0.20/0.50 thf(f146,plain,(
% 0.20/0.50 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ (f @ Y0)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ (f @ Y0))))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ (f @ Y0))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ (f @ Y0))))))))))))),
% 0.20/0.50 inference(definition_unfolding,[],[f127,f124,f138,f116,f139,f116,f132,f137,f116,f116,f136,f116,f132,f116,f116,f139,f116,f136,f116,f132,f116,f116,f132,f137,f116])).
% 0.20/0.50 thf(f136,plain,(
% 0.20/0.50 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f106])).
% 0.20/0.50 thf(f106,plain,(
% 0.20/0.50 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.50 inference(fool_elimination,[],[f105])).
% 0.20/0.50 thf(f105,plain,(
% 0.20/0.50 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.20/0.50 inference(rectify,[],[f15])).
% 0.20/0.50 thf(f15,axiom,(
% 0.20/0.50 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.20/0.50 thf(f137,plain,(
% 0.20/0.50 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.20/0.50 inference(definition_unfolding,[],[f133,f132,f136,f132])).
% 0.20/0.50 thf(f133,plain,(
% 0.20/0.50 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f78])).
% 0.20/0.50 thf(f78,plain,(
% 0.20/0.50 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.20/0.50 inference(fool_elimination,[],[f77])).
% 0.20/0.50 thf(f77,plain,(
% 0.20/0.50 (mexists_ind = (^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))))),
% 0.20/0.50 inference(rectify,[],[f16])).
% 0.20/0.50 thf(f16,axiom,(
% 0.20/0.50 (mexists_ind = (^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.20/0.50 thf(f132,plain,(
% 0.20/0.50 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f72])).
% 0.20/0.50 thf(f72,plain,(
% 0.20/0.50 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.50 inference(fool_elimination,[],[f71])).
% 0.20/0.50 thf(f71,plain,(
% 0.20/0.50 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.50 inference(rectify,[],[f2])).
% 0.20/0.50 thf(f2,axiom,(
% 0.20/0.50 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.50 thf(f139,plain,(
% 0.20/0.50 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.50 inference(definition_unfolding,[],[f123,f126,f132])).
% 0.20/0.50 thf(f126,plain,(
% 0.20/0.50 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f82])).
% 0.20/0.50 thf(f82,plain,(
% 0.20/0.50 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.50 inference(fool_elimination,[],[f81])).
% 0.20/0.50 thf(f81,plain,(
% 0.20/0.50 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.50 inference(rectify,[],[f3])).
% 0.20/0.50 thf(f3,axiom,(
% 0.20/0.50 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.50 thf(f123,plain,(
% 0.20/0.50 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.50 inference(cnf_transformation,[],[f43])).
% 0.20/0.50 thf(f43,plain,(
% 0.20/0.50 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.50 inference(fool_elimination,[],[f42])).
% 0.20/0.50 thf(f42,plain,(
% 0.20/0.50 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.50 inference(rectify,[],[f9])).
% 0.20/0.50 thf(f9,axiom,(
% 0.20/0.50 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.50 thf(f116,plain,(
% 0.20/0.50 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f96])).
% 0.20/0.50 thf(f96,plain,(
% 0.20/0.50 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.20/0.50 inference(fool_elimination,[],[f95])).
% 0.20/0.50 thf(f95,plain,(
% 0.20/0.50 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))))),
% 0.20/0.50 inference(rectify,[],[f32])).
% 0.20/0.50 thf(f32,axiom,(
% 0.20/0.50 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : (~(rel_s4 @ X2 @ X6) | (X3 @ X6)))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.50 thf(f138,plain,(
% 0.20/0.50 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.50 inference(definition_unfolding,[],[f115,f132,f126,f132,f132])).
% 0.20/0.50 thf(f115,plain,(
% 0.20/0.50 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f57])).
% 0.20/0.50 thf(f57,plain,(
% 0.20/0.50 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.50 inference(fool_elimination,[],[f56])).
% 0.20/0.50 thf(f56,plain,(
% 0.20/0.50 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.50 inference(rectify,[],[f8])).
% 0.20/0.50 thf(f8,axiom,(
% 0.20/0.50 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.50 thf(f124,plain,(
% 0.20/0.50 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.50 inference(cnf_transformation,[],[f76])).
% 0.20/0.50 thf(f76,plain,(
% 0.20/0.50 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.50 inference(fool_elimination,[],[f75])).
% 0.20/0.50 thf(f75,plain,(
% 0.20/0.50 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.20/0.50 inference(rectify,[],[f28])).
% 0.20/0.50 thf(f28,axiom,(
% 0.20/0.50 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.50 thf(f127,plain,(
% 0.20/0.50 ($true = (~ (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (f @ Y0)))))) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ Y0))))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ Y0))))))) @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (f @ Y0))))))))))))),
% 0.20/0.50 inference(cnf_transformation,[],[f55])).
% 0.20/0.50 thf(f55,plain,(
% 0.20/0.50 ($true = (~ (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (f @ Y0)))))) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ Y0))))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ Y0))))))) @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (f @ Y0))))))))))))),
% 0.20/0.50 inference(fool_elimination,[],[f54])).
% 0.20/0.50 thf(f54,plain,(
% 0.20/0.50 ~(mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (f @ X0)))))) @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X1))))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X2 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X2))))))) @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X3 : mu] : (mbox_s4 @ (f @ X3))))))))))),
% 0.20/0.50 inference(rectify,[],[f38])).
% 0.20/0.50 thf(f38,negated_conjecture,(
% 0.20/0.50 ~(mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (f @ X0)))))) @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X1))))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X1))))))) @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (f @ X0))))))))))),
% 0.20/0.50 inference(negated_conjecture,[],[f37])).
% 0.20/0.50 thf(f37,conjecture,(
% 0.20/0.50 (mvalid @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (f @ X0)))))) @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X1))))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (mnot @ (mbox_s4 @ (f @ X1))))))) @ (mbox_s4 @ (mnot @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (f @ X0))))))))))),
% 0.20/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish204)).
% 0.20/0.50 thf(f517,plain,(
% 0.20/0.50 spl0_9 | spl0_2),
% 0.20/0.50 inference(avatar_split_clause,[],[f516,f213,f370])).
% 0.20/0.50 thf(f516,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK10 @ X2) = $false) | ((rel_s4 @ sK5 @ X1) = $false) | ($true = (f @ sK9 @ X2)) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f515])).
% 0.20/0.50 thf(f515,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (($true = (f @ sK9 @ X2)) | ($true = (f @ sK6 @ X1)) | ((~ (rel_s4 @ sK10 @ X2)) = $true) | ((rel_s4 @ sK5 @ X1) = $false)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f514])).
% 0.20/0.50 thf(f514,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK5 @ X1) = $false) | ($true = ((f @ sK9 @ X2) | (~ (rel_s4 @ sK10 @ X2)))) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f513])).
% 0.20/0.50 thf(f513,plain,(
% 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (($true = (f @ sK6 @ X1)) | ((rel_s4 @ sK5 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))) @ X2))) )),
% 0.20/0.50 inference(pi_clausification,[],[f512])).
% 0.20/0.50 thf(f512,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((rel_s4 @ sK5 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f511])).
% 0.20/0.50 thf(f511,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false) | ((rel_s4 @ sK5 @ X1) = $false) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f510])).
% 0.20/0.50 thf(f510,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((~ (rel_s4 @ sK5 @ X1)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f509])).
% 0.20/0.50 thf(f509,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((f @ sK6 @ X1) | (~ (rel_s4 @ sK5 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false)) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f508])).
% 0.20/0.50 thf(f508,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))) @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false)) )),
% 0.20/0.50 inference(pi_clausification,[],[f501])).
% 0.20/0.50 thf(f501,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f499])).
% 0.20/0.50 thf(f499,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f498])).
% 0.20/0.50 thf(f498,plain,(
% 0.20/0.50 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))) @ sK10) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(sigma_clausification,[],[f496])).
% 0.20/0.50 thf(f496,plain,(
% 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f495])).
% 0.20/0.50 thf(f507,plain,(
% 0.20/0.50 spl0_2 | spl0_10),
% 0.20/0.50 inference(avatar_split_clause,[],[f506,f376,f213])).
% 0.20/0.50 thf(f506,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (f @ sK6 @ X1)) | ($true = (rel_s4 @ sK8 @ sK10)) | ((rel_s4 @ sK5 @ X1) = $false)) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f505])).
% 0.20/0.50 thf(f505,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((~ (rel_s4 @ sK5 @ X1)) = $true) | ($true = (rel_s4 @ sK8 @ sK10)) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f504])).
% 0.20/0.50 thf(f504,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ sK8 @ sK10)) | ($true = ((f @ sK6 @ X1) | (~ (rel_s4 @ sK5 @ X1))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f503])).
% 0.20/0.50 thf(f503,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ sK8 @ sK10)) | ($true = ((^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))) @ X1))) )),
% 0.20/0.50 inference(pi_clausification,[],[f502])).
% 0.20/0.50 thf(f502,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) | ($true = (rel_s4 @ sK8 @ sK10))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f500])).
% 0.20/0.50 thf(f500,plain,(
% 0.20/0.50 ($false = (~ (rel_s4 @ sK8 @ sK10))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f499])).
% 0.20/0.50 thf(f492,plain,(
% 0.20/0.50 spl0_10 | spl0_4),
% 0.20/0.50 inference(avatar_split_clause,[],[f491,f231,f376])).
% 0.20/0.50 thf(f491,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK8 @ sK10)) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f483])).
% 0.20/0.50 thf(f483,plain,(
% 0.20/0.50 ($false = (~ (rel_s4 @ sK8 @ sK10))) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f482])).
% 0.20/0.50 thf(f482,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f481])).
% 0.20/0.50 thf(f481,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK6 @ sK5)) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))) @ sK10) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f478])).
% 0.20/0.50 thf(f478,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK6 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f477])).
% 0.20/0.50 thf(f477,plain,(
% 0.20/0.50 (((exists_in_world @ sK9 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))))) = $false) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f476])).
% 0.20/0.50 thf(f476,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK6 @ sK5)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1))))))) @ sK9) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f475])).
% 0.20/0.50 thf(f475,plain,(
% 0.20/0.50 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f473])).
% 0.20/0.50 thf(f490,plain,(
% 0.20/0.50 spl0_4 | spl0_9),
% 0.20/0.50 inference(avatar_split_clause,[],[f489,f370,f231])).
% 0.20/0.50 thf(f489,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($false = (rel_s4 @ sK10 @ X1)) | ($true = (exists_in_world @ sK6 @ sK5)) | ($true = (f @ sK9 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f488])).
% 0.20/0.50 thf(f488,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ($true = (f @ sK9 @ X1)) | ((~ (rel_s4 @ sK10 @ X1)) = $true)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f487])).
% 0.20/0.50 thf(f487,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ($true = ((f @ sK9 @ X1) | (~ (rel_s4 @ sK10 @ X1))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f486])).
% 0.20/0.50 thf(f486,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ($true = ((^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))) @ X1))) )),
% 0.20/0.50 inference(pi_clausification,[],[f485])).
% 0.20/0.50 thf(f485,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f484])).
% 0.20/0.50 thf(f484,plain,(
% 0.20/0.50 ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f482])).
% 0.20/0.50 thf(f480,plain,(
% 0.20/0.50 spl0_11 | spl0_4),
% 0.20/0.50 inference(avatar_split_clause,[],[f479,f231,f402])).
% 0.20/0.50 thf(f479,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK9 @ sK8)) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f477])).
% 0.20/0.50 thf(f471,plain,(
% 0.20/0.50 spl0_11 | spl0_5),
% 0.20/0.50 inference(avatar_split_clause,[],[f458,f251,f402])).
% 0.20/0.50 thf(f458,plain,(
% 0.20/0.50 ($true = (exists_in_world @ sK9 @ sK8)) | ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f456])).
% 0.20/0.50 thf(f456,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | (((exists_in_world @ sK9 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))))) = $false)),
% 0.20/0.50 inference(not_proxy_clausification,[],[f455])).
% 0.20/0.50 thf(f455,plain,(
% 0.20/0.50 ((~ (rel_s4 @ sK4 @ sK5)) = $false) | (((exists_in_world @ sK9 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))))) = $false)),
% 0.20/0.50 inference(beta_eta_normalization,[],[f454])).
% 0.20/0.50 thf(f454,plain,(
% 0.20/0.50 ((~ (rel_s4 @ sK4 @ sK5)) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1))))))) @ sK9) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f452])).
% 0.20/0.50 thf(f452,plain,(
% 0.20/0.50 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ((~ (rel_s4 @ sK4 @ sK5)) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f435])).
% 0.20/0.50 thf(f470,plain,(
% 0.20/0.50 spl0_9 | spl0_5),
% 0.20/0.50 inference(avatar_split_clause,[],[f469,f251,f370])).
% 0.20/0.50 thf(f469,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ sK4 @ sK5)) | ($false = (rel_s4 @ sK10 @ X1)) | ($true = (f @ sK9 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f468])).
% 0.20/0.50 thf(f468,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((~ (rel_s4 @ sK10 @ X1)) = $true) | ($true = (rel_s4 @ sK4 @ sK5)) | ($true = (f @ sK9 @ X1))) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f467])).
% 0.20/0.50 thf(f467,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((f @ sK9 @ X1) | (~ (rel_s4 @ sK10 @ X1)))) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f466])).
% 0.20/0.50 thf(f466,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ sK4 @ sK5)) | ($true = ((^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))) @ X1))) )),
% 0.20/0.50 inference(pi_clausification,[],[f465])).
% 0.20/0.50 thf(f465,plain,(
% 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f462])).
% 0.20/0.50 thf(f462,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f460])).
% 0.20/0.50 thf(f460,plain,(
% 0.20/0.50 (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false) | ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f459])).
% 0.20/0.50 thf(f459,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))) @ sK10) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f457])).
% 0.20/0.50 thf(f457,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f456])).
% 0.20/0.50 thf(f464,plain,(
% 0.20/0.50 spl0_10 | spl0_5),
% 0.20/0.50 inference(avatar_split_clause,[],[f463,f251,f376])).
% 0.20/0.50 thf(f463,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK8 @ sK10)) | ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f461])).
% 0.20/0.50 thf(f461,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK4 @ sK5)) | ($false = (~ (rel_s4 @ sK8 @ sK10)))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f460])).
% 0.20/0.50 thf(f451,plain,(
% 0.20/0.50 spl0_5 | spl0_12),
% 0.20/0.50 inference(avatar_split_clause,[],[f450,f426,f251])).
% 0.20/0.50 thf(f450,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f437])).
% 0.20/0.50 thf(f437,plain,(
% 0.20/0.50 ((~ (rel_s4 @ sK4 @ sK5)) = $false) | ($true = (rel_s4 @ sK3 @ sK8))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f436])).
% 0.20/0.50 thf(f436,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))) | (~ (rel_s4 @ sK4 @ sK5))) = $false)),
% 0.20/0.50 inference(not_proxy_clausification,[],[f434])).
% 0.20/0.50 thf(f434,plain,(
% 0.20/0.50 ((~ (rel_s4 @ sK3 @ sK8)) = $false) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))) | (~ (rel_s4 @ sK4 @ sK5))) = $false)),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f433])).
% 0.20/0.50 thf(f449,plain,(
% 0.20/0.50 spl0_12 | spl0_2),
% 0.20/0.50 inference(avatar_split_clause,[],[f448,f213,f426])).
% 0.20/0.50 thf(f448,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (((rel_s4 @ sK5 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ($true = (f @ sK6 @ X1))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f447])).
% 0.20/0.50 thf(f447,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (f @ sK6 @ X1)) | ($true = (rel_s4 @ sK3 @ sK8)) | ((~ (rel_s4 @ sK5 @ X1)) = $true)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f446])).
% 0.20/0.50 thf(f446,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = (rel_s4 @ sK3 @ sK8)) | ($true = ((f @ sK6 @ X1) | (~ (rel_s4 @ sK5 @ X1))))) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f445])).
% 0.20/0.50 thf(f445,plain,(
% 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))) @ X1)) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.50 inference(pi_clausification,[],[f444])).
% 0.20/0.50 thf(f444,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))),
% 0.20/0.50 inference(not_proxy_clausification,[],[f441])).
% 0.20/0.50 thf(f441,plain,(
% 0.20/0.50 ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) = $false) | ($true = (rel_s4 @ sK3 @ sK8))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f440])).
% 0.20/0.50 thf(f440,plain,(
% 0.20/0.50 ($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))))) | ($true = (rel_s4 @ sK3 @ sK8))),
% 0.20/0.50 inference(beta_eta_normalization,[],[f439])).
% 0.20/0.50 thf(f439,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))) @ sK6) = $false)),
% 0.20/0.50 inference(sigma_clausification,[],[f438])).
% 0.20/0.50 thf(f438,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f436])).
% 0.20/0.50 thf(f443,plain,(
% 0.20/0.50 spl0_12 | spl0_4),
% 0.20/0.50 inference(avatar_split_clause,[],[f442,f231,f426])).
% 0.20/0.50 thf(f442,plain,(
% 0.20/0.50 ($true = (rel_s4 @ sK3 @ sK8)) | ($true = (exists_in_world @ sK6 @ sK5))),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f440])).
% 0.20/0.50 thf(f431,plain,(
% 0.20/0.50 spl0_12 | spl0_6),
% 0.20/0.50 inference(avatar_split_clause,[],[f430,f290,f426])).
% 0.20/0.50 thf(f430,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (rel_s4 @ sK3 @ sK8)) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f423])).
% 0.20/0.50 thf(f423,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2))) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.50 inference(binary_proxy_clausification,[],[f422])).
% 0.20/0.50 thf(f422,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X3) = $false) | (((f @ X2 @ (sK7 @ X3 @ X2)) | (~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2)))) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.50 inference(beta_eta_normalization,[],[f421])).
% 0.20/0.50 thf(f421,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ($false = ((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0)))) @ (sK7 @ X3 @ X2)))) )),
% 0.20/0.50 inference(sigma_clausification,[],[f420])).
% 0.20/0.50 thf(f420,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.50 inference(not_proxy_clausification,[],[f419])).
% 0.20/0.50 thf(f419,plain,(
% 0.20/0.50 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))))) | ((rel_s4 @ X1 @ X3) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f418])).
% 0.20/0.51 thf(f418,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (rel_s4 @ sK3 @ sK8)) | ($true = (~ (rel_s4 @ X1 @ X3))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))))) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f417])).
% 0.20/0.51 thf(f417,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (rel_s4 @ sK3 @ sK8)) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0)))))) | (~ (rel_s4 @ X1 @ X3)))) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f416])).
% 0.20/0.51 thf(f416,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))) @ X3)) | ($true = (rel_s4 @ sK3 @ sK8)) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f415])).
% 0.20/0.51 thf(f415,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))))) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8)) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f414])).
% 0.20/0.51 thf(f414,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ($true = ((exists_in_world @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f413])).
% 0.20/0.51 thf(f413,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ sK3 @ sK8)) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ($true = ((exists_in_world @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))))))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f412])).
% 0.20/0.51 thf(f412,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((~ (rel_s4 @ sK4 @ X1)) = $true) | ($true = (rel_s4 @ sK3 @ sK8)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1))))))) @ X2) = $true)) )),
% 0.20/0.51 inference(pi_clausification,[],[f411])).
% 0.20/0.51 thf(f411,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1)))))))) = $true) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f410])).
% 0.20/0.51 thf(f410,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ X1)))) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f409])).
% 0.20/0.51 thf(f409,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ X1)) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.51 inference(pi_clausification,[],[f408])).
% 0.20/0.51 thf(f408,plain,(
% 0.20/0.51 ($true = (rel_s4 @ sK3 @ sK8)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f407])).
% 0.20/0.51 thf(f407,plain,(
% 0.20/0.51 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))) | ($true = (rel_s4 @ sK3 @ sK8))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f337])).
% 0.20/0.51 thf(f337,plain,(
% 0.20/0.51 ((~ (rel_s4 @ sK3 @ sK8)) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f336])).
% 0.20/0.51 thf(f336,plain,(
% 0.20/0.51 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) | (~ (rel_s4 @ sK3 @ sK8))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f334])).
% 0.20/0.51 thf(f429,plain,(
% 0.20/0.51 spl0_12 | spl0_7),
% 0.20/0.51 inference(avatar_split_clause,[],[f424,f295,f426])).
% 0.20/0.51 thf(f424,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (rel_s4 @ sK3 @ sK8))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f422])).
% 0.20/0.51 thf(f406,plain,(
% 0.20/0.51 spl0_11 | spl0_7),
% 0.20/0.51 inference(avatar_split_clause,[],[f399,f295,f402])).
% 0.20/0.51 thf(f399,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (exists_in_world @ sK9 @ sK8)) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f397])).
% 0.20/0.51 thf(f397,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | (((f @ X2 @ (sK7 @ X3 @ X2)) | (~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2)))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (exists_in_world @ sK9 @ sK8)) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f396])).
% 0.20/0.51 thf(f396,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ($false = ((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0)))) @ (sK7 @ X3 @ X2))) | ((rel_s4 @ X1 @ X3) = $false) | ($true = (exists_in_world @ sK9 @ sK8)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f395])).
% 0.20/0.51 thf(f395,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ($true = (exists_in_world @ sK9 @ sK8)) | ((exists_in_world @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f394])).
% 0.20/0.51 thf(f394,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (~ (rel_s4 @ X1 @ X3))) | ($true = (exists_in_world @ sK9 @ sK8)) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f353])).
% 0.20/0.51 thf(f353,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ($true = (exists_in_world @ sK9 @ sK8))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f351])).
% 0.20/0.51 thf(f351,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((exists_in_world @ sK9 @ sK8) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((~ (rel_s4 @ sK4 @ X1)) = $true)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f350])).
% 0.20/0.51 thf(f350,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1))))))) @ sK9) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (rel_s4 @ X1 @ X3)))) )),
% 0.20/0.51 inference(sigma_clausification,[],[f349])).
% 0.20/0.51 thf(f349,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((~ (rel_s4 @ sK4 @ X1)) = $true)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f348])).
% 0.20/0.51 thf(f348,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))))) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f347])).
% 0.20/0.51 thf(f347,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0)))))) | (~ (rel_s4 @ X1 @ X3)))) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f346])).
% 0.20/0.51 thf(f346,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))) @ X3)) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f345])).
% 0.20/0.51 thf(f345,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((~ (rel_s4 @ sK4 @ X1)) = $true)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f344])).
% 0.20/0.51 thf(f344,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = ((exists_in_world @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X2 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0))))))) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f343])).
% 0.20/0.51 thf(f343,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1))))))) @ X2) = $true) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f342])).
% 0.20/0.51 thf(f342,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1)))))))) = $true) | ((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f341])).
% 0.20/0.51 thf(f341,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X1 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ X1)))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f340])).
% 0.20/0.51 thf(f340,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ X1)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f339])).
% 0.20/0.51 thf(f339,plain,(
% 0.20/0.51 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.51 inference(not_proxy_clausification,[],[f338])).
% 0.20/0.51 thf(f338,plain,(
% 0.20/0.51 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK8) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK8 @ Y1)))))))) = $false)),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f336])).
% 0.20/0.51 thf(f405,plain,(
% 0.20/0.51 spl0_11 | spl0_6),
% 0.20/0.51 inference(avatar_split_clause,[],[f400,f290,f402])).
% 0.20/0.51 thf(f400,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ($true = (exists_in_world @ sK9 @ sK8))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f398])).
% 0.20/0.51 thf(f398,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (exists_in_world @ sK9 @ sK8))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f397])).
% 0.20/0.51 thf(f393,plain,(
% 0.20/0.51 spl0_10 | spl0_6),
% 0.20/0.51 inference(avatar_split_clause,[],[f392,f290,f376])).
% 0.20/0.51 thf(f392,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ($true = (rel_s4 @ sK8 @ sK10)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f384])).
% 0.20/0.51 thf(f384,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($false = (~ (rel_s4 @ sK8 @ sK10))) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f383])).
% 0.20/0.51 thf(f383,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ sK4 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f382])).
% 0.20/0.51 thf(f382,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f381])).
% 0.20/0.51 thf(f381,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (~ (rel_s4 @ X1 @ X3))) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))) @ sK10) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f380])).
% 0.20/0.51 thf(f380,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f357])).
% 0.20/0.51 thf(f357,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f356])).
% 0.20/0.51 thf(f356,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((f @ X2 @ (sK7 @ X3 @ X2)) | (~ (rel_s4 @ X3 @ (sK7 @ X3 @ X2)))) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f355])).
% 0.20/0.51 thf(f355,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0)))) @ (sK7 @ X3 @ X2))) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f354])).
% 0.20/0.51 thf(f354,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f352])).
% 0.20/0.51 thf(f352,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (rel_s4 @ sK4 @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X3 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f351])).
% 0.20/0.51 thf(f391,plain,(
% 0.20/0.51 spl0_6 | spl0_9),
% 0.20/0.51 inference(avatar_split_clause,[],[f390,f370,f290])).
% 0.20/0.51 thf(f390,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (f @ sK9 @ X4)) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ($false = (rel_s4 @ sK10 @ X4)) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f389])).
% 0.20/0.51 thf(f389,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((~ (rel_s4 @ sK10 @ X4)) = $true) | ($true = (f @ sK9 @ X4)) | ((rel_s4 @ X1 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f388])).
% 0.20/0.51 thf(f388,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((rel_s4 @ X1 @ X3) = $false) | (((f @ sK9 @ X4) | (~ (rel_s4 @ sK10 @ X4))) = $true) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f387])).
% 0.20/0.51 thf(f387,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))) @ X4) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f386])).
% 0.20/0.51 thf(f386,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f385])).
% 0.20/0.51 thf(f385,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ X3 @ (sK7 @ X3 @ X2)) = $true) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f383])).
% 0.20/0.51 thf(f379,plain,(
% 0.20/0.51 spl0_10 | spl0_7),
% 0.20/0.51 inference(avatar_split_clause,[],[f374,f295,f376])).
% 0.20/0.51 thf(f374,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (rel_s4 @ sK8 @ sK10)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f373])).
% 0.20/0.51 thf(f373,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ($false = (~ (rel_s4 @ sK8 @ sK10)))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f361])).
% 0.20/0.51 thf(f361,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (~ (rel_s4 @ X1 @ X3))) | ((exists_in_world @ X2 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ($false = (~ (rel_s4 @ sK8 @ sK10))) | ((rel_s4 @ sK4 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f360])).
% 0.20/0.51 thf(f360,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) | (~ (rel_s4 @ sK8 @ sK10))) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f359])).
% 0.20/0.51 thf(f359,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (~ (rel_s4 @ X1 @ X3))) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0)))) @ sK10) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f358])).
% 0.20/0.51 thf(f358,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ sK9 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK8 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f356])).
% 0.20/0.51 thf(f372,plain,(
% 0.20/0.51 spl0_7 | spl0_9),
% 0.20/0.51 inference(avatar_split_clause,[],[f368,f370,f295])).
% 0.20/0.51 thf(f368,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ($true = (f @ sK9 @ X4)) | ((rel_s4 @ sK4 @ X1) = $false) | ($false = (rel_s4 @ sK10 @ X4)) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f367])).
% 0.20/0.51 thf(f367,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((~ (rel_s4 @ sK10 @ X4)) = $true) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ($true = (f @ sK9 @ X4)) | ((rel_s4 @ sK4 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f366])).
% 0.20/0.51 thf(f366,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | (((f @ sK9 @ X4) | (~ (rel_s4 @ sK10 @ X4))) = $true) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f365])).
% 0.20/0.51 thf(f365,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i,X4 : $i] : (((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | (((^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))) @ X4) = $true)) )),
% 0.20/0.51 inference(pi_clausification,[],[f364])).
% 0.20/0.51 thf(f364,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ sK4 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0))))))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f363])).
% 0.20/0.51 thf(f363,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ((rel_s4 @ X1 @ X3) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f362])).
% 0.20/0.51 thf(f362,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((f @ X2 @ (sK7 @ X3 @ X2)) = $false) | ($true = (~ (rel_s4 @ X1 @ X3))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK9 @ Y0) | (~ (rel_s4 @ sK10 @ Y0)))))) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f360])).
% 0.20/0.51 thf(f309,plain,(
% 0.20/0.51 spl0_7 | spl0_1),
% 0.20/0.51 inference(avatar_split_clause,[],[f306,f210,f295])).
% 0.20/0.51 thf(f306,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((f @ X4 @ (sK7 @ X5 @ X4)) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ X2 @ X5) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f304])).
% 0.20/0.51 thf(f304,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ X2 @ X5) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | (((f @ X4 @ (sK7 @ X5 @ X4)) | (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f303])).
% 0.20/0.51 thf(f303,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | (((f @ X4 @ (sK7 @ X5 @ X4)) | (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f302])).
% 0.20/0.51 thf(f302,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | (((^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))) @ (sK7 @ X5 @ X4)) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f301])).
% 0.20/0.51 thf(f301,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0))))) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($true = (~ (rel_s4 @ X2 @ X5)))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f300])).
% 0.20/0.51 thf(f300,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))))) = $true) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X3 @ X1) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f299])).
% 0.20/0.51 thf(f299,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))))) | (~ (rel_s4 @ X2 @ X5)))) | ((exists_in_world @ X3 @ X1) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f298])).
% 0.20/0.51 thf(f298,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))) @ X5)) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f277])).
% 0.20/0.51 thf(f277,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ sK4 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X3 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) | ((rel_s4 @ sK3 @ X1) = $false) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f275])).
% 0.20/0.51 thf(f275,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($false = (exists_in_world @ X4 @ X2)) | (((f @ X3 @ (sK7 @ X1 @ X3)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3)))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f274])).
% 0.20/0.51 thf(f274,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ sK4 @ X2) = $false) | (((exists_in_world @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | (((f @ X3 @ (sK7 @ X1 @ X3)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3)))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f273])).
% 0.20/0.51 thf(f273,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : ((((exists_in_world @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | (((^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK7 @ X1 @ X3)) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f272])).
% 0.20/0.51 thf(f272,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | (((exists_in_world @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) = $true)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f271])).
% 0.20/0.51 thf(f271,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | (((exists_in_world @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f270])).
% 0.20/0.51 thf(f270,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ sK4 @ X2) = $false) | ($true = ((exists_in_world @ X3 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | (((exists_in_world @ X4 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f269])).
% 0.20/0.51 thf(f269,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($true = ((exists_in_world @ X3 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1))))))) @ X4) = $true)) )),
% 0.20/0.51 inference(pi_clausification,[],[f268])).
% 0.20/0.51 thf(f268,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) = $true) | ($true = ((exists_in_world @ X3 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X3 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f267])).
% 0.20/0.51 thf(f267,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) = $true) | ((rel_s4 @ sK4 @ X2) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1)))))))) @ X3) = $true)) )),
% 0.20/0.51 inference(pi_clausification,[],[f266])).
% 0.20/0.51 thf(f266,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK4 @ X2) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f265])).
% 0.20/0.51 thf(f265,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_s4 @ sK4 @ X2))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f264])).
% 0.20/0.51 thf(f264,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ X2)))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f263])).
% 0.20/0.51 thf(f263,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_s4 @ sK3 @ X1))) | ($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ X2)))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f262])).
% 0.20/0.51 thf(f262,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true) | ($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ X2 @ Y1)))))))) | (~ (rel_s4 @ sK4 @ X2))))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f261])).
% 0.20/0.51 thf(f261,plain,(
% 0.20/0.51 ( ! [X2 : $i,X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true) | ($true = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ X2))) )),
% 0.20/0.51 inference(pi_clausification,[],[f260])).
% 0.20/0.51 thf(f260,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f259])).
% 0.20/0.51 thf(f259,plain,(
% 0.20/0.51 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ X1) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))) )),
% 0.20/0.51 inference(pi_clausification,[],[f258])).
% 0.20/0.51 thf(f258,plain,(
% 0.20/0.51 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f257])).
% 0.20/0.51 thf(f257,plain,(
% 0.20/0.51 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f182])).
% 0.20/0.51 thf(f182,plain,(
% 0.20/0.51 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0))))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f180])).
% 0.20/0.51 thf(f180,plain,(
% 0.20/0.51 (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f178])).
% 0.20/0.51 thf(f178,plain,(
% 0.20/0.51 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((f @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y0 @ Y2)))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))))) | (~ (rel_s4 @ sK2 @ sK4)))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f176])).
% 0.20/0.51 thf(f308,plain,(
% 0.20/0.51 spl0_1 | spl0_6),
% 0.20/0.51 inference(avatar_split_clause,[],[f307,f290,f210])).
% 0.20/0.51 thf(f307,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($true = (rel_s4 @ X5 @ (sK7 @ X5 @ X4))) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ X2 @ X5) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f305])).
% 0.20/0.51 thf(f305,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($false = (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((f @ X3 @ (sK7 @ X1 @ X3)) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ X2 @ X5) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f304])).
% 0.20/0.51 thf(f297,plain,(
% 0.20/0.51 spl0_3 | spl0_7),
% 0.20/0.51 inference(avatar_split_clause,[],[f293,f295,f219])).
% 0.20/0.51 thf(f293,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ((f @ X4 @ (sK7 @ X5 @ X4)) = $false) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ X2 @ X5) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f286])).
% 0.20/0.51 thf(f286,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((f @ X4 @ (sK7 @ X5 @ X4)) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((rel_s4 @ sK4 @ X2) = $false) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) | ($false = (exists_in_world @ X4 @ X2)) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f284])).
% 0.20/0.51 thf(f284,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | (((f @ X4 @ (sK7 @ X5 @ X4)) | (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3)))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f283])).
% 0.20/0.51 thf(f283,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | (((f @ X4 @ (sK7 @ X5 @ X4)) | (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($true = (~ (rel_s4 @ X2 @ X5)))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f282])).
% 0.20/0.51 thf(f282,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($true = (~ (rel_s4 @ X2 @ X5))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | (((^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))) @ (sK7 @ X5 @ X4)) = $false) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f281])).
% 0.20/0.51 thf(f281,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0))))) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f280])).
% 0.20/0.51 thf(f280,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))))) = $true) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f279])).
% 0.20/0.51 thf(f279,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ X4 @ Y0) | (~ (rel_s4 @ X5 @ Y0)))))) | (~ (rel_s4 @ X2 @ X5)))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f278])).
% 0.20/0.51 thf(f278,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))) @ X5)) | ((rel_s4 @ sK4 @ X2) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f276])).
% 0.20/0.51 thf(f276,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((f @ X4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X2 @ Y0)))))) | ((exists_in_world @ X3 @ X1) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) = $false) | ((rel_s4 @ sK4 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f275])).
% 0.20/0.51 thf(f292,plain,(
% 0.20/0.51 spl0_6 | spl0_3),
% 0.20/0.51 inference(avatar_split_clause,[],[f288,f219,f290])).
% 0.20/0.51 thf(f288,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($true = (rel_s4 @ X5 @ (sK7 @ X5 @ X4))) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ X2 @ X5) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) | ((rel_s4 @ sK4 @ X2) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f287])).
% 0.20/0.51 thf(f287,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (((rel_s4 @ X2 @ X5) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ sK4 @ X2) = $false) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3)))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f285])).
% 0.20/0.51 thf(f285,plain,(
% 0.20/0.51 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : $i] : (($false = (exists_in_world @ X4 @ X2)) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X3))) | ($true = (~ (rel_s4 @ X2 @ X5))) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (~ (rel_s4 @ X5 @ (sK7 @ X5 @ X4)))) | ((rel_s4 @ sK4 @ X2) = $false) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f284])).
% 0.20/0.51 thf(f256,plain,(
% 0.20/0.51 spl0_5 | spl0_3),
% 0.20/0.51 inference(avatar_split_clause,[],[f255,f219,f251])).
% 0.20/0.51 thf(f255,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) | ($true = (rel_s4 @ sK4 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f248])).
% 0.20/0.51 thf(f248,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) = $false) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f247])).
% 0.20/0.51 thf(f247,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ($true = (rel_s4 @ sK4 @ sK5)) | (((f @ X2 @ (sK7 @ X1 @ X2)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2)))) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f246])).
% 0.20/0.51 thf(f246,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ sK4 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | (((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK7 @ X1 @ X2)) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f245])).
% 0.20/0.51 thf(f245,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ($true = (rel_s4 @ sK4 @ sK5)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f244])).
% 0.20/0.51 thf(f244,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f243])).
% 0.20/0.51 thf(f243,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ sK4 @ sK5)) | ($true = ((exists_in_world @ X2 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f242])).
% 0.20/0.51 thf(f242,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ sK4 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1)))))))) @ X2))) )),
% 0.20/0.51 inference(pi_clausification,[],[f241])).
% 0.20/0.51 thf(f241,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f240])).
% 0.20/0.51 thf(f240,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK3 @ X1))) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f239])).
% 0.20/0.51 thf(f239,plain,(
% 0.20/0.51 ( ! [X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f238])).
% 0.20/0.51 thf(f238,plain,(
% 0.20/0.51 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ X1) = $true) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(pi_clausification,[],[f237])).
% 0.20/0.51 thf(f237,plain,(
% 0.20/0.51 ($true = (rel_s4 @ sK4 @ sK5)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f236])).
% 0.20/0.51 thf(f236,plain,(
% 0.20/0.51 ($true = (rel_s4 @ sK4 @ sK5)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f185])).
% 0.20/0.51 thf(f185,plain,(
% 0.20/0.51 ((~ (rel_s4 @ sK4 @ sK5)) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f184])).
% 0.20/0.51 thf(f184,plain,(
% 0.20/0.51 (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))) | (~ (rel_s4 @ sK4 @ sK5))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(beta_eta_normalization,[],[f183])).
% 0.20/0.51 thf(f183,plain,(
% 0.20/0.51 ($false = ((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0)))) @ sK5)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(sigma_clausification,[],[f181])).
% 0.20/0.51 thf(f181,plain,(
% 0.20/0.51 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK4 @ Y0))))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f180])).
% 0.20/0.51 thf(f254,plain,(
% 0.20/0.51 spl0_1 | spl0_5),
% 0.20/0.51 inference(avatar_split_clause,[],[f249,f251,f210])).
% 0.20/0.51 thf(f249,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($false = (f @ X2 @ (sK7 @ X1 @ X2))) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = (rel_s4 @ sK4 @ sK5))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f247])).
% 0.20/0.51 thf(f235,plain,(
% 0.20/0.51 spl0_1 | spl0_4),
% 0.20/0.51 inference(avatar_split_clause,[],[f228,f231,f210])).
% 0.20/0.51 thf(f228,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (f @ X2 @ (sK7 @ X1 @ X2)))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f226])).
% 0.20/0.51 thf(f226,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : ((((f @ X2 @ (sK7 @ X1 @ X2)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2)))) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = (exists_in_world @ sK6 @ sK5)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f225])).
% 0.20/0.51 thf(f225,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | (((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK7 @ X1 @ X2)) = $false) | ($true = (exists_in_world @ sK6 @ sK5)) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f224])).
% 0.20/0.51 thf(f224,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f223])).
% 0.20/0.51 thf(f223,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f222])).
% 0.20/0.51 thf(f222,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (exists_in_world @ sK6 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ($true = ((exists_in_world @ X2 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f196])).
% 0.20/0.51 thf(f196,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (~ (rel_s4 @ sK3 @ X1))) | ($true = ((exists_in_world @ X2 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ($true = (exists_in_world @ sK6 @ sK5))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f194])).
% 0.20/0.51 thf(f194,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))))) | ($true = (~ (rel_s4 @ sK3 @ X1))) | ($true = ((exists_in_world @ X2 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f193])).
% 0.20/0.51 thf(f193,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))))) | ($true = (~ (rel_s4 @ sK3 @ X1))) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1)))))))) @ X2))) )),
% 0.20/0.51 inference(pi_clausification,[],[f192])).
% 0.20/0.51 thf(f192,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) = $true) | ($true = (~ (rel_s4 @ sK3 @ X1))) | ($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f191])).
% 0.20/0.51 thf(f191,plain,(
% 0.20/0.51 ( ! [X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true) | ($false = ((exists_in_world @ sK6 @ sK5) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0))))))))) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f190])).
% 0.20/0.51 thf(f190,plain,(
% 0.20/0.51 ( ! [X1 : $i] : ((((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))) @ sK6) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f189])).
% 0.20/0.51 thf(f189,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))))) | (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ X1 @ Y1))))))))) | (~ (rel_s4 @ sK3 @ X1))) = $true)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f188])).
% 0.20/0.51 thf(f188,plain,(
% 0.20/0.51 ( ! [X1 : $i] : (($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1)))))))))) | (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ X1) = $true)) )),
% 0.20/0.51 inference(pi_clausification,[],[f187])).
% 0.20/0.51 thf(f187,plain,(
% 0.20/0.51 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0)))))) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))))),
% 0.20/0.51 inference(not_proxy_clausification,[],[f186])).
% 0.20/0.51 thf(f186,plain,(
% 0.20/0.51 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s4 @ Y0 @ Y2))))))))) | (~ (rel_s4 @ sK3 @ Y0))))))) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s4 @ sK5 @ Y1))))))))))),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f184])).
% 0.20/0.51 thf(f234,plain,(
% 0.20/0.51 spl0_4 | spl0_3),
% 0.20/0.51 inference(avatar_split_clause,[],[f229,f219,f231])).
% 0.20/0.51 thf(f229,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) | ($true = (exists_in_world @ sK6 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f227])).
% 0.20/0.51 thf(f227,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) = $false) | ($true = (exists_in_world @ sK6 @ sK5)) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f226])).
% 0.20/0.51 thf(f221,plain,(
% 0.20/0.51 spl0_2 | spl0_3),
% 0.20/0.51 inference(avatar_split_clause,[],[f217,f219,f213])).
% 0.20/0.51 thf(f217,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (f @ sK6 @ X3)) | ($true = (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) | ((rel_s4 @ sK3 @ X1) = $false) | ((rel_s4 @ sK5 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f216])).
% 0.20/0.51 thf(f216,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (f @ sK6 @ X3)) | ((rel_s4 @ sK3 @ X1) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) = $false) | ((rel_s4 @ sK5 @ X3) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f206])).
% 0.20/0.51 thf(f206,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (f @ sK6 @ X3)) | ((~ (rel_s4 @ sK5 @ X3)) = $true) | ((rel_s4 @ sK3 @ X1) = $false) | ((~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2))) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f205])).
% 0.20/0.51 thf(f205,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | (((f @ X2 @ (sK7 @ X1 @ X2)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2)))) = $false) | ($true = (f @ sK6 @ X3)) | ((~ (rel_s4 @ sK5 @ X3)) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f204])).
% 0.20/0.51 thf(f204,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | (((f @ sK6 @ X3) | (~ (rel_s4 @ sK5 @ X3))) = $true) | (((f @ X2 @ (sK7 @ X1 @ X2)) | (~ (rel_s4 @ X1 @ (sK7 @ X1 @ X2)))) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f203])).
% 0.20/0.51 thf(f203,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK7 @ X1 @ X2)) = $false) | (((f @ sK6 @ X3) | (~ (rel_s4 @ sK5 @ X3))) = $true) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(sigma_clausification,[],[f202])).
% 0.20/0.51 thf(f202,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | (((f @ sK6 @ X3) | (~ (rel_s4 @ sK5 @ X3))) = $true) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(beta_eta_normalization,[],[f201])).
% 0.20/0.51 thf(f201,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ($true = ((^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))) @ X3)) | ((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(pi_clausification,[],[f200])).
% 0.20/0.51 thf(f200,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f199])).
% 0.20/0.51 thf(f199,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) | ((rel_s4 @ sK3 @ X1) = $false)) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f198])).
% 0.20/0.51 thf(f198,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f197])).
% 0.20/0.51 thf(f197,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (((exists_in_world @ X2 @ X1) = $false) | ($true = (~ (rel_s4 @ sK3 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f195])).
% 0.20/0.51 thf(f195,plain,(
% 0.20/0.51 ( ! [X2 : mu,X1 : $i] : (($true = ((exists_in_world @ X2 @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((f @ X2 @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK6 @ Y0) | (~ (rel_s4 @ sK5 @ Y0)))))) = $false) | ($true = (~ (rel_s4 @ sK3 @ X1)))) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f194])).
% 0.20/0.51 thf(f215,plain,(
% 0.20/0.51 spl0_1 | spl0_2),
% 0.20/0.51 inference(avatar_split_clause,[],[f208,f213,f210])).
% 0.20/0.51 thf(f208,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($true = (f @ sK6 @ X3)) | ((rel_s4 @ sK5 @ X3) = $false) | ((exists_in_world @ X2 @ X1) = $false) | ((rel_s4 @ sK3 @ X1) = $false) | ($false = (f @ X2 @ (sK7 @ X1 @ X2)))) )),
% 0.20/0.51 inference(not_proxy_clausification,[],[f207])).
% 0.20/0.51 thf(f207,plain,(
% 0.20/0.51 ( ! [X2 : mu,X3 : $i,X1 : $i] : (($false = (f @ X2 @ (sK7 @ X1 @ X2))) | ($true = (f @ sK6 @ X3)) | ((rel_s4 @ sK3 @ X1) = $false) | ((~ (rel_s4 @ sK5 @ X3)) = $true) | ((exists_in_world @ X2 @ X1) = $false)) )),
% 0.20/0.51 inference(binary_proxy_clausification,[],[f205])).
% 0.20/0.51 % SZS output end Proof for theBenchmark
% 0.20/0.51 % (5186)------------------------------
% 0.20/0.51 % (5186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.51 % (5186)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (5186)Memory used [KB]: 6140
% 0.20/0.51 % (5186)Time elapsed: 0.080 s
% 0.20/0.51 % (5186)Instructions burned: 78 (million)
% 0.20/0.51 % (5186)------------------------------
% 0.20/0.51 % (5186)------------------------------
% 0.20/0.51 % (5158)Success in time 0.154 s
% 0.20/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------