TSTP Solution File: KRS272^7 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : KRS272^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n027.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 : Mon Jun 24 10:16:06 EDT 2024
% Result : Theorem 2.02s 0.63s
% Output : Refutation 2.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS272^7 : TPTP v8.2.0. Released v5.5.0.
% 0.10/0.11 % Command : run_vampire %s %d THM
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jun 19 13:52:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 Running higher-order theorem proving
% 0.11/0.33 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.11/0.35 % (28622)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)
% 0.11/0.35 % (28623)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.35 % (28624)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)
% 0.11/0.35 % (28620)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.35 % (28621)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)
% 0.11/0.35 % (28625)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)
% 0.11/0.35 % (28626)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.36 % (28623)Instruction limit reached!
% 0.11/0.36 % (28623)------------------------------
% 0.11/0.36 % (28623)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (28623)Termination reason: Unknown
% 0.11/0.36 % (28624)Instruction limit reached!
% 0.11/0.36 % (28624)------------------------------
% 0.11/0.36 % (28624)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (28624)Termination reason: Unknown
% 0.11/0.36 % (28624)Termination phase: shuffling
% 0.11/0.36
% 0.11/0.36 % (28624)Memory used [KB]: 1023
% 0.11/0.36 % (28624)Time elapsed: 0.004 s
% 0.11/0.36 % (28624)Instructions burned: 3 (million)
% 0.11/0.36 % (28624)------------------------------
% 0.11/0.36 % (28624)------------------------------
% 0.11/0.36 % (28623)Termination phase: shuffling
% 0.11/0.36
% 0.11/0.36 % (28623)Memory used [KB]: 1023
% 0.11/0.36 % (28623)Time elapsed: 0.004 s
% 0.11/0.36 % (28623)Instructions burned: 3 (million)
% 0.11/0.36 % (28623)------------------------------
% 0.11/0.36 % (28623)------------------------------
% 0.11/0.36 % (28621)Instruction limit reached!
% 0.11/0.36 % (28621)------------------------------
% 0.11/0.36 % (28621)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (28621)Termination reason: Unknown
% 0.11/0.36 % (28621)Termination phase: Property scanning
% 0.11/0.36
% 0.11/0.36 % (28621)Memory used [KB]: 1023
% 0.11/0.36 % (28621)Time elapsed: 0.004 s
% 0.11/0.36 % (28621)Instructions burned: 5 (million)
% 0.11/0.36 % (28621)------------------------------
% 0.11/0.36 % (28621)------------------------------
% 0.11/0.36 % (28626)Instruction limit reached!
% 0.11/0.36 % (28626)------------------------------
% 0.11/0.36 % (28626)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (28626)Termination reason: Unknown
% 0.11/0.36 % (28626)Termination phase: Saturation
% 0.11/0.36
% 0.11/0.36 % (28626)Memory used [KB]: 5628
% 0.11/0.36 % (28626)Time elapsed: 0.011 s
% 0.11/0.36 % (28626)Instructions burned: 18 (million)
% 0.11/0.36 % (28626)------------------------------
% 0.11/0.36 % (28626)------------------------------
% 0.11/0.36 % (28625)Refutation not found, incomplete strategy
% 0.11/0.36 % (28625)------------------------------
% 0.11/0.36 % (28625)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (28625)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36
% 0.11/0.36
% 0.11/0.36 % (28625)Memory used [KB]: 5756
% 0.11/0.36 % (28625)Time elapsed: 0.011 s
% 0.11/0.36 % (28625)Instructions burned: 18 (million)
% 0.11/0.36 % (28625)------------------------------
% 0.11/0.36 % (28625)------------------------------
% 0.11/0.37 % (28622)Instruction limit reached!
% 0.11/0.37 % (28622)------------------------------
% 0.11/0.37 % (28622)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (28622)Termination reason: Unknown
% 0.11/0.37 % (28622)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (28622)Memory used [KB]: 5756
% 0.11/0.37 % (28622)Time elapsed: 0.015 s
% 0.11/0.37 % (28622)Instructions burned: 27 (million)
% 0.11/0.37 % (28622)------------------------------
% 0.11/0.37 % (28622)------------------------------
% 0.11/0.37 % (28629)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)
% 0.11/0.37 % (28628)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)
% 0.11/0.37 % (28627)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)
% 0.11/0.37 % (28627)Instruction limit reached!
% 0.11/0.37 % (28627)------------------------------
% 0.11/0.37 % (28627)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (28627)Termination reason: Unknown
% 0.11/0.37 % (28627)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (28627)Memory used [KB]: 1023
% 0.11/0.37 % (28627)Time elapsed: 0.004 s
% 0.11/0.37 % (28627)Instructions burned: 4 (million)
% 0.11/0.37 % (28627)------------------------------
% 0.11/0.37 % (28627)------------------------------
% 0.11/0.38 % (28629)Instruction limit reached!
% 0.11/0.38 % (28629)------------------------------
% 0.11/0.38 % (28629)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (28629)Termination reason: Unknown
% 0.11/0.38 % (28629)Termination phase: Saturation
% 0.11/0.38
% 0.11/0.38 % (28629)Memory used [KB]: 1151
% 0.11/0.38 % (28629)Time elapsed: 0.009 s
% 0.11/0.38 % (28629)Instructions burned: 15 (million)
% 0.11/0.38 % (28629)------------------------------
% 0.11/0.38 % (28629)------------------------------
% 0.11/0.38 % (28631)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)
% 0.11/0.38 % (28630)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)
% 0.11/0.38 % (28630)Instruction limit reached!
% 0.11/0.38 % (28630)------------------------------
% 0.11/0.38 % (28630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (28630)Termination reason: Unknown
% 0.11/0.38 % (28630)Termination phase: shuffling
% 0.11/0.38
% 0.11/0.38 % (28630)Memory used [KB]: 1023
% 0.11/0.38 % (28630)Time elapsed: 0.003 s
% 0.11/0.38 % (28630)Instructions burned: 3 (million)
% 0.11/0.38 % (28630)------------------------------
% 0.11/0.38 % (28630)------------------------------
% 0.11/0.38 % (28632)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.39 % (28632)Instruction limit reached!
% 0.11/0.39 % (28632)------------------------------
% 0.11/0.39 % (28632)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (28632)Termination reason: Unknown
% 0.11/0.39 % (28632)Termination phase: SInE selection
% 0.11/0.39
% 0.11/0.39 % (28632)Memory used [KB]: 1151
% 0.11/0.39 % (28632)Time elapsed: 0.006 s
% 0.11/0.39 % (28632)Instructions burned: 7 (million)
% 0.11/0.39 % (28632)------------------------------
% 0.11/0.39 % (28632)------------------------------
% 0.11/0.39 % (28628)Instruction limit reached!
% 0.11/0.39 % (28628)------------------------------
% 0.11/0.39 % (28628)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (28633)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.11/0.39 % (28628)Termination reason: Unknown
% 0.11/0.39 % (28628)Termination phase: Saturation
% 0.11/0.39
% 0.11/0.39 % (28628)Memory used [KB]: 5884
% 0.11/0.39 % (28628)Time elapsed: 0.019 s
% 0.11/0.39 % (28628)Instructions burned: 37 (million)
% 0.11/0.39 % (28628)------------------------------
% 0.11/0.39 % (28628)------------------------------
% 0.11/0.39 % (28634)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)
% 0.11/0.40 % (28635)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)
% 0.11/0.40 % (28634)Instruction limit reached!
% 0.11/0.40 % (28634)------------------------------
% 0.11/0.40 % (28634)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.40 % (28634)Termination reason: Unknown
% 0.11/0.40 % (28634)Termination phase: shuffling
% 0.11/0.40
% 0.11/0.40 % (28634)Memory used [KB]: 1023
% 0.11/0.40 % (28634)Time elapsed: 0.004 s
% 0.11/0.40 % (28634)Instructions burned: 3 (million)
% 0.11/0.40 % (28634)------------------------------
% 0.11/0.40 % (28634)------------------------------
% 0.11/0.40 % (28633)Instruction limit reached!
% 0.11/0.40 % (28633)------------------------------
% 0.11/0.40 % (28633)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.40 % (28633)Termination reason: Unknown
% 0.11/0.40 % (28633)Termination phase: Saturation
% 0.11/0.40
% 0.11/0.40 % (28633)Memory used [KB]: 5628
% 0.11/0.40 % (28633)Time elapsed: 0.010 s
% 0.11/0.40 % (28633)Instructions burned: 18 (million)
% 0.11/0.40 % (28633)------------------------------
% 0.11/0.40 % (28633)------------------------------
% 0.11/0.40 % (28635)Instruction limit reached!
% 0.11/0.40 % (28635)------------------------------
% 0.11/0.40 % (28635)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.40 % (28635)Termination reason: Unknown
% 0.11/0.40 % (28635)Termination phase: shuffling
% 0.11/0.40
% 0.11/0.40 % (28635)Memory used [KB]: 1023
% 0.11/0.40 % (28635)Time elapsed: 0.004 s
% 0.11/0.40 % (28635)Instructions burned: 4 (million)
% 0.11/0.40 % (28635)------------------------------
% 0.11/0.40 % (28635)------------------------------
% 0.18/0.40 % (28636)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)
% 0.18/0.40 % (28636)Instruction limit reached!
% 0.18/0.40 % (28636)------------------------------
% 0.18/0.40 % (28636)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.40 % (28637)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)
% 0.18/0.40 % (28636)Termination reason: Unknown
% 0.18/0.40 % (28636)Termination phase: Preprocessing 2
% 0.18/0.40
% 0.18/0.40 % (28636)Memory used [KB]: 1023
% 0.18/0.40 % (28636)Time elapsed: 0.005 s
% 0.18/0.40 % (28636)Instructions burned: 7 (million)
% 0.18/0.40 % (28636)------------------------------
% 0.18/0.40 % (28636)------------------------------
% 0.18/0.41 % (28637)Instruction limit reached!
% 0.18/0.41 % (28637)------------------------------
% 0.18/0.41 % (28637)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.41 % (28637)Termination reason: Unknown
% 0.18/0.41 % (28637)Termination phase: shuffling
% 0.18/0.41
% 0.18/0.41 % (28637)Memory used [KB]: 1023
% 0.18/0.41 % (28637)Time elapsed: 0.003 s
% 0.18/0.41 % (28637)Instructions burned: 3 (million)
% 0.18/0.41 % (28637)------------------------------
% 0.18/0.41 % (28637)------------------------------
% 0.18/0.41 % (28639)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)
% 0.18/0.41 % (28638)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.41 % (28640)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.41 % (28638)Instruction limit reached!
% 0.18/0.41 % (28638)------------------------------
% 0.18/0.41 % (28638)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.41 % (28638)Termination reason: Unknown
% 0.18/0.41 % (28638)Termination phase: Property scanning
% 0.18/0.41
% 0.18/0.41 % (28638)Memory used [KB]: 1023
% 0.18/0.41 % (28638)Time elapsed: 0.005 s
% 0.18/0.41 % (28638)Instructions burned: 5 (million)
% 0.18/0.41 % (28638)------------------------------
% 0.18/0.41 % (28638)------------------------------
% 0.18/0.42 % (28641)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.42 % (28642)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)
% 0.18/0.42 % (28639)Instruction limit reached!
% 0.18/0.42 % (28639)------------------------------
% 0.18/0.42 % (28639)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.42 % (28639)Termination reason: Unknown
% 0.18/0.42 % (28639)Termination phase: Saturation
% 0.18/0.42
% 0.18/0.42 % (28639)Memory used [KB]: 5756
% 0.18/0.42 % (28639)Time elapsed: 0.012 s
% 0.18/0.42 % (28639)Instructions burned: 19 (million)
% 0.18/0.42 % (28639)------------------------------
% 0.18/0.42 % (28639)------------------------------
% 0.18/0.42 % (28641)Instruction limit reached!
% 0.18/0.42 % (28641)------------------------------
% 0.18/0.42 % (28641)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.42 % (28641)Termination reason: Unknown
% 0.18/0.42 % (28641)Termination phase: Property scanning
% 0.18/0.42
% 0.18/0.42 % (28641)Memory used [KB]: 1151
% 0.18/0.42 % (28641)Time elapsed: 0.006 s
% 0.18/0.42 % (28641)Instructions burned: 7 (million)
% 0.18/0.42 % (28641)------------------------------
% 0.18/0.42 % (28641)------------------------------
% 0.18/0.43 % (28642)Refutation not found, incomplete strategy
% 0.18/0.43 % (28642)------------------------------
% 0.18/0.43 % (28642)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.43 % (28642)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 % (28642)Memory used [KB]: 5628
% 0.18/0.43 % (28642)Time elapsed: 0.008 s
% 0.18/0.43 % (28642)Instructions burned: 10 (million)
% 0.18/0.43 % (28642)------------------------------
% 0.18/0.43 % (28642)------------------------------
% 0.18/0.43 % (28643)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)
% 0.18/0.43 % (28644)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.18/0.44 % (28644)Instruction limit reached!
% 0.18/0.44 % (28644)------------------------------
% 0.18/0.44 % (28644)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (28644)Termination reason: Unknown
% 0.18/0.44 % (28644)Termination phase: Property scanning
% 0.18/0.44
% 0.18/0.44 % (28644)Memory used [KB]: 1023
% 0.18/0.44 % (28644)Time elapsed: 0.005 s
% 0.18/0.44 % (28644)Instructions burned: 5 (million)
% 0.18/0.44 % (28644)------------------------------
% 0.18/0.44 % (28644)------------------------------
% 0.18/0.44 % (28645)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)
% 0.18/0.44 % (28643)Instruction limit reached!
% 0.18/0.44 % (28643)------------------------------
% 0.18/0.44 % (28643)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (28643)Termination reason: Unknown
% 0.18/0.44 % (28643)Termination phase: Saturation
% 0.18/0.44
% 0.18/0.44 % (28643)Memory used [KB]: 5756
% 0.18/0.44 % (28643)Time elapsed: 0.012 s
% 0.18/0.44 % (28643)Instructions burned: 23 (million)
% 0.18/0.44 % (28643)------------------------------
% 0.18/0.44 % (28643)------------------------------
% 0.18/0.44 % (28645)Instruction limit reached!
% 0.18/0.44 % (28645)------------------------------
% 0.18/0.44 % (28645)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (28645)Termination reason: Unknown
% 0.18/0.44 % (28645)Termination phase: SInE selection
% 0.18/0.44
% 0.18/0.44 % (28645)Memory used [KB]: 1151
% 0.18/0.44 % (28645)Time elapsed: 0.005 s
% 0.18/0.44 % (28645)Instructions burned: 7 (million)
% 0.18/0.44 % (28645)------------------------------
% 0.18/0.44 % (28645)------------------------------
% 0.18/0.44 % (28646)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.18/0.44 % (28620)Instruction limit reached!
% 0.18/0.44 % (28620)------------------------------
% 0.18/0.44 % (28620)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.44 % (28620)Termination reason: Unknown
% 0.18/0.44 % (28620)Termination phase: Saturation
% 0.18/0.44
% 0.18/0.44 % (28620)Memory used [KB]: 6524
% 0.18/0.44 % (28620)Time elapsed: 0.089 s
% 0.18/0.44 % (28620)Instructions burned: 184 (million)
% 0.18/0.44 % (28620)------------------------------
% 0.18/0.44 % (28620)------------------------------
% 0.18/0.45 % (28647)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)
% 0.18/0.45 % (28648)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)
% 0.18/0.45 % (28649)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)
% 0.18/0.46 % (28650)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.18/0.46 % (28648)Instruction limit reached!
% 0.18/0.46 % (28648)------------------------------
% 0.18/0.46 % (28648)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.46 % (28648)Termination reason: Unknown
% 0.18/0.46 % (28648)Termination phase: Saturation
% 0.18/0.46
% 0.18/0.46 % (28648)Memory used [KB]: 5628
% 0.18/0.46 % (28648)Time elapsed: 0.011 s
% 0.18/0.46 % (28648)Instructions burned: 20 (million)
% 0.18/0.46 % (28648)------------------------------
% 0.18/0.46 % (28648)------------------------------
% 0.18/0.47 % (28650)Instruction limit reached!
% 0.18/0.47 % (28650)------------------------------
% 0.18/0.47 % (28650)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.47 % (28650)Termination reason: Unknown
% 0.18/0.47 % (28650)Termination phase: Saturation
% 0.18/0.47
% 0.18/0.47 % (28650)Memory used [KB]: 5628
% 0.18/0.47 % (28650)Time elapsed: 0.010 s
% 0.18/0.47 % (28650)Instructions burned: 17 (million)
% 0.18/0.47 % (28650)------------------------------
% 0.18/0.47 % (28650)------------------------------
% 0.18/0.48 % (28651)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.18/0.48 % (28651)Instruction limit reached!
% 0.18/0.48 % (28651)------------------------------
% 0.18/0.48 % (28651)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.48 % (28652)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.18/0.48 % (28651)Termination reason: Unknown
% 0.18/0.48 % (28651)Termination phase: shuffling
% 0.18/0.48
% 0.18/0.48 % (28651)Memory used [KB]: 1023
% 0.18/0.48 % (28651)Time elapsed: 0.004 s
% 0.18/0.48 % (28651)Instructions burned: 3 (million)
% 0.18/0.48 % (28651)------------------------------
% 0.18/0.48 % (28651)------------------------------
% 0.18/0.49 % (28652)Instruction limit reached!
% 0.18/0.49 % (28652)------------------------------
% 0.18/0.49 % (28652)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.49 % (28652)Termination reason: Unknown
% 0.18/0.49 % (28652)Termination phase: Saturation
% 0.18/0.49
% 0.18/0.49 % (28652)Memory used [KB]: 5756
% 0.18/0.49 % (28652)Time elapsed: 0.017 s
% 0.18/0.49 % (28652)Instructions burned: 30 (million)
% 0.18/0.49 % (28652)------------------------------
% 0.18/0.49 % (28652)------------------------------
% 0.18/0.50 % (28653)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)
% 0.18/0.51 % (28654)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)
% 0.18/0.56 % (28653)Instruction limit reached!
% 0.18/0.56 % (28653)------------------------------
% 0.18/0.56 % (28653)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.56 % (28653)Termination reason: Unknown
% 0.18/0.56 % (28653)Termination phase: Saturation
% 0.18/0.56
% 0.18/0.56 % (28653)Memory used [KB]: 6268
% 0.18/0.56 % (28653)Time elapsed: 0.064 s
% 0.18/0.56 % (28653)Instructions burned: 127 (million)
% 0.18/0.56 % (28653)------------------------------
% 0.18/0.56 % (28653)------------------------------
% 0.18/0.56 % (28654)Instruction limit reached!
% 0.18/0.56 % (28654)------------------------------
% 0.18/0.56 % (28654)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.56 % (28654)Termination reason: Unknown
% 0.18/0.56 % (28654)Termination phase: Saturation
% 0.18/0.56
% 0.18/0.56 % (28654)Memory used [KB]: 6140
% 0.18/0.56 % (28654)Time elapsed: 0.049 s
% 0.18/0.56 % (28654)Instructions burned: 102 (million)
% 0.18/0.56 % (28654)------------------------------
% 0.18/0.56 % (28654)------------------------------
% 0.18/0.57 % (28655)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi)
% 0.18/0.57 % (28656)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 0.18/0.58 % (28655)Instruction limit reached!
% 0.18/0.58 % (28655)------------------------------
% 0.18/0.58 % (28655)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.58 % (28655)Termination reason: Unknown
% 0.18/0.58 % (28655)Termination phase: Property scanning
% 0.18/0.58
% 0.18/0.58 % (28655)Memory used [KB]: 1023
% 0.18/0.58 % (28655)Time elapsed: 0.004 s
% 0.18/0.58 % (28655)Instructions burned: 5 (million)
% 0.18/0.58 % (28655)------------------------------
% 0.18/0.58 % (28655)------------------------------
% 0.18/0.58 % (28656)Instruction limit reached!
% 0.18/0.58 % (28656)------------------------------
% 0.18/0.58 % (28656)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.58 % (28656)Termination reason: Unknown
% 0.18/0.58 % (28656)Termination phase: Saturation
% 0.18/0.58
% 0.18/0.58 % (28656)Memory used [KB]: 5628
% 0.18/0.58 % (28656)Time elapsed: 0.012 s
% 0.18/0.58 % (28656)Instructions burned: 20 (million)
% 0.18/0.58 % (28656)------------------------------
% 0.18/0.58 % (28656)------------------------------
% 0.18/0.60 % (28658)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 0.18/0.60 % (28657)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 0.18/0.61 % (28646)First to succeed.
% 2.02/0.63 % (28646)Refutation found. Thanks to Tanya!
% 2.02/0.63 % SZS status Theorem for theBenchmark
% 2.02/0.63 % SZS output start Proof for theBenchmark
% 2.02/0.63 thf(type_def_5, type, mu: $tType).
% 2.02/0.63 thf(func_def_0, type, mu: $tType).
% 2.02/0.63 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 2.02/0.63 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_8, type, mtrue: $i > $o).
% 2.02/0.63 thf(func_def_9, type, mfalse: $i > $o).
% 2.02/0.63 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 2.02/0.63 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 2.02/0.63 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 2.02/0.63 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 2.02/0.63 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 2.02/0.63 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 2.02/0.63 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 2.02/0.63 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 2.02/0.63 thf(func_def_37, type, string: mu > $i > $o).
% 2.02/0.63 thf(func_def_38, type, in: mu > mu > mu > $i > $o).
% 2.02/0.63 thf(func_def_39, type, do: mu > mu > mu > $i > $o).
% 2.02/0.63 thf(func_def_40, type, number: mu > mu > $i > $o).
% 2.02/0.63 thf(func_def_41, type, entry_box: mu > $i > $o).
% 2.02/0.63 thf(func_def_42, type, userid: mu > mu > $i > $o).
% 2.02/0.63 thf(func_def_43, type, one: mu).
% 2.02/0.63 thf(func_def_44, type, u: mu).
% 2.02/0.63 thf(func_def_60, type, sK0: $i > mu).
% 2.02/0.63 thf(func_def_62, type, sK2: $i > mu).
% 2.02/0.63 thf(func_def_63, type, sK3: $i > mu).
% 2.02/0.63 thf(func_def_69, type, sK6: mu > mu > $i).
% 2.02/0.63 thf(func_def_70, type, sK7: mu > mu > mu > mu > $i).
% 2.02/0.63 thf(func_def_71, type, sK8: mu > mu > mu > mu > mu).
% 2.02/0.63 thf(func_def_72, type, sK9: mu > mu > mu > mu > mu).
% 2.02/0.63 thf(func_def_73, type, sK10: $i > mu > mu > mu > mu).
% 2.02/0.63 thf(f1490,plain,(
% 2.02/0.63 $false),
% 2.02/0.63 inference(avatar_sat_refutation,[],[f544,f574,f578,f834,f851,f889,f1115,f1161,f1176,f1425,f1434,f1489])).
% 2.02/0.63 thf(f1489,plain,(
% 2.02/0.63 spl1_28 | ~spl1_37),
% 2.02/0.63 inference(avatar_split_clause,[],[f1485,f1418,f1172])).
% 2.02/0.63 thf(f1172,plain,(
% 2.02/0.63 spl1_28 <=> ($false = (rel_s4 @ sK5 @ sK5))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_28])])).
% 2.02/0.63 thf(f1418,plain,(
% 2.02/0.63 spl1_37 <=> ((entry_box @ (sK2 @ sK5) @ sK5) = $false)),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_37])])).
% 2.02/0.63 thf(f1485,plain,(
% 2.02/0.63 ($false = (rel_s4 @ sK5 @ sK5)) | ~spl1_37),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1483])).
% 2.02/0.63 thf(f1483,plain,(
% 2.02/0.63 ($false = $true) | ($false = (rel_s4 @ sK5 @ sK5)) | ~spl1_37),
% 2.02/0.63 inference(superposition,[],[f1420,f206])).
% 2.02/0.63 thf(f206,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((entry_box @ (sK2 @ X1) @ X2) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f203])).
% 2.02/0.63 thf(f203,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (~ (entry_box @ (sK2 @ X1) @ X2)))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f202])).
% 2.02/0.63 thf(f202,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (($false = ((~ (number @ (sK2 @ X1) @ one @ X2)) | (~ (entry_box @ (sK2 @ X1) @ X2)))) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f201])).
% 2.02/0.63 thf(f201,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ($false = ((~ (number @ (sK2 @ X1) @ one @ X2)) | (~ (entry_box @ (sK2 @ X1) @ X2))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f200])).
% 2.02/0.63 thf(f200,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((~ ((~ (number @ (sK2 @ X1) @ one @ X2)) | (~ (entry_box @ (sK2 @ X1) @ X2)))) = $true) | ((~ (rel_s4 @ X1 @ X2)) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f199])).
% 2.02/0.63 thf(f199,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s4 @ X1 @ X2)) | (~ ((~ (number @ (sK2 @ X1) @ one @ X2)) | (~ (entry_box @ (sK2 @ X1) @ X2))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f198])).
% 2.02/0.63 thf(f198,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (number @ (sK2 @ X1) @ one @ Y0)) | (~ (entry_box @ (sK2 @ X1) @ Y0)))))) @ X2) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f197])).
% 2.02/0.63 thf(f197,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (number @ (sK2 @ X1) @ one @ Y0)) | (~ (entry_box @ (sK2 @ X1) @ Y0))))))) = $true)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f195])).
% 2.02/0.63 thf(f195,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (number @ (sK2 @ X1) @ one @ Y0)) | (~ (entry_box @ (sK2 @ X1) @ Y0)))))))))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f194])).
% 2.02/0.63 thf(f194,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (($false = ((exists_in_world @ (sK2 @ X1) @ X1) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ ((~ (number @ (sK2 @ X1) @ one @ Y0)) | (~ (entry_box @ (sK2 @ X1) @ Y0))))))))))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f193])).
% 2.02/0.63 thf(f193,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (number @ Y0 @ one @ Y1)) | (~ (entry_box @ Y0 @ Y1)))))))))) @ (sK2 @ X1)))) )),
% 2.02/0.63 inference(sigma_clausification,[],[f192])).
% 2.02/0.63 thf(f192,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (number @ Y0 @ one @ Y1)) | (~ (entry_box @ Y0 @ Y1))))))))))) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f191])).
% 2.02/0.63 thf(f191,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ ((~ (number @ Y0 @ one @ Y1)) | (~ (entry_box @ Y0 @ Y1)))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f190])).
% 2.02/0.63 thf(f190,plain,(
% 2.02/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (number @ Y1 @ one @ Y2)) | (~ (entry_box @ Y1 @ Y2))))))))))))) @ X1) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f189])).
% 2.02/0.63 thf(f189,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (number @ Y1 @ one @ Y2)) | (~ (entry_box @ Y1 @ Y2)))))))))))))) = $true)),
% 2.02/0.63 inference(beta_eta_normalization,[],[f184])).
% 2.02/0.63 thf(f184,plain,(
% 2.02/0.63 (((^[Y0 : $i > $o]: (!! @ $i @ (^[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]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ (entry_box @ Y0) @ (number @ Y0 @ one)))))) = $true)),
% 2.02/0.63 inference(definition_unfolding,[],[f147,f140,f180,f172,f174])).
% 2.02/0.63 thf(f174,plain,(
% 2.02/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 2.02/0.63 inference(definition_unfolding,[],[f151,f149,f144,f149,f149])).
% 2.02/0.63 thf(f144,plain,(
% 2.02/0.63 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f113])).
% 2.02/0.63 thf(f113,plain,(
% 2.02/0.63 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.02/0.63 inference(fool_elimination,[],[f112])).
% 2.02/0.63 thf(f112,plain,(
% 2.02/0.63 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 2.02/0.63 inference(rectify,[],[f3])).
% 2.02/0.63 thf(f3,axiom,(
% 2.02/0.63 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 2.02/0.63 thf(f149,plain,(
% 2.02/0.63 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f64])).
% 2.02/0.63 thf(f64,plain,(
% 2.02/0.63 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 2.02/0.63 inference(fool_elimination,[],[f63])).
% 2.02/0.63 thf(f63,plain,(
% 2.02/0.63 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 2.02/0.63 inference(rectify,[],[f2])).
% 2.02/0.63 thf(f2,axiom,(
% 2.02/0.63 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 2.02/0.63 thf(f151,plain,(
% 2.02/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f103])).
% 2.02/0.63 thf(f103,plain,(
% 2.02/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 2.02/0.63 inference(fool_elimination,[],[f102])).
% 2.02/0.63 thf(f102,plain,(
% 2.02/0.63 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 2.02/0.63 inference(rectify,[],[f8])).
% 2.02/0.63 thf(f8,axiom,(
% 2.02/0.63 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 2.02/0.63 thf(f172,plain,(
% 2.02/0.63 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f107])).
% 2.02/0.63 thf(f107,plain,(
% 2.02/0.63 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 2.02/0.63 inference(fool_elimination,[],[f106])).
% 2.02/0.63 thf(f106,plain,(
% 2.02/0.63 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 2.02/0.63 inference(rectify,[],[f32])).
% 2.02/0.63 thf(f32,axiom,(
% 2.02/0.63 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 2.02/0.63 thf(f180,plain,(
% 2.02/0.63 (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)))))))),
% 2.02/0.63 inference(definition_unfolding,[],[f141,f149,f134,f149])).
% 2.02/0.63 thf(f134,plain,(
% 2.02/0.63 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f88])).
% 2.02/0.63 thf(f88,plain,(
% 2.02/0.63 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.02/0.63 inference(fool_elimination,[],[f87])).
% 2.02/0.63 thf(f87,plain,(
% 2.02/0.63 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_ind)),
% 2.02/0.63 inference(rectify,[],[f15])).
% 2.02/0.63 thf(f15,axiom,(
% 2.02/0.63 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))) = mforall_ind)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 2.02/0.63 thf(f141,plain,(
% 2.02/0.63 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f105])).
% 2.02/0.63 thf(f105,plain,(
% 2.02/0.63 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 2.02/0.63 inference(fool_elimination,[],[f104])).
% 2.02/0.63 thf(f104,plain,(
% 2.02/0.63 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 2.02/0.63 inference(rectify,[],[f16])).
% 2.02/0.63 thf(f16,axiom,(
% 2.02/0.63 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 2.02/0.63 thf(f140,plain,(
% 2.02/0.63 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 2.02/0.63 inference(cnf_transformation,[],[f101])).
% 2.02/0.63 thf(f101,plain,(
% 2.02/0.63 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 2.02/0.63 inference(fool_elimination,[],[f100])).
% 2.02/0.63 thf(f100,plain,(
% 2.02/0.63 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 2.02/0.63 inference(rectify,[],[f28])).
% 2.02/0.63 thf(f28,axiom,(
% 2.02/0.63 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 2.02/0.63 thf(f147,plain,(
% 2.02/0.63 ((mvalid @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))) = $true)),
% 2.02/0.63 inference(cnf_transformation,[],[f58])).
% 2.02/0.63 thf(f58,plain,(
% 2.02/0.63 ((mvalid @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (entry_box @ Y0) @ (number @ Y0 @ one)))))) = $true)),
% 2.02/0.63 inference(fool_elimination,[],[f57])).
% 2.02/0.63 thf(f57,plain,(
% 2.02/0.63 (mvalid @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (mand @ (entry_box @ X0) @ (number @ X0 @ one))))))),
% 2.02/0.63 inference(rectify,[],[f40])).
% 2.02/0.63 thf(f40,axiom,(
% 2.02/0.63 (mvalid @ (mexists_ind @ (^[X12 : mu] : (mbox_s4 @ (mand @ (entry_box @ X12) @ (number @ X12 @ one))))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)).
% 2.02/0.63 thf(f1420,plain,(
% 2.02/0.63 ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ~spl1_37),
% 2.02/0.63 inference(avatar_component_clause,[],[f1418])).
% 2.02/0.63 thf(f1434,plain,(
% 2.02/0.63 ~spl1_28),
% 2.02/0.63 inference(avatar_contradiction_clause,[],[f1433])).
% 2.02/0.63 thf(f1433,plain,(
% 2.02/0.63 $false | ~spl1_28),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1427])).
% 2.02/0.63 thf(f1427,plain,(
% 2.02/0.63 ($false = $true) | ~spl1_28),
% 2.02/0.63 inference(superposition,[],[f1174,f218])).
% 2.02/0.63 thf(f218,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f217])).
% 2.02/0.63 thf(f217,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 2.02/0.63 inference(pi_clausification,[],[f216])).
% 2.02/0.63 thf(f216,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 2.02/0.63 inference(beta_eta_normalization,[],[f185])).
% 2.02/0.63 thf(f185,plain,(
% 2.02/0.63 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 2.02/0.63 inference(definition_unfolding,[],[f150,f164])).
% 2.02/0.63 thf(f164,plain,(
% 2.02/0.63 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 2.02/0.63 inference(cnf_transformation,[],[f48])).
% 2.02/0.63 thf(f48,plain,(
% 2.02/0.63 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 2.02/0.63 inference(fool_elimination,[],[f47])).
% 2.02/0.63 thf(f47,plain,(
% 2.02/0.63 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 2.02/0.63 inference(rectify,[],[f18])).
% 2.02/0.63 thf(f18,axiom,(
% 2.02/0.63 ((^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))) = mreflexive)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 2.02/0.63 thf(f150,plain,(
% 2.02/0.63 ((mreflexive @ rel_s4) = $true)),
% 2.02/0.63 inference(cnf_transformation,[],[f72])).
% 2.02/0.63 thf(f72,plain,(
% 2.02/0.63 ((mreflexive @ rel_s4) = $true)),
% 2.02/0.63 inference(fool_elimination,[],[f71])).
% 2.02/0.63 thf(f71,plain,(
% 2.02/0.63 (mreflexive @ rel_s4)),
% 2.02/0.63 inference(rectify,[],[f34])).
% 2.02/0.63 thf(f34,axiom,(
% 2.02/0.63 (mreflexive @ rel_s4)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 2.02/0.63 thf(f1174,plain,(
% 2.02/0.63 ($false = (rel_s4 @ sK5 @ sK5)) | ~spl1_28),
% 2.02/0.63 inference(avatar_component_clause,[],[f1172])).
% 2.02/0.63 thf(f1425,plain,(
% 2.02/0.63 spl1_37 | spl1_23 | spl1_21 | ~spl1_8 | ~spl1_22),
% 2.02/0.63 inference(avatar_split_clause,[],[f1424,f1108,f571,f1104,f1111,f1418])).
% 2.02/0.63 thf(f1111,plain,(
% 2.02/0.63 spl1_23 <=> ($false = (string @ (sK3 @ sK5) @ sK5))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_23])])).
% 2.02/0.63 thf(f1104,plain,(
% 2.02/0.63 spl1_21 <=> ($false = (exists_in_world @ (sK3 @ sK5) @ sK5))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_21])])).
% 2.02/0.63 thf(f571,plain,(
% 2.02/0.63 spl1_8 <=> ! [X0 : mu,X1 : mu] : (((rel_s4 @ sK5 @ (sK6 @ X1 @ X0)) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (string @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (exists_in_world @ X0 @ sK5)))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 2.02/0.63 thf(f1108,plain,(
% 2.02/0.63 spl1_22 <=> ! [X0] : (($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ sK5) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_22])])).
% 2.02/0.63 thf(f1424,plain,(
% 2.02/0.63 ($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | (~spl1_8 | ~spl1_22)),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1423])).
% 2.02/0.63 thf(f1423,plain,(
% 2.02/0.63 ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ($false = $true) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = (string @ (sK3 @ sK5) @ sK5)) | (~spl1_8 | ~spl1_22)),
% 2.02/0.63 inference(forward_demodulation,[],[f1394,f196])).
% 2.02/0.63 thf(f196,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (($true = (exists_in_world @ (sK2 @ X1) @ X1))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f194])).
% 2.02/0.63 thf(f1394,plain,(
% 2.02/0.63 ($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ($false = (exists_in_world @ (sK2 @ sK5) @ sK5)) | (~spl1_8 | ~spl1_22)),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1393])).
% 2.02/0.63 thf(f1393,plain,(
% 2.02/0.63 ($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = $true) | ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = (exists_in_world @ (sK2 @ sK5) @ sK5)) | (~spl1_8 | ~spl1_22)),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f1381])).
% 2.02/0.63 thf(f1381,plain,(
% 2.02/0.63 ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ((entry_box @ (sK2 @ sK5) @ sK5) = $false) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = $true) | ($false = (exists_in_world @ (sK2 @ sK5) @ sK5)) | ($false = (exists_in_world @ (sK2 @ sK5) @ sK5)) | ($false = (string @ (sK3 @ sK5) @ sK5)) | (~spl1_8 | ~spl1_22)),
% 2.02/0.63 inference(superposition,[],[f1109,f572])).
% 2.02/0.63 thf(f572,plain,(
% 2.02/0.63 ( ! [X0 : mu,X1 : mu] : (((rel_s4 @ sK5 @ (sK6 @ X1 @ X0)) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (string @ X1 @ sK5))) ) | ~spl1_8),
% 2.02/0.63 inference(avatar_component_clause,[],[f571])).
% 2.02/0.63 thf(f1109,plain,(
% 2.02/0.63 ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ sK5) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5))) ) | ~spl1_22),
% 2.02/0.63 inference(avatar_component_clause,[],[f1108])).
% 2.02/0.63 thf(f1176,plain,(
% 2.02/0.63 spl1_28 | spl1_1 | ~spl1_23),
% 2.02/0.63 inference(avatar_split_clause,[],[f1168,f1111,f522,f1172])).
% 2.02/0.63 thf(f522,plain,(
% 2.02/0.63 spl1_1 <=> ! [X3] : ($false = (rel_s4 @ X3 @ sK5))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 2.02/0.63 thf(f1168,plain,(
% 2.02/0.63 ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK5)) | ($false = (rel_s4 @ sK5 @ sK5))) ) | ~spl1_23),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1167])).
% 2.02/0.63 thf(f1167,plain,(
% 2.02/0.63 ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK5)) | ($false = $true) | ($false = (rel_s4 @ sK5 @ sK5))) ) | ~spl1_23),
% 2.02/0.63 inference(superposition,[],[f239,f1113])).
% 2.02/0.63 thf(f1113,plain,(
% 2.02/0.63 ($false = (string @ (sK3 @ sK5) @ sK5)) | ~spl1_23),
% 2.02/0.63 inference(avatar_component_clause,[],[f1111])).
% 2.02/0.63 thf(f239,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((string @ (sK3 @ X2) @ X3) = $true) | ($false = (rel_s4 @ X2 @ X3)) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f238])).
% 2.02/0.63 thf(f238,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ((string @ (sK3 @ X2) @ X3) = $true) | ((~ (rel_s4 @ X2 @ X3)) = $true)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f237])).
% 2.02/0.63 thf(f237,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (~ (string @ (sK3 @ X2) @ X3))) | ((rel_s4 @ X1 @ X2) = $false) | ((~ (rel_s4 @ X2 @ X3)) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f235])).
% 2.02/0.63 thf(f235,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((~ (string @ (sK3 @ X2) @ X3)) | (~ (userid @ u @ (sK3 @ X2) @ X3)))) | ((~ (rel_s4 @ X2 @ X3)) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f234])).
% 2.02/0.63 thf(f234,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (~ ((~ (string @ (sK3 @ X2) @ X3)) | (~ (userid @ u @ (sK3 @ X2) @ X3))))) | ((rel_s4 @ X1 @ X2) = $false) | ((~ (rel_s4 @ X2 @ X3)) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f233])).
% 2.02/0.63 thf(f233,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | (((~ (rel_s4 @ X2 @ X3)) | (~ ((~ (string @ (sK3 @ X2) @ X3)) | (~ (userid @ u @ (sK3 @ X2) @ X3))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f232])).
% 2.02/0.63 thf(f232,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (string @ (sK3 @ X2) @ Y0)) | (~ (userid @ u @ (sK3 @ X2) @ Y0)))))) @ X3) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f231])).
% 2.02/0.63 thf(f231,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (string @ (sK3 @ X2) @ Y0)) | (~ (userid @ u @ (sK3 @ X2) @ Y0))))))) = $true)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f229])).
% 2.02/0.63 thf(f229,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (string @ (sK3 @ X2) @ Y0)) | (~ (userid @ u @ (sK3 @ X2) @ Y0)))))))) = $false) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f228])).
% 2.02/0.63 thf(f228,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (($false = ((exists_in_world @ (sK3 @ X2) @ X2) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (~ ((~ (string @ (sK3 @ X2) @ Y0)) | (~ (userid @ u @ (sK3 @ X2) @ Y0)))))))))) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f227])).
% 2.02/0.63 thf(f227,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (string @ Y0 @ Y1)) | (~ (userid @ u @ Y0 @ Y1)))))))))) @ (sK3 @ X2))) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(sigma_clausification,[],[f226])).
% 2.02/0.63 thf(f226,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (string @ Y0 @ Y1)) | (~ (userid @ u @ Y0 @ Y1))))))))))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f225])).
% 2.02/0.63 thf(f225,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (string @ Y0 @ Y1)) | (~ (userid @ u @ Y0 @ Y1)))))))))))) = $true)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f224])).
% 2.02/0.63 thf(f224,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (string @ Y0 @ Y1)) | (~ (userid @ u @ Y0 @ Y1)))))))))))) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f223])).
% 2.02/0.63 thf(f223,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s4 @ X1 @ X2)) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (~ ((~ (string @ Y0 @ Y1)) | (~ (userid @ u @ Y0 @ Y1))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f222])).
% 2.02/0.63 thf(f222,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (string @ Y1 @ Y2)) | (~ (userid @ u @ Y1 @ Y2)))))))))))))) @ X2) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f221])).
% 2.02/0.63 thf(f221,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ ((~ (string @ Y1 @ Y2)) | (~ (userid @ u @ Y1 @ Y2))))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f220])).
% 2.02/0.63 thf(f220,plain,(
% 2.02/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ ((~ (string @ Y2 @ Y3)) | (~ (userid @ u @ Y2 @ Y3)))))))))))))))) @ X1) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f219])).
% 2.02/0.63 thf(f219,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ ((~ (string @ Y2 @ Y3)) | (~ (userid @ u @ Y2 @ Y3))))))))))))))))) = $true)),
% 2.02/0.63 inference(beta_eta_normalization,[],[f186])).
% 2.02/0.63 thf(f186,plain,(
% 2.02/0.63 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 2.02/0.63 inference(definition_unfolding,[],[f157,f140,f172,f180,f172,f174])).
% 2.02/0.63 thf(f157,plain,(
% 2.02/0.63 ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 2.02/0.63 inference(cnf_transformation,[],[f125])).
% 2.02/0.63 thf(f125,plain,(
% 2.02/0.63 ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (string @ Y0))))))) = $true)),
% 2.02/0.63 inference(fool_elimination,[],[f124])).
% 2.02/0.63 thf(f124,plain,(
% 2.02/0.63 (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X0 : mu] : (mbox_s4 @ (mand @ (userid @ u @ X0) @ (string @ X0)))))))),
% 2.02/0.63 inference(rectify,[],[f39])).
% 2.02/0.63 thf(f39,axiom,(
% 2.02/0.63 (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mbox_s4 @ (mand @ (userid @ u @ X11) @ (string @ X11)))))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)).
% 2.02/0.63 thf(f1161,plain,(
% 2.02/0.63 spl1_1 | ~spl1_21),
% 2.02/0.63 inference(avatar_split_clause,[],[f1156,f1104,f522])).
% 2.02/0.63 thf(f1156,plain,(
% 2.02/0.63 ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK5))) ) | ~spl1_21),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1153])).
% 2.02/0.63 thf(f1153,plain,(
% 2.02/0.63 ( ! [X0 : $i] : (($false = $true) | ($false = (rel_s4 @ X0 @ sK5))) ) | ~spl1_21),
% 2.02/0.63 inference(superposition,[],[f230,f1106])).
% 2.02/0.63 thf(f1106,plain,(
% 2.02/0.63 ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ~spl1_21),
% 2.02/0.63 inference(avatar_component_clause,[],[f1104])).
% 2.02/0.63 thf(f230,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((exists_in_world @ (sK3 @ X2) @ X2) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f228])).
% 2.02/0.63 thf(f1115,plain,(
% 2.02/0.63 spl1_21 | spl1_22 | spl1_23 | spl1_1 | ~spl1_8 | ~spl1_15),
% 2.02/0.63 inference(avatar_split_clause,[],[f1075,f848,f571,f522,f1111,f1108,f1104])).
% 2.02/0.63 thf(f848,plain,(
% 2.02/0.63 spl1_15 <=> ! [X0 : mu,X1 : mu] : (($false = (exists_in_world @ X0 @ sK5)) | ($false = (number @ X0 @ one @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X0))) | ($false = (string @ X1 @ sK5)) | ($false = (entry_box @ X0 @ (sK6 @ X1 @ X0))))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_15])])).
% 2.02/0.63 thf(f1075,plain,(
% 2.02/0.63 ( ! [X0 : $i,X1 : $i] : (($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = (rel_s4 @ X1 @ sK5)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ sK5) @ (sK2 @ X0))))) ) | (~spl1_8 | ~spl1_15)),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1074])).
% 2.02/0.63 thf(f1074,plain,(
% 2.02/0.63 ( ! [X0 : $i,X1 : $i] : (($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = $true) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ sK5) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X1 @ sK5)) | ($false = (string @ (sK3 @ sK5) @ sK5))) ) | (~spl1_8 | ~spl1_15)),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f1056])).
% 2.02/0.63 thf(f1056,plain,(
% 2.02/0.63 ( ! [X0 : $i,X1 : $i] : (($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = (string @ (sK3 @ sK5) @ sK5)) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ sK5) @ (sK2 @ X0)))) | ($false = $true) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X1 @ sK5)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (exists_in_world @ (sK3 @ sK5) @ sK5))) ) | (~spl1_8 | ~spl1_15)),
% 2.02/0.63 inference(superposition,[],[f1053,f572])).
% 2.02/0.63 thf(f1053,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (string @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5))) ) | ~spl1_15),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1052])).
% 2.02/0.63 thf(f1052,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s4 @ X2 @ X1)) | ($false = (string @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X1 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK3 @ X1) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = $true) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0))))) ) | ~spl1_15),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f1048])).
% 2.02/0.63 thf(f1048,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X1 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (string @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (exists_in_world @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0))))) ) | ~spl1_15),
% 2.02/0.63 inference(superposition,[],[f206,f1019])).
% 2.02/0.63 thf(f1019,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (entry_box @ (sK2 @ X0) @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (rel_s4 @ X1 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (exists_in_world @ (sK3 @ X1) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (string @ (sK3 @ X1) @ sK5)) | ($false = (entry_box @ (sK2 @ X0) @ sK5))) ) | ~spl1_15),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1016])).
% 2.02/0.63 thf(f1016,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = $true) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (exists_in_world @ (sK3 @ X1) @ sK5)) | ($false = (exists_in_world @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X1 @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (entry_box @ (sK2 @ X0) @ (sK6 @ (sK3 @ X1) @ (sK2 @ X0)))) | ($false = (entry_box @ (sK2 @ X0) @ sK5)) | ($false = (rel_s4 @ X2 @ X1)) | ($false = (string @ (sK3 @ X1) @ sK5))) ) | ~spl1_15),
% 2.02/0.63 inference(superposition,[],[f205,f1004])).
% 2.02/0.63 thf(f1004,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : mu] : (($false = (number @ X1 @ one @ (sK6 @ (sK3 @ X0) @ X1))) | ($false = (rel_s4 @ X2 @ X0)) | ($false = (entry_box @ X1 @ (sK6 @ (sK3 @ X0) @ X1))) | ($false = (exists_in_world @ (sK3 @ X0) @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X0) @ X1))) | ($false = (string @ (sK3 @ X0) @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5))) ) | ~spl1_15),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f1002])).
% 2.02/0.63 thf(f1002,plain,(
% 2.02/0.63 ( ! [X2 : $i,X0 : $i,X1 : mu] : (($false = (entry_box @ X1 @ sK5)) | ($false = (rel_s4 @ X0 @ (sK6 @ (sK3 @ X0) @ X1))) | ($false = $true) | ($false = (exists_in_world @ (sK3 @ X0) @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ (sK3 @ X0) @ X1))) | ($false = (string @ (sK3 @ X0) @ sK5)) | ($false = (rel_s4 @ X2 @ X0)) | ($false = (number @ X1 @ one @ (sK6 @ (sK3 @ X0) @ X1)))) ) | ~spl1_15),
% 2.02/0.63 inference(superposition,[],[f241,f849])).
% 2.02/0.63 thf(f849,plain,(
% 2.02/0.63 ( ! [X0 : mu,X1 : mu] : (($false = (userid @ u @ X1 @ (sK6 @ X1 @ X0))) | ($false = (number @ X0 @ one @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (string @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (entry_box @ X0 @ (sK6 @ X1 @ X0)))) ) | ~spl1_15),
% 2.02/0.63 inference(avatar_component_clause,[],[f848])).
% 2.02/0.63 thf(f241,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((userid @ u @ (sK3 @ X2) @ X3) = $true) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (rel_s4 @ X2 @ X3))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f240])).
% 2.02/0.63 thf(f240,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (rel_s4 @ X2 @ X3)) = $true) | ((userid @ u @ (sK3 @ X2) @ X3) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f236])).
% 2.02/0.63 thf(f236,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (~ (userid @ u @ (sK3 @ X2) @ X3))) | ((rel_s4 @ X1 @ X2) = $false) | ((~ (rel_s4 @ X2 @ X3)) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f235])).
% 2.02/0.63 thf(f205,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((number @ (sK2 @ X1) @ one @ X2) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f204])).
% 2.02/0.63 thf(f204,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (~ (number @ (sK2 @ X1) @ one @ X2)))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f202])).
% 2.02/0.63 thf(f889,plain,(
% 2.02/0.63 ~spl1_7),
% 2.02/0.63 inference(avatar_contradiction_clause,[],[f888])).
% 2.02/0.63 thf(f888,plain,(
% 2.02/0.63 $false | ~spl1_7),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f863])).
% 2.02/0.63 thf(f863,plain,(
% 2.02/0.63 ($false = $true) | ~spl1_7),
% 2.02/0.63 inference(superposition,[],[f196,f569])).
% 2.02/0.63 thf(f569,plain,(
% 2.02/0.63 ( ! [X2 : mu] : (($false = (exists_in_world @ X2 @ sK5))) ) | ~spl1_7),
% 2.02/0.63 inference(avatar_component_clause,[],[f568])).
% 2.02/0.63 thf(f568,plain,(
% 2.02/0.63 spl1_7 <=> ! [X2 : mu] : ($false = (exists_in_world @ X2 @ sK5))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 2.02/0.63 thf(f851,plain,(
% 2.02/0.63 spl1_15 | spl1_7 | spl1_1 | ~spl1_14),
% 2.02/0.63 inference(avatar_split_clause,[],[f841,f831,f522,f568,f848])).
% 2.02/0.63 thf(f831,plain,(
% 2.02/0.63 spl1_14 <=> ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X0 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X2 @ X1))) | ($false = (string @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)))),
% 2.02/0.63 introduced(avatar_definition,[new_symbols(naming,[spl1_14])])).
% 2.02/0.63 thf(f841,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((entry_box @ X0 @ sK5) = $false) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X0))) | ($false = (string @ X1 @ sK5)) | ($false = (number @ X0 @ one @ (sK6 @ X1 @ X0))) | ($false = (entry_box @ X0 @ (sK6 @ X1 @ X0))) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) ) | ~spl1_14),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f840])).
% 2.02/0.63 thf(f840,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (rel_s4 @ X3 @ sK5)) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X1 @ sK5)) | ($false = (number @ X0 @ one @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (entry_box @ X0 @ (sK6 @ X1 @ X0)))) ) | ~spl1_14),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f836])).
% 2.02/0.63 thf(f836,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ($false = (userid @ u @ X1 @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X2 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (entry_box @ X0 @ (sK6 @ X1 @ X0))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (string @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (string @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (number @ X0 @ one @ (sK6 @ X1 @ X0)))) ) | ~spl1_14),
% 2.02/0.63 inference(superposition,[],[f832,f342])).
% 2.02/0.63 thf(f342,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((exists_in_world @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X2) = $true) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f340])).
% 2.02/0.63 thf(f340,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = ((exists_in_world @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X2) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X4 @ X5 @ Y1 @ Y0) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y1 @ Y0))))))))))))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f339])).
% 2.02/0.63 thf(f339,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))) @ (sK10 @ X2 @ X5 @ X4 @ X3))) | ($false = (exists_in_world @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2))) )),
% 2.02/0.63 inference(sigma_clausification,[],[f338])).
% 2.02/0.63 thf(f338,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1))))))))))))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f337])).
% 2.02/0.63 thf(f337,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ((~ (string @ X4 @ X2)) = $true) | ($false = (entry_box @ X5 @ X2)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))))) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f336])).
% 2.02/0.63 thf(f336,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((~ (entry_box @ X5 @ X2)) = $true) | ((~ (string @ X4 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1))))))))))))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f335])).
% 2.02/0.63 thf(f335,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))))) = $true) | ((~ (entry_box @ X5 @ X2)) = $true) | ((~ (string @ X4 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X5 @ X2))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f334])).
% 2.02/0.63 thf(f334,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X5 @ X2)) | ($true = ((~ (entry_box @ X5 @ X2)) | (~ (string @ X4 @ X2)))) | ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))))) = $true) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f333])).
% 2.02/0.63 thf(f333,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | (((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))))) | ((~ (entry_box @ X5 @ X2)) | (~ (string @ X4 @ X2)))) = $true) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f332])).
% 2.02/0.63 thf(f332,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ($true = ((exists_in_world @ X5 @ X2) => ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X4 @ X5 @ Y2 @ Y1) | (~ (do @ X3 @ Y0 @ Y2 @ Y1)))))))))))))) | ((~ (entry_box @ X5 @ X2)) | (~ (string @ X4 @ X2)))))) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f331])).
% 2.02/0.63 thf(f331,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (((rel_s4 @ X1 @ X2) = $false) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X4 @ Y0 @ Y3 @ Y2) | (~ (do @ X3 @ Y1 @ Y3 @ Y2)))))))))))))) | ((~ (entry_box @ Y0 @ X2)) | (~ (string @ X4 @ X2)))))) @ X5) = $true) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 2.02/0.63 inference(pi_clausification,[],[f330])).
% 2.02/0.63 thf(f330,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X4 @ Y0 @ Y3 @ Y2) | (~ (do @ X3 @ Y1 @ Y3 @ Y2)))))))))))))) | ((~ (entry_box @ Y0 @ X2)) | (~ (string @ X4 @ X2))))))) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f329])).
% 2.02/0.63 thf(f329,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ X1 @ X2) = $false) | (((exists_in_world @ X4 @ X2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => ((~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X4 @ Y0 @ Y3 @ Y2) | (~ (do @ X3 @ Y1 @ Y3 @ Y2)))))))))))))) | ((~ (entry_box @ Y0 @ X2)) | (~ (string @ X4 @ X2)))))))) = $true) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f328])).
% 2.02/0.63 thf(f328,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ Y0 @ Y1 @ Y4 @ Y3) | (~ (do @ X3 @ Y2 @ Y4 @ Y3)))))))))))))) | ((~ (entry_box @ Y1 @ X2)) | (~ (string @ Y0 @ X2))))))))) @ X4) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f327])).
% 2.02/0.63 thf(f327,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X3 @ X2)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ Y0 @ Y1 @ Y4 @ Y3) | (~ (do @ X3 @ Y2 @ Y4 @ Y3)))))))))))))) | ((~ (entry_box @ Y1 @ X2)) | (~ (string @ Y0 @ X2)))))))))) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f326])).
% 2.02/0.63 thf(f326,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i] : ((((exists_in_world @ X3 @ X2) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => ((~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ X2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ Y0 @ Y1 @ Y4 @ Y3) | (~ (do @ X3 @ Y2 @ Y4 @ Y3)))))))))))))) | ((~ (entry_box @ Y1 @ X2)) | (~ (string @ Y0 @ X2))))))))))) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f325])).
% 2.02/0.63 thf(f325,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X1 : $i] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => ((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y1 @ Y2 @ Y5 @ Y4) | (~ (do @ Y0 @ Y3 @ Y5 @ Y4)))))))))))))) | ((~ (entry_box @ Y2 @ X2)) | (~ (string @ Y1 @ X2)))))))))))) @ X3) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(pi_clausification,[],[f324])).
% 2.02/0.63 thf(f324,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => ((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y1 @ Y2 @ Y5 @ Y4) | (~ (do @ Y0 @ Y3 @ Y5 @ Y4)))))))))))))) | ((~ (entry_box @ Y2 @ X2)) | (~ (string @ Y1 @ X2)))))))))))))) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f323])).
% 2.02/0.63 thf(f323,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => ((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y1 @ Y2 @ Y5 @ Y4) | (~ (do @ Y0 @ Y3 @ Y5 @ Y4)))))))))))))) | ((~ (entry_box @ Y2 @ X2)) | (~ (string @ Y1 @ X2))))))))))))))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f322])).
% 2.02/0.63 thf(f322,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_s4 @ X1 @ X2)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ X2) => ((~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ X2) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ X2 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y1 @ Y2 @ Y5 @ Y4) | (~ (do @ Y0 @ Y3 @ Y5 @ Y4)))))))))))))) | ((~ (entry_box @ Y2 @ X2)) | (~ (string @ Y1 @ X2)))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f321])).
% 2.02/0.63 thf(f321,plain,(
% 2.02/0.63 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((in @ Y2 @ Y3 @ Y6 @ Y5) | (~ (do @ Y1 @ Y4 @ Y6 @ Y5)))))))))))))) | ((~ (entry_box @ Y3 @ Y0)) | (~ (string @ Y2 @ Y0))))))))))))))) @ X2) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f320])).
% 2.02/0.63 thf(f320,plain,(
% 2.02/0.63 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => ((~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((in @ Y2 @ Y3 @ Y6 @ Y5) | (~ (do @ Y1 @ Y4 @ Y6 @ Y5)))))))))))))) | ((~ (entry_box @ Y3 @ Y0)) | (~ (string @ Y2 @ Y0)))))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f319])).
% 2.02/0.63 thf(f319,plain,(
% 2.02/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => ((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y3 @ Y4 @ Y7 @ Y6) | (~ (do @ Y2 @ Y5 @ Y7 @ Y6)))))))))))))) | ((~ (entry_box @ Y4 @ Y1)) | (~ (string @ Y3 @ Y1))))))))))))))))) @ X1) = $true)) )),
% 2.02/0.63 inference(pi_clausification,[],[f318])).
% 2.02/0.63 thf(f318,plain,(
% 2.02/0.63 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => ((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y3 @ Y4 @ Y7 @ Y6) | (~ (do @ Y2 @ Y5 @ Y7 @ Y6)))))))))))))) | ((~ (entry_box @ Y4 @ Y1)) | (~ (string @ Y3 @ Y1)))))))))))))))))))),
% 2.02/0.63 inference(boolean_simplification,[],[f317])).
% 2.02/0.63 thf(f317,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => ((~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y3 @ Y4 @ Y7 @ Y6) | (~ (do @ Y2 @ Y5 @ Y7 @ Y6)))))))))))))) | (~ (~ ((~ (entry_box @ Y4 @ Y1)) | (~ (string @ Y3 @ Y1)))))))))))))))))))) = $true)),
% 2.02/0.63 inference(beta_eta_normalization,[],[f187])).
% 2.02/0.63 thf(f187,plain,(
% 2.02/0.63 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ Y4)))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y6 @ Y7) | (Y5 @ Y7))))))) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ Y4)))))) @ (string @ Y1) @ (entry_box @ Y2)) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ (Y3 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: ((Y8 @ Y9) | (Y7 @ Y9))))))) @ ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (~ (Y7 @ Y8))))) @ Y5) @ Y6)))) @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))) = $true)),
% 2.02/0.63 inference(definition_unfolding,[],[f158,f140,f172,f134,f134,f134,f175,f174,f180,f172,f134,f175])).
% 2.02/0.63 thf(f175,plain,(
% 2.02/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 2.02/0.63 inference(definition_unfolding,[],[f168,f144,f149])).
% 2.02/0.63 thf(f168,plain,(
% 2.02/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 2.02/0.63 inference(cnf_transformation,[],[f74])).
% 2.02/0.63 thf(f74,plain,(
% 2.02/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 2.02/0.63 inference(fool_elimination,[],[f73])).
% 2.02/0.63 thf(f73,plain,(
% 2.02/0.63 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 2.02/0.63 inference(rectify,[],[f9])).
% 2.02/0.63 thf(f9,axiom,(
% 2.02/0.63 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 2.02/0.63 thf(f158,plain,(
% 2.02/0.63 ($true = (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_ind @ (^[Y3 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))))),
% 2.02/0.63 inference(cnf_transformation,[],[f80])).
% 2.02/0.63 thf(f80,plain,(
% 2.02/0.63 ($true = (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mforall_ind @ (^[Y2 : mu]: (mimplies @ (mand @ (string @ Y1) @ (entry_box @ Y2)) @ (mexists_ind @ (^[Y3 : mu]: (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y0 @ Y3 @ Y4) @ (in @ Y1 @ Y2 @ Y4)))))))))))))))))),
% 2.02/0.63 inference(fool_elimination,[],[f79])).
% 2.02/0.63 thf(f79,plain,(
% 2.02/0.63 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mforall_ind @ (^[X2 : mu] : (mimplies @ (mand @ (string @ X1) @ (entry_box @ X2)) @ (mexists_ind @ (^[X3 : mu] : (mbox_s4 @ (mforall_ind @ (^[X4 : mu] : (mimplies @ (do @ X0 @ X3 @ X4) @ (in @ X1 @ X2 @ X4))))))))))))))))),
% 2.02/0.63 inference(rectify,[],[f41])).
% 2.02/0.63 thf(f41,axiom,(
% 2.02/0.63 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X8 : mu] : (mforall_ind @ (^[X11 : mu] : (mforall_ind @ (^[X12 : mu] : (mimplies @ (mand @ (string @ X11) @ (entry_box @ X12)) @ (mexists_ind @ (^[X13 : mu] : (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 2.02/0.63 thf(f832,plain,(
% 2.02/0.63 ( ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (entry_box @ X1 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X2 @ X1)))) ) | ~spl1_14),
% 2.02/0.63 inference(avatar_component_clause,[],[f831])).
% 2.02/0.63 thf(f834,plain,(
% 2.02/0.63 spl1_14 | spl1_1),
% 2.02/0.63 inference(avatar_split_clause,[],[f809,f522,f831])).
% 2.02/0.63 thf(f809,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X2 @ X1))) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5))) )),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f808])).
% 2.02/0.63 thf(f808,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (number @ X1 @ one @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = $true) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (string @ X2 @ sK5))) )),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f804])).
% 2.02/0.63 thf(f804,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = $true) | ($false = (userid @ u @ X2 @ (sK6 @ X2 @ X1))) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (number @ X1 @ one @ (sK6 @ X2 @ X1))) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X2 @ X1))) | ($false = (entry_box @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5))) )),
% 2.02/0.63 inference(superposition,[],[f286,f798])).
% 2.02/0.63 thf(f798,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : $i] : (((rel_s4 @ X1 @ (sK7 @ X3 @ (sK10 @ X1 @ X2 @ X0 @ X3) @ X0 @ X2)) = $false) | ($false = (string @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ((rel_s4 @ X4 @ X1) = $false) | ((exists_in_world @ (sK10 @ X1 @ X2 @ X0 @ X3) @ sK5) = $false) | ($false = (entry_box @ X2 @ X1)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2)))) )),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f797])).
% 2.02/0.63 thf(f797,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : $i] : (((rel_s4 @ X1 @ (sK7 @ X3 @ (sK10 @ X1 @ X2 @ X0 @ X3) @ X0 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ X1)) | ((rel_s4 @ X4 @ X1) = $false) | ((exists_in_world @ (sK10 @ X1 @ X2 @ X0 @ X3) @ sK5) = $false) | ($false = (string @ X0 @ X1)) | ($false = $true) | ($false = (entry_box @ X2 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X0 @ sK5))) )),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f790])).
% 2.02/0.63 thf(f790,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X4 : $i] : (((exists_in_world @ (sK10 @ X1 @ X2 @ X0 @ X3) @ sK5) = $false) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (entry_box @ X2 @ X1)) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X0 @ X1)) | ($false = (entry_box @ X2 @ (sK6 @ X0 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X0 @ X2))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = $true) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ((rel_s4 @ X4 @ X1) = $false) | ($false = (exists_in_world @ X0 @ X1)) | ((rel_s4 @ X1 @ (sK7 @ X3 @ (sK10 @ X1 @ X2 @ X0 @ X3) @ X0 @ X2)) = $false) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (userid @ u @ X0 @ (sK6 @ X0 @ X2))) | ((exists_in_world @ (sK10 @ X1 @ X2 @ X0 @ X3) @ sK5) = $false) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(superposition,[],[f307,f786])).
% 2.02/0.63 thf(f786,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ (sK9 @ X0 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3 @ X1) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X0 @ sK5)) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ X2)) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (entry_box @ X1 @ X2)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (string @ X0 @ X2))) )),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f785])).
% 2.02/0.63 thf(f785,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ X0 @ sK5)) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = $true) | ($false = (string @ X0 @ X2)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ (sK9 @ X0 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3 @ X1) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(duplicate_literal_removal,[],[f781])).
% 2.02/0.63 thf(f781,plain,(
% 2.02/0.63 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ X0 @ sK5)) | ((exists_in_world @ X0 @ X2) = $false) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ((userid @ u @ X0 @ (sK6 @ X0 @ X1)) = $false) | ($false = (number @ X1 @ one @ (sK6 @ X0 @ X1))) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (entry_box @ X1 @ (sK6 @ X0 @ X1))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ (sK9 @ X0 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3 @ X1) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ($false = (string @ X0 @ X2)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (exists_in_world @ X1 @ X2)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = $true)) )),
% 2.02/0.63 inference(superposition,[],[f475,f312])).
% 2.02/0.63 thf(f312,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2)))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f311])).
% 2.02/0.63 thf(f311,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f310])).
% 2.02/0.63 thf(f310,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f309])).
% 2.02/0.63 thf(f309,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f303])).
% 2.02/0.63 thf(f303,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = ((in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f302])).
% 2.02/0.63 thf(f302,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = ((exists_in_world @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)))))) | ($false = (exists_in_world @ X1 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f301])).
% 2.02/0.63 thf(f301,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))) @ (sK9 @ X1 @ X3 @ X4 @ X2))) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(sigma_clausification,[],[f300])).
% 2.02/0.63 thf(f300,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))))) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f299])).
% 2.02/0.63 thf(f299,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ((~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))))) | ($false = (exists_in_world @ X1 @ sK5)) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f298])).
% 2.02/0.63 thf(f298,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2))))))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f287])).
% 2.02/0.63 thf(f287,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2)))))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))))) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f275])).
% 2.02/0.63 thf(f275,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))))))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f274])).
% 2.02/0.63 thf(f274,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = ((~ (rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2))) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2))))))))) | ($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))))))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f273])).
% 2.02/0.63 thf(f273,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | (((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $false) | ($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2)))))))) )),
% 2.02/0.63 inference(sigma_clausification,[],[f272])).
% 2.02/0.63 thf(f272,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))))))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f271])).
% 2.02/0.63 thf(f271,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X4 @ sK5)) | ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0)))))) @ (sK6 @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(sigma_clausification,[],[f270])).
% 2.02/0.63 thf(f270,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0)))))))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0))))))))))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f269])).
% 2.02/0.63 thf(f269,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0)))))))) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) | ($false = (exists_in_world @ X4 @ sK5))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f268])).
% 2.02/0.63 thf(f268,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0)))))))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f267])).
% 2.02/0.63 thf(f267,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0))))))))) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f266])).
% 2.02/0.63 thf(f266,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : ((((exists_in_world @ X4 @ sK5) => ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X1 @ X2 @ Y1 @ Y0) | (~ (do @ X4 @ X3 @ Y1 @ Y0)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (((~ (number @ X2 @ one @ Y0)) | (~ (entry_box @ X2 @ Y0))) | (~ (userid @ u @ X1 @ Y0)))))))))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f265])).
% 2.02/0.63 thf(f265,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X1 @ X2 @ Y2 @ Y1) | (~ (do @ Y0 @ X3 @ Y2 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (((~ (number @ X2 @ one @ Y1)) | (~ (entry_box @ X2 @ Y1))) | (~ (userid @ u @ X1 @ Y1))))))))))) @ X4)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(pi_clausification,[],[f264])).
% 2.02/0.63 thf(f264,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X1 @ X2 @ Y2 @ Y1) | (~ (do @ Y0 @ X3 @ Y2 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (((~ (number @ X2 @ one @ Y1)) | (~ (entry_box @ X2 @ Y1))) | (~ (userid @ u @ X1 @ Y1)))))))))))) = $true)) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f263])).
% 2.02/0.63 thf(f263,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | (((exists_in_world @ X3 @ sK5) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((in @ X1 @ X2 @ Y2 @ Y1) | (~ (do @ Y0 @ X3 @ Y2 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (((~ (number @ X2 @ one @ Y1)) | (~ (entry_box @ X2 @ Y1))) | (~ (userid @ u @ X1 @ Y1))))))))))))) = $true) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f262])).
% 2.02/0.63 thf(f262,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X1 @ X2 @ Y3 @ Y2) | (~ (do @ Y1 @ Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (~ (((~ (number @ X2 @ one @ Y2)) | (~ (entry_box @ X2 @ Y2))) | (~ (userid @ u @ X1 @ Y2)))))))))))))) @ X3) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.63 inference(pi_clausification,[],[f261])).
% 2.02/0.63 thf(f261,plain,(
% 2.02/0.63 ( ! [X2 : mu,X1 : mu] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X1 @ X2 @ Y3 @ Y2) | (~ (do @ Y1 @ Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (~ (((~ (number @ X2 @ one @ Y2)) | (~ (entry_box @ X2 @ Y2))) | (~ (userid @ u @ X1 @ Y2)))))))))))))))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f260])).
% 2.02/0.63 thf(f260,plain,(
% 2.02/0.63 ( ! [X2 : mu,X1 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | (((exists_in_world @ X2 @ sK5) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((in @ X1 @ X2 @ Y3 @ Y2) | (~ (do @ Y1 @ Y0 @ Y3 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK5 @ Y2)) | (~ (((~ (number @ X2 @ one @ Y2)) | (~ (entry_box @ X2 @ Y2))) | (~ (userid @ u @ X1 @ Y2)))))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f259])).
% 2.02/0.63 thf(f259,plain,(
% 2.02/0.63 ( ! [X2 : mu,X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ X1 @ Y0 @ Y4 @ Y3) | (~ (do @ Y2 @ Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (~ (((~ (number @ Y0 @ one @ Y3)) | (~ (entry_box @ Y0 @ Y3))) | (~ (userid @ u @ X1 @ Y3))))))))))))))))) @ X2) = $true) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.63 inference(pi_clausification,[],[f258])).
% 2.02/0.63 thf(f258,plain,(
% 2.02/0.63 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ X1 @ Y0 @ Y4 @ Y3) | (~ (do @ Y2 @ Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (~ (((~ (number @ Y0 @ one @ Y3)) | (~ (entry_box @ Y0 @ Y3))) | (~ (userid @ u @ X1 @ Y3)))))))))))))))))))) )),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f257])).
% 2.02/0.63 thf(f257,plain,(
% 2.02/0.63 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK5) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => ((in @ X1 @ Y0 @ Y4 @ Y3) | (~ (do @ Y2 @ Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ sK5 @ Y3)) | (~ (((~ (number @ Y0 @ one @ Y3)) | (~ (entry_box @ Y0 @ Y3))) | (~ (userid @ u @ X1 @ Y3))))))))))))))))))) = $true)) )),
% 2.02/0.63 inference(beta_eta_normalization,[],[f256])).
% 2.02/0.63 thf(f256,plain,(
% 2.02/0.63 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK5) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y0 @ Y1 @ Y5 @ Y4) | (~ (do @ Y3 @ Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (~ (((~ (number @ Y1 @ one @ Y4)) | (~ (entry_box @ Y1 @ Y4))) | (~ (userid @ u @ Y0 @ Y4)))))))))))))))))))) @ X1))) )),
% 2.02/0.63 inference(pi_clausification,[],[f255])).
% 2.02/0.63 thf(f255,plain,(
% 2.02/0.63 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK5) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y0 @ Y1 @ Y5 @ Y4) | (~ (do @ Y3 @ Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (~ (((~ (number @ Y1 @ one @ Y4)) | (~ (entry_box @ Y1 @ Y4))) | (~ (userid @ u @ Y0 @ Y4))))))))))))))))))))) = $true)),
% 2.02/0.63 inference(not_proxy_clausification,[],[f252])).
% 2.02/0.63 thf(f252,plain,(
% 2.02/0.63 ($false = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK5) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y0 @ Y1 @ Y5 @ Y4) | (~ (do @ Y3 @ Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (~ (((~ (number @ Y1 @ one @ Y4)) | (~ (entry_box @ Y1 @ Y4))) | (~ (userid @ u @ Y0 @ Y4)))))))))))))))))))))))),
% 2.02/0.63 inference(binary_proxy_clausification,[],[f251])).
% 2.02/0.63 thf(f251,plain,(
% 2.02/0.63 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK5) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ sK5) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ sK5) => ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => ((in @ Y0 @ Y1 @ Y5 @ Y4) | (~ (do @ Y3 @ Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ sK5 @ Y4)) | (~ (((~ (number @ Y1 @ one @ Y4)) | (~ (entry_box @ Y1 @ Y4))) | (~ (userid @ u @ Y0 @ Y4))))))))))))))))))))))))),
% 2.02/0.63 inference(beta_eta_normalization,[],[f250])).
% 2.02/0.63 thf(f250,plain,(
% 2.02/0.63 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((in @ Y1 @ Y2 @ Y6 @ Y5) | (~ (do @ Y4 @ Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (~ (((~ (number @ Y2 @ one @ Y5)) | (~ (entry_box @ Y2 @ Y5))) | (~ (userid @ u @ Y1 @ Y5)))))))))))))))))))))))) @ sK5))),
% 2.02/0.63 inference(sigma_clausification,[],[f249])).
% 2.02/0.63 thf(f249,plain,(
% 2.02/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y0) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y0) => ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => ((in @ Y1 @ Y2 @ Y6 @ Y5) | (~ (do @ Y4 @ Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y0 @ Y5)) | (~ (((~ (number @ Y2 @ one @ Y5)) | (~ (entry_box @ Y2 @ Y5))) | (~ (userid @ u @ Y1 @ Y5))))))))))))))))))))))))))),
% 2.02/0.63 inference(beta_eta_normalization,[],[f248])).
% 2.02/0.63 thf(f248,plain,(
% 2.02/0.63 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ (((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))) | (~ (userid @ u @ Y2 @ Y6)))))))))))))))))))))))))) @ sK4))),
% 2.02/0.63 inference(sigma_clausification,[],[f247])).
% 2.02/0.63 thf(f247,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ (((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))) != $true)),
% 2.02/0.63 inference(boolean_simplification,[],[f246])).
% 2.02/0.63 thf(f246,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (~ ((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))) != $true)),
% 2.02/0.63 inference(boolean_simplification,[],[f245])).
% 2.02/0.63 thf(f245,plain,(
% 2.02/0.63 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (~ ((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))))))),
% 2.02/0.63 inference(boolean_simplification,[],[f244])).
% 2.02/0.63 thf(f244,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (~ ((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))))))) != $true)),
% 2.02/0.63 inference(boolean_simplification,[],[f243])).
% 2.02/0.63 thf(f243,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (~ ((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))))))))) != $true)),
% 2.02/0.63 inference(boolean_simplification,[],[f242])).
% 2.02/0.63 thf(f242,plain,(
% 2.02/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (~ (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y1) => (~ (~ (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y1) => (~ (~ ((~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (!! @ mu @ (^[Y7 : mu]: ((exists_in_world @ Y7 @ Y6) => ((in @ Y2 @ Y3 @ Y7 @ Y6) | (~ (do @ Y5 @ Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y1 @ Y6)) | (~ ((~ (~ ((~ (number @ Y3 @ one @ Y6)) | (~ (entry_box @ Y3 @ Y6))))) | (~ (userid @ u @ Y2 @ Y6))))))))))))))))))))))))))))))))))) != $true)),
% 2.02/0.63 inference(beta_eta_normalization,[],[f183])).
% 2.02/0.63 thf(f183,plain,(
% 2.02/0.63 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((exists_in_world @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ (Y2 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (~ (Y5 @ Y6))))) @ (Y3 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ (userid @ u @ Y0) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (rel_s4 @ Y5 @ Y6)) | (Y4 @ Y6))))))) @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((exists_in_world @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: ((Y8 @ Y9) | (Y7 @ Y9))))))) @ ((^[Y7 : $i > $o]: ((^[Y8 : $i]: (~ (Y7 @ Y8))))) @ Y5) @ Y6)))) @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))))),
% 2.02/0.63 inference(definition_unfolding,[],[f138,f140,f172,f180,f180,f180,f180,f174,f172,f174,f174,f172,f134,f175])).
% 2.02/0.63 thf(f138,plain,(
% 2.02/0.63 ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 2.02/0.63 inference(cnf_transformation,[],[f126])).
% 2.02/0.63 thf(f126,plain,(
% 2.02/0.63 ((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) != $true)),
% 2.02/0.63 inference(flattening,[],[f115])).
% 2.02/0.63 thf(f115,plain,(
% 2.02/0.63 ~((mvalid @ (mbox_s4 @ (mexists_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mexists_ind @ (^[Y2 : mu]: (mexists_ind @ (^[Y3 : mu]: (mand @ (mbox_s4 @ (mand @ (userid @ u @ Y0) @ (mand @ (entry_box @ Y1) @ (number @ Y1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[Y4 : mu]: (mimplies @ (do @ Y3 @ Y2 @ Y4) @ (in @ Y0 @ Y1 @ Y4)))))))))))))))) = $true)),
% 2.02/0.63 inference(fool_elimination,[],[f114])).
% 2.02/0.63 thf(f114,plain,(
% 2.02/0.63 ~(mvalid @ (mbox_s4 @ (mexists_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mexists_ind @ (^[X2 : mu] : (mexists_ind @ (^[X3 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X0) @ (mand @ (entry_box @ X1) @ (number @ X1 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X4 : mu] : (mimplies @ (do @ X3 @ X2 @ X4) @ (in @ X0 @ X1 @ X4))))))))))))))))),
% 2.02/0.63 inference(rectify,[],[f43])).
% 2.02/0.63 thf(f43,negated_conjecture,(
% 2.02/0.63 ~(mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mexists_ind @ (^[X12 : mu] : (mexists_ind @ (^[X13 : mu] : (mexists_ind @ (^[X8 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X11) @ (mand @ (entry_box @ X12) @ (number @ X12 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 2.02/0.63 inference(negated_conjecture,[],[f42])).
% 2.02/0.63 thf(f42,conjecture,(
% 2.02/0.63 (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X11 : mu] : (mexists_ind @ (^[X12 : mu] : (mexists_ind @ (^[X13 : mu] : (mexists_ind @ (^[X8 : mu] : (mand @ (mbox_s4 @ (mand @ (userid @ u @ X11) @ (mand @ (entry_box @ X12) @ (number @ X12 @ one)))) @ (mbox_s4 @ (mforall_ind @ (^[X14 : mu] : (mimplies @ (do @ X8 @ X13 @ X14) @ (in @ X11 @ X12 @ X14))))))))))))))))),
% 2.02/0.63 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 2.02/0.63 thf(f475,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (((in @ X3 @ X2 @ (sK9 @ X4 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5)) = $true) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (entry_box @ X2 @ X1)) | ($false = (rel_s4 @ X6 @ X1)) | ($false = (exists_in_world @ (sK10 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (string @ X3 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (userid @ u @ X4 @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ (sK9 @ X4 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (number @ X5 @ one @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ X5 @ sK5)) | ($false = (entry_box @ X5 @ (sK6 @ X4 @ X5)))) )),
% 2.02/0.63 inference(trivial_inequality_removal,[],[f473])).
% 2.02/0.63 thf(f473,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (userid @ u @ X4 @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ X2 @ X1)) | ((in @ X3 @ X2 @ (sK9 @ X4 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5)) = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = $true) | ($false = (entry_box @ X2 @ X1)) | ($false = (exists_in_world @ X5 @ sK5)) | ($false = (string @ X3 @ X1)) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (entry_box @ X5 @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ (sK10 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (exists_in_world @ (sK9 @ X4 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0 @ X5) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (number @ X5 @ one @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (rel_s4 @ X6 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5)))) )),
% 2.02/0.63 inference(superposition,[],[f352,f316])).
% 2.02/0.63 thf(f316,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($true = (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f315])).
% 2.02/0.63 thf(f315,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($true = (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true)) )),
% 2.02/0.63 inference(not_proxy_clausification,[],[f314])).
% 2.02/0.63 thf(f314,plain,(
% 2.02/0.63 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($true = (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f313])).
% 2.02/0.64 thf(f313,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($true = (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f308])).
% 2.02/0.64 thf(f308,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (~ (do @ X4 @ X3 @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)))) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f303])).
% 2.02/0.64 thf(f352,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X7 @ X6)) | ($false = (entry_box @ X5 @ X2)) | ($true = (in @ X4 @ X5 @ X7 @ X6)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ((rel_s4 @ X2 @ X6) = $false) | ($false = (exists_in_world @ X7 @ X6)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f351])).
% 2.02/0.64 thf(f351,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((rel_s4 @ X2 @ X6) = $false) | ($false = (exists_in_world @ X7 @ X6)) | ($true = (in @ X4 @ X5 @ X7 @ X6)) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ((~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X7 @ X6)) = $true)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f350])).
% 2.02/0.64 thf(f350,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X7 @ X6)) | ((rel_s4 @ X2 @ X6) = $false) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($true = ((in @ X4 @ X5 @ X7 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X7 @ X6))))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f349])).
% 2.02/0.64 thf(f349,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ((rel_s4 @ X2 @ X6) = $false) | (((exists_in_world @ X7 @ X6) => ((in @ X4 @ X5 @ X7 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X7 @ X6)))) = $true) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (string @ X4 @ X2))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f348])).
% 2.02/0.64 thf(f348,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ((~ (rel_s4 @ X2 @ X6)) = $true) | ($false = (string @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | (((exists_in_world @ X7 @ X6) => ((in @ X4 @ X5 @ X7 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ X7 @ X6)))) = $true)) )),
% 2.02/0.64 inference(beta_eta_normalization,[],[f347])).
% 2.02/0.64 thf(f347,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X7 : mu,X4 : mu,X5 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((in @ X4 @ X5 @ Y0 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y0 @ X6))))) @ X7) = $true) | ($false = (exists_in_world @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((~ (rel_s4 @ X2 @ X6)) = $true)) )),
% 2.02/0.64 inference(pi_clausification,[],[f346])).
% 2.02/0.64 thf(f346,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((in @ X4 @ X5 @ Y0 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y0 @ X6)))))) = $true) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X4 @ X2)) | ((~ (rel_s4 @ X2 @ X6)) = $true)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f345])).
% 2.02/0.64 thf(f345,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X5 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($true = ((~ (rel_s4 @ X2 @ X6)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X6) => ((in @ X4 @ X5 @ Y0 @ X6) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y0 @ X6)))))))) | ($false = (exists_in_world @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.64 inference(beta_eta_normalization,[],[f344])).
% 2.02/0.64 thf(f344,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (exists_in_world @ X5 @ X2)) | ($true = ((^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X4 @ X5 @ Y1 @ Y0) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y1 @ Y0)))))))) @ X6)) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X4 @ X2))) )),
% 2.02/0.64 inference(pi_clausification,[],[f343])).
% 2.02/0.64 thf(f343,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (string @ X4 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X4 @ X5 @ Y1 @ Y0) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y1 @ Y0))))))))) = $true) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (entry_box @ X5 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f341])).
% 2.02/0.64 thf(f341,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : mu,X5 : mu] : (($false = (entry_box @ X5 @ X2)) | ((rel_s4 @ X1 @ X2) = $false) | ($false = (string @ X4 @ X2)) | ($false = (exists_in_world @ X5 @ X2)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((in @ X4 @ X5 @ Y1 @ Y0) | (~ (do @ X3 @ (sK10 @ X2 @ X5 @ X4 @ X3) @ Y1 @ Y0))))))))))) | ($false = (exists_in_world @ X4 @ X2)) | ($false = (exists_in_world @ X3 @ X2))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f340])).
% 2.02/0.64 thf(f307,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f306])).
% 2.02/0.64 thf(f306,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f305])).
% 2.02/0.64 thf(f305,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ((exists_in_world @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $true) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f304])).
% 2.02/0.64 thf(f304,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X4 @ sK5)) | ((exists_in_world @ (sK9 @ X1 @ X3 @ X4 @ X2) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f302])).
% 2.02/0.64 thf(f286,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ((userid @ u @ X1 @ (sK6 @ X1 @ X2)) = $false) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2)))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f285])).
% 2.02/0.64 thf(f285,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X4 @ sK5)) | ((~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))) = $true) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (entry_box @ X2 @ (sK6 @ X1 @ X2))) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f284])).
% 2.02/0.64 thf(f284,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (number @ X2 @ one @ (sK6 @ X1 @ X2))) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ((~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))) = $true)) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f283])).
% 2.02/0.64 thf(f283,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ((~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))) = $true) | ((~ (entry_box @ X2 @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f282])).
% 2.02/0.64 thf(f282,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : ((((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ((~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f281])).
% 2.02/0.64 thf(f281,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ((((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2)))) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f278])).
% 2.02/0.64 thf(f278,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2)))))) | ($false = (exists_in_world @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f277])).
% 2.02/0.64 thf(f277,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))))))) | ((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f276])).
% 2.02/0.64 thf(f276,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X4 @ sK5)) | ($false = (~ (rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) | (~ (((~ (number @ X2 @ one @ (sK6 @ X1 @ X2))) | (~ (entry_box @ X2 @ (sK6 @ X1 @ X2)))) | (~ (userid @ u @ X1 @ (sK6 @ X1 @ X2))))))) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f274])).
% 2.02/0.64 thf(f578,plain,(
% 2.02/0.64 ~spl1_1),
% 2.02/0.64 inference(avatar_contradiction_clause,[],[f577])).
% 2.02/0.64 thf(f577,plain,(
% 2.02/0.64 $false | ~spl1_1),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f575])).
% 2.02/0.64 thf(f575,plain,(
% 2.02/0.64 ($false = $true) | ~spl1_1),
% 2.02/0.64 inference(backward_demodulation,[],[f254,f523])).
% 2.02/0.64 thf(f523,plain,(
% 2.02/0.64 ( ! [X3 : $i] : (($false = (rel_s4 @ X3 @ sK5))) ) | ~spl1_1),
% 2.02/0.64 inference(avatar_component_clause,[],[f522])).
% 2.02/0.64 thf(f254,plain,(
% 2.02/0.64 ((rel_s4 @ sK4 @ sK5) = $true)),
% 2.02/0.64 inference(not_proxy_clausification,[],[f253])).
% 2.02/0.64 thf(f253,plain,(
% 2.02/0.64 ($false = (~ (rel_s4 @ sK4 @ sK5)))),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f251])).
% 2.02/0.64 thf(f574,plain,(
% 2.02/0.64 spl1_1 | spl1_7 | spl1_8 | ~spl1_5),
% 2.02/0.64 inference(avatar_split_clause,[],[f562,f537,f571,f568,f522])).
% 2.02/0.64 thf(f537,plain,(
% 2.02/0.64 spl1_5 <=> ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (string @ X2 @ sK5)))),
% 2.02/0.64 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 2.02/0.64 thf(f562,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (((entry_box @ X0 @ sK5) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X0)) = $true) | ($false = (string @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (rel_s4 @ X3 @ sK5))) ) | ~spl1_5),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f561])).
% 2.02/0.64 thf(f561,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = $true) | ($false = (rel_s4 @ X3 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X0)) = $true)) ) | ~spl1_5),
% 2.02/0.64 inference(duplicate_literal_removal,[],[f558])).
% 2.02/0.64 thf(f558,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (string @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (string @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = $true) | ($false = (exists_in_world @ X1 @ sK5)) | ((entry_box @ X0 @ sK5) = $false) | ($false = (rel_s4 @ X3 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X0)) = $true) | ($false = (exists_in_world @ X2 @ sK5))) ) | ~spl1_5),
% 2.02/0.64 inference(superposition,[],[f342,f538])).
% 2.02/0.64 thf(f538,plain,(
% 2.02/0.64 ( ! [X2 : mu,X0 : mu,X1 : mu] : (($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (string @ X2 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (entry_box @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) ) | ~spl1_5),
% 2.02/0.64 inference(avatar_component_clause,[],[f537])).
% 2.02/0.64 thf(f544,plain,(
% 2.02/0.64 spl1_1 | spl1_5),
% 2.02/0.64 inference(avatar_split_clause,[],[f509,f537,f522])).
% 2.02/0.64 thf(f509,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (entry_box @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = (rel_s4 @ X3 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5))) )),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f508])).
% 2.02/0.64 thf(f508,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (entry_box @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.64 inference(duplicate_literal_removal,[],[f497])).
% 2.02/0.64 thf(f497,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : $i,X0 : mu,X1 : mu] : (($false = (entry_box @ X1 @ sK5)) | ($false = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (string @ X2 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ (sK10 @ sK5 @ X1 @ X2 @ X0) @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (rel_s4 @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X2 @ X1)) = $true) | ($false = (exists_in_world @ X0 @ sK5))) )),
% 2.02/0.64 inference(superposition,[],[f492,f280])).
% 2.02/0.64 thf(f280,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f279])).
% 2.02/0.64 thf(f279,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((rel_s4 @ sK5 @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f277])).
% 2.02/0.64 thf(f492,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X1 @ X2)) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (string @ X0 @ X2)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (entry_box @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5))) )),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f491])).
% 2.02/0.64 thf(f491,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = $true) | ($false = (entry_box @ X1 @ X2)) | ($false = (exists_in_world @ X3 @ X2)) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((exists_in_world @ X0 @ X2) = $false) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X1 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (string @ X0 @ X2))) )),
% 2.02/0.64 inference(duplicate_literal_removal,[],[f484])).
% 2.02/0.64 thf(f484,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (entry_box @ X1 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (string @ X0 @ X2)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = $true) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X1 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5))) )),
% 2.02/0.64 inference(superposition,[],[f482,f293])).
% 2.02/0.64 thf(f293,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f292])).
% 2.02/0.64 thf(f292,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((exists_in_world @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f290])).
% 2.02/0.64 thf(f290,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = ((exists_in_world @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)))))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(beta_eta_normalization,[],[f289])).
% 2.02/0.64 thf(f289,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = (exists_in_world @ X2 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | (((^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))) @ (sK8 @ X1 @ X2 @ X3 @ X4)) = $false) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5))) )),
% 2.02/0.64 inference(sigma_clausification,[],[f288])).
% 2.02/0.64 thf(f288,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) => ((in @ X1 @ X2 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ Y0 @ (sK7 @ X4 @ X3 @ X1 @ X2)))))))) | ($false = (exists_in_world @ X3 @ sK5)) | ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f275])).
% 2.02/0.64 thf(f482,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ (sK8 @ X0 @ X1 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ X1 @ X2)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (entry_box @ X1 @ X2)) | ($false = (string @ X0 @ X2)) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ((exists_in_world @ X0 @ X2) = $false) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true)) )),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f481])).
% 2.02/0.64 thf(f481,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ (sK8 @ X0 @ X1 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (string @ X0 @ X2)) | ($false = (exists_in_world @ X3 @ sK5)) | ((rel_s4 @ X4 @ X2) = $false) | ($false = $true) | ($false = (exists_in_world @ X1 @ X2)) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (entry_box @ X1 @ X2)) | ((exists_in_world @ X0 @ X2) = $false) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(duplicate_literal_removal,[],[f478])).
% 2.02/0.64 thf(f478,plain,(
% 2.02/0.64 ( ! [X2 : $i,X3 : mu,X0 : mu,X1 : mu,X4 : $i] : (($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ X1 @ X2)) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = $true) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ($false = (exists_in_world @ (sK10 @ X2 @ X1 @ X0 @ X3) @ sK5)) | ($false = (exists_in_world @ X3 @ X2)) | ($false = (rel_s4 @ X2 @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ (sK8 @ X0 @ X1 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X3) @ (sK7 @ X3 @ (sK10 @ X2 @ X1 @ X0 @ X3) @ X0 @ X1))) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (entry_box @ X1 @ X2)) | ((rel_s4 @ sK5 @ (sK6 @ X0 @ X1)) = $true) | ((rel_s4 @ X4 @ X2) = $false) | ($false = (string @ X0 @ X2)) | ((exists_in_world @ X0 @ X2) = $false)) )),
% 2.02/0.64 inference(superposition,[],[f296,f467])).
% 2.02/0.64 thf(f467,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (((in @ X3 @ X2 @ (sK8 @ X4 @ X5 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5)) = $true) | ($false = (exists_in_world @ X5 @ sK5)) | ($false = (exists_in_world @ (sK10 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (entry_box @ X2 @ X1)) | ($false = (exists_in_world @ (sK8 @ X4 @ X5 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X0 @ sK5)) | ($true = (rel_s4 @ sK5 @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (string @ X3 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (rel_s4 @ X6 @ X1))) )),
% 2.02/0.64 inference(trivial_inequality_removal,[],[f463])).
% 2.02/0.64 thf(f463,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X0 : mu,X1 : $i,X6 : $i,X4 : mu,X5 : mu] : (((in @ X3 @ X2 @ (sK8 @ X4 @ X5 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5)) = $true) | ($false = (exists_in_world @ X0 @ X1)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (string @ X3 @ X1)) | ($false = (rel_s4 @ X1 @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (rel_s4 @ X6 @ X1)) | ($false = (exists_in_world @ X3 @ X1)) | ($false = (exists_in_world @ X2 @ X1)) | ($false = $true) | ($true = (rel_s4 @ sK5 @ (sK6 @ X4 @ X5))) | ($false = (exists_in_world @ (sK10 @ X1 @ X2 @ X3 @ X0) @ sK5)) | ($false = (exists_in_world @ X0 @ sK5)) | ($false = (exists_in_world @ (sK8 @ X4 @ X5 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X0) @ (sK7 @ X0 @ (sK10 @ X1 @ X2 @ X3 @ X0) @ X4 @ X5))) | ($false = (entry_box @ X2 @ X1)) | ($false = (exists_in_world @ X5 @ sK5))) )),
% 2.02/0.64 inference(superposition,[],[f352,f297])).
% 2.02/0.64 thf(f297,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (((do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f295])).
% 2.02/0.64 thf(f295,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X2 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true) | ((~ (do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2))) = $false)) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f294])).
% 2.02/0.64 thf(f294,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ($false = ((in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2))))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true)) )),
% 2.02/0.64 inference(not_proxy_clausification,[],[f291])).
% 2.02/0.64 thf(f291,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (exists_in_world @ X2 @ sK5)) | ((~ (rel_s4 @ sK5 @ (sK6 @ X1 @ X2))) = $false) | ($false = ((in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2)) | (~ (do @ X4 @ X3 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2))))) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f290])).
% 2.02/0.64 thf(f296,plain,(
% 2.02/0.64 ( ! [X2 : mu,X3 : mu,X1 : mu,X4 : mu] : (($false = (in @ X1 @ X2 @ (sK8 @ X1 @ X2 @ X3 @ X4) @ (sK7 @ X4 @ X3 @ X1 @ X2))) | ($false = (exists_in_world @ X2 @ sK5)) | ((rel_s4 @ sK5 @ (sK6 @ X1 @ X2)) = $true) | ($false = (exists_in_world @ X4 @ sK5)) | ($false = (exists_in_world @ X3 @ sK5)) | ($false = (exists_in_world @ X1 @ sK5))) )),
% 2.02/0.64 inference(binary_proxy_clausification,[],[f294])).
% 2.02/0.64 % SZS output end Proof for theBenchmark
% 2.02/0.64 % (28646)------------------------------
% 2.02/0.64 % (28646)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.02/0.64 % (28646)Termination reason: Refutation
% 2.02/0.64
% 2.02/0.64 % (28646)Memory used [KB]: 6908
% 2.02/0.64 % (28646)Time elapsed: 0.192 s
% 2.02/0.64 % (28646)Instructions burned: 334 (million)
% 2.02/0.64 % (28646)------------------------------
% 2.02/0.64 % (28646)------------------------------
% 2.02/0.64 % (28619)Success in time 0.271 s
%------------------------------------------------------------------------------