0.04/0.13	% Problem    : Vampire---4.8_31691 : TPTP v0.0.0. Released v0.0.0.
0.14/0.15	% Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
0.15/0.36	% Computer : n013.cluster.edu
0.15/0.36	% Model    : x86_64 x86_64
0.15/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.36	% Memory   : 8042.1875MB
0.15/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.15/0.36	% CPULimit   : 1440
0.15/0.36	% WCLimit    : 180
0.15/0.36	% DateTime   : Mon Jul  3 12:53:17 EDT 2023
0.15/0.36	% CPUTime    : 
0.15/0.36	This is a THF_ problem
0.15/0.37	Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.fHMY77o5nw/Vampire---4.8_31691 -m 12000  -t 180
0.15/0.38	% (31938)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi)
0.15/0.38	% (31939)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi)
0.15/0.38	% (31937)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi)
0.15/0.38	% (31941)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi)
0.15/0.38	% (31940)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1799ds/385Mi)
0.15/0.39	% (31942)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1799ds/74Mi)
0.15/0.39	% (31944)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi)
0.15/0.39	% (31945)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1799ds/915Mi)
0.15/0.39	% (31944)Instruction limit reached!
0.15/0.39	% (31944)------------------------------
0.15/0.39	% (31944)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.39	% (31944)Termination reason: Unknown
0.15/0.39	% (31944)Termination phase: Preprocessing 3
0.15/0.39	
0.15/0.39	% (31944)Memory used [KB]: 1023
0.15/0.39	% (31944)Time elapsed: 0.005 s
0.15/0.39	% (31944)Instructions burned: 5 (million)
0.15/0.39	% (31944)------------------------------
0.15/0.39	% (31944)------------------------------
0.15/0.39	% (31941)Instruction limit reached!
0.15/0.39	% (31941)------------------------------
0.15/0.39	% (31941)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.39	% (31941)Termination reason: Unknown
0.15/0.39	% (31941)Termination phase: Saturation
0.15/0.39	
0.15/0.39	% (31941)Memory used [KB]: 5756
0.15/0.39	% (31941)Time elapsed: 0.011 s
0.15/0.39	% (31941)Instructions burned: 17 (million)
0.15/0.39	% (31941)------------------------------
0.15/0.39	% (31941)------------------------------
0.15/0.40	% (31946)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (1799ds/21Mi)
0.15/0.40	% (31939)Instruction limit reached!
0.15/0.40	% (31939)------------------------------
0.15/0.40	% (31939)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.40	% (31939)Termination reason: Unknown
0.15/0.40	% (31939)Termination phase: Saturation
0.15/0.40	
0.15/0.40	% (31939)Memory used [KB]: 5756
0.15/0.40	% (31939)Time elapsed: 0.022 s
0.15/0.40	% (31939)Instructions burned: 34 (million)
0.15/0.40	% (31939)------------------------------
0.15/0.40	% (31939)------------------------------
0.15/0.41	% (31938)Instruction limit reached!
0.15/0.41	% (31938)------------------------------
0.15/0.41	% (31938)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.41	% (31938)Termination reason: Unknown
0.15/0.41	% (31938)Termination phase: Saturation
0.15/0.41	
0.15/0.41	% (31938)Memory used [KB]: 5756
0.15/0.41	% (31938)Time elapsed: 0.023 s
0.15/0.41	% (31938)Instructions burned: 36 (million)
0.15/0.41	% (31938)------------------------------
0.15/0.41	% (31938)------------------------------
0.15/0.41	% (31947)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi)
0.15/0.41	% (31947)Instruction limit reached!
0.15/0.41	% (31947)------------------------------
0.15/0.41	% (31947)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.41	% (31947)Termination reason: Unknown
0.15/0.41	% (31947)Termination phase: Property scanning
0.15/0.41	
0.15/0.41	% (31947)Memory used [KB]: 1151
0.15/0.41	% (31947)Time elapsed: 0.006 s
0.15/0.41	% (31947)Instructions burned: 7 (million)
0.15/0.41	% (31947)------------------------------
0.15/0.41	% (31947)------------------------------
0.15/0.41	% (31946)Instruction limit reached!
0.15/0.41	% (31946)------------------------------
0.15/0.41	% (31946)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.41	% (31946)Termination reason: Unknown
0.15/0.41	% (31946)Termination phase: Saturation
0.15/0.41	
0.15/0.41	% (31946)Memory used [KB]: 5628
0.15/0.41	% (31946)Time elapsed: 0.014 s
0.15/0.41	% (31946)Instructions burned: 21 (million)
0.15/0.41	% (31946)------------------------------
0.15/0.41	% (31946)------------------------------
0.15/0.42	% (31948)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (1799ds/1021Mi)
0.15/0.42	% (31949)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (1799ds/71Mi)
0.15/0.43	% (31942)Instruction limit reached!
0.15/0.43	% (31942)------------------------------
0.15/0.43	% (31942)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.43	% (31942)Termination reason: Unknown
0.15/0.43	% (31942)Termination phase: Saturation
0.15/0.43	
0.15/0.43	% (31942)Memory used [KB]: 5756
0.15/0.43	% (31942)Time elapsed: 0.044 s
0.15/0.43	% (31942)Instructions burned: 75 (million)
0.15/0.43	% (31942)------------------------------
0.15/0.43	% (31942)------------------------------
0.15/0.43	% (31950)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on Vampire---4 for (1799ds/9Mi)
0.15/0.43	% (31951)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on Vampire---4 for (1799ds/1044Mi)
0.15/0.43	% (31950)Instruction limit reached!
0.15/0.43	% (31950)------------------------------
0.15/0.43	% (31950)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.15/0.43	% (31950)Termination reason: Unknown
0.15/0.43	% (31950)Termination phase: Property scanning
0.15/0.43	
0.15/0.43	% (31950)Memory used [KB]: 1151
0.15/0.43	% (31950)Time elapsed: 0.007 s
0.15/0.43	% (31950)Instructions burned: 9 (million)
0.15/0.43	% (31950)------------------------------
0.15/0.43	% (31950)------------------------------
0.23/0.44	% (31952)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on Vampire---4 for (1799ds/128Mi)
0.23/0.44	% (31937)Instruction limit reached!
0.23/0.44	% (31937)------------------------------
0.23/0.44	% (31937)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.44	% (31937)Termination reason: Unknown
0.23/0.44	% (31937)Termination phase: Saturation
0.23/0.44	
0.23/0.44	% (31937)Memory used [KB]: 6012
0.23/0.44	% (31937)Time elapsed: 0.061 s
0.23/0.44	% (31937)Instructions burned: 96 (million)
0.23/0.44	% (31937)------------------------------
0.23/0.44	% (31937)------------------------------
0.23/0.45	% (31955)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi)
0.23/0.46	% (31959)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi)
0.23/0.47	% (31959)Instruction limit reached!
0.23/0.47	% (31959)------------------------------
0.23/0.47	% (31959)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.47	% (31959)Termination reason: Unknown
0.23/0.47	% (31959)Termination phase: Saturation
0.23/0.47	
0.23/0.47	% (31959)Memory used [KB]: 5628
0.23/0.47	% (31959)Time elapsed: 0.009 s
0.23/0.47	% (31959)Instructions burned: 14 (million)
0.23/0.47	% (31959)------------------------------
0.23/0.47	% (31959)------------------------------
0.23/0.47	% (31949)Instruction limit reached!
0.23/0.47	% (31949)------------------------------
0.23/0.47	% (31949)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.47	% (31949)Termination reason: Unknown
0.23/0.47	% (31949)Termination phase: Saturation
0.23/0.47	
0.23/0.47	% (31949)Memory used [KB]: 5884
0.23/0.47	% (31949)Time elapsed: 0.051 s
0.23/0.47	% (31949)Instructions burned: 72 (million)
0.23/0.47	% (31949)------------------------------
0.23/0.47	% (31949)------------------------------
0.23/0.48	% (31963)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on Vampire---4 for (1799ds/2Mi)
0.23/0.48	% (31963)Instruction limit reached!
0.23/0.48	% (31963)------------------------------
0.23/0.48	% (31963)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.48	% (31963)Termination reason: Unknown
0.23/0.48	% (31963)Termination phase: shuffling
0.23/0.48	
0.23/0.48	% (31963)Memory used [KB]: 1023
0.23/0.48	% (31963)Time elapsed: 0.003 s
0.23/0.48	% (31963)Instructions burned: 3 (million)
0.23/0.48	% (31963)------------------------------
0.23/0.48	% (31963)------------------------------
0.23/0.48	% (31955)Instruction limit reached!
0.23/0.48	% (31955)------------------------------
0.23/0.48	% (31955)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.48	% (31955)Termination reason: Unknown
0.23/0.48	% (31955)Termination phase: Saturation
0.23/0.48	
0.23/0.48	% (31955)Memory used [KB]: 6012
0.23/0.48	% (31955)Time elapsed: 0.038 s
0.23/0.48	% (31955)Instructions burned: 62 (million)
0.23/0.48	% (31955)------------------------------
0.23/0.48	% (31955)------------------------------
0.23/0.49	% (31965)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (1799ds/1041Mi)
0.23/0.49	% (31971)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1798ds/11Mi)
0.23/0.49	% (31973)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1798ds/140Mi)
0.23/0.50	% (31971)Instruction limit reached!
0.23/0.50	% (31971)------------------------------
0.23/0.50	% (31971)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.50	% (31971)Termination reason: Unknown
0.23/0.50	% (31971)Termination phase: Saturation
0.23/0.50	
0.23/0.50	% (31971)Memory used [KB]: 5500
0.23/0.50	% (31971)Time elapsed: 0.005 s
0.23/0.50	% (31971)Instructions burned: 12 (million)
0.23/0.50	% (31971)------------------------------
0.23/0.50	% (31971)------------------------------
0.23/0.50	% (31940)First to succeed.
0.23/0.51	% (31985)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (1798ds/26Mi)
0.23/0.51	% (31952)Instruction limit reached!
0.23/0.51	% (31952)------------------------------
0.23/0.51	% (31952)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.51	% (31952)Termination reason: Unknown
0.23/0.51	% (31952)Termination phase: Saturation
0.23/0.51	
0.23/0.51	% (31952)Memory used [KB]: 6140
0.23/0.51	% (31952)Time elapsed: 0.066 s
0.23/0.51	% (31952)Instructions burned: 128 (million)
0.23/0.51	% (31952)------------------------------
0.23/0.51	% (31952)------------------------------
0.23/0.51	% (31973)Refutation not found, incomplete strategy
0.23/0.51	% (31973)------------------------------
0.23/0.51	% (31973)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.51	% (31973)Termination reason: Refutation not found, incomplete strategy
0.23/0.51	
0.23/0.51	
0.23/0.51	% (31973)Memory used [KB]: 5756
0.23/0.51	% (31973)Time elapsed: 0.016 s
0.23/0.51	% (31973)Instructions burned: 38 (million)
0.23/0.51	% (31973)------------------------------
0.23/0.51	% (31973)------------------------------
0.23/0.51	% (31985)Instruction limit reached!
0.23/0.51	% (31985)------------------------------
0.23/0.51	% (31985)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.51	% (31985)Termination reason: Unknown
0.23/0.51	% (31985)Termination phase: Saturation
0.23/0.51	
0.23/0.51	% (31985)Memory used [KB]: 5628
0.23/0.51	% (31985)Time elapsed: 0.009 s
0.23/0.51	% (31985)Instructions burned: 28 (million)
0.23/0.51	% (31985)------------------------------
0.23/0.51	% (31985)------------------------------
0.23/0.52	% (31992)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi)
0.23/0.52	% (31940)Refutation found. Thanks to Tanya!
0.23/0.52	% SZS status Theorem for Vampire---4
0.23/0.52	% SZS output start Proof for Vampire---4
0.23/0.52	thf(type_def_5, type, a: $tType).
0.23/0.52	thf(func_def_0, type, a: $tType).
0.23/0.52	thf(func_def_1, type, cR: a > a).
0.23/0.52	thf(func_def_2, type, cL: a > a).
0.23/0.52	thf(func_def_3, type, cPSI: (a > $o) > a > $o).
0.23/0.52	thf(func_def_4, type, cP: a > a > a).
0.23/0.52	thf(func_def_5, type, cZ: a).
0.23/0.52	thf(func_def_6, type, cPHI: (a > $o) > a > $o).
0.23/0.52	thf(func_def_20, type, sP0: a > (a > $o) > $o).
0.23/0.52	thf(func_def_21, type, sP1: a > (a > $o) > $o).
0.23/0.52	thf(func_def_22, type, sK2: a > (a > $o) > a).
0.23/0.52	thf(func_def_23, type, sK3: (a > $o) > a > (a > $o) > a).
0.23/0.52	thf(func_def_24, type, sK4: (a > $o) > a).
0.23/0.52	thf(func_def_25, type, sK5: a > (a > $o) > a).
0.23/0.52	thf(func_def_26, type, sK6: a > a > (a > $o) > a > $o).
0.23/0.52	thf(func_def_27, type, sK7: a > (a > $o) > a).
0.23/0.52	thf(func_def_28, type, sK8: (a > $o) > a > (a > $o) > a).
0.23/0.52	thf(func_def_29, type, sK9: (a > $o) > a).
0.23/0.52	thf(func_def_30, type, sK10: a > (a > $o) > a).
0.23/0.52	thf(func_def_31, type, sK11: a > a > (a > $o) > a > $o).
0.23/0.52	thf(func_def_32, type, sK12: (a > $o) > a).
0.23/0.52	thf(func_def_35, type, ph14: !>[X0: $tType]:(X0)).
0.23/0.52	thf(func_def_36, type, sK15: a).
0.23/0.52	thf(func_def_37, type, sK16: a).
0.23/0.52	thf(func_def_38, type, sK17: a).
0.23/0.52	thf(func_def_39, type, sK18: a).
0.23/0.52	thf(func_def_40, type, sK19: a).
0.23/0.52	thf(func_def_41, type, sK20: a).
0.23/0.52	thf(func_def_42, type, sK21: a).
0.23/0.52	thf(func_def_43, type, sK22: a).
0.23/0.52	thf(func_def_44, type, sK23: a).
0.23/0.52	thf(func_def_45, type, sK24: a).
0.23/0.52	thf(func_def_46, type, sK25: a).
0.23/0.52	thf(func_def_47, type, sK26: a).
0.23/0.52	thf(f1098,plain,(
0.23/0.52	  $false),
0.23/0.52	  inference(avatar_sat_refutation,[],[f275,f280,f289,f294,f307,f312,f317,f318,f330,f332,f334,f762,f813,f862,f947,f1012,f1095,f1097])).
0.23/0.52	thf(f1097,plain,(
0.23/0.52	  ~spl13_7 | ~spl13_10 | ~spl13_18),
0.23/0.52	  inference(avatar_split_clause,[],[f1074,f325,f286,f272])).
0.23/0.52	thf(f272,plain,(
0.23/0.52	  spl13_7 <=> ((cP @ sK22 @ sK18) = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_7])])).
0.23/0.52	thf(f286,plain,(
0.23/0.52	  spl13_10 <=> ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_10])])).
0.23/0.52	thf(f325,plain,(
0.23/0.52	  spl13_18 <=> ! [X2 : a,X1 : a] : (((cP @ X2 @ X1) != sK15) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_18])])).
0.23/0.52	thf(f1074,plain,(
0.23/0.52	  ((cP @ sK22 @ sK18) != sK15) | (~spl13_10 | ~spl13_18)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f1073])).
0.23/0.52	thf(f1073,plain,(
0.23/0.52	  ($false = $true) | ((cP @ sK22 @ sK18) != sK15) | (~spl13_10 | ~spl13_18)),
0.23/0.52	  inference(superposition,[],[f326,f288])).
0.23/0.52	thf(f288,plain,(
0.23/0.52	  ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ~spl13_10),
0.23/0.52	  inference(avatar_component_clause,[],[f286])).
0.23/0.52	thf(f326,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15)) ) | ~spl13_18),
0.23/0.52	  inference(avatar_component_clause,[],[f325])).
0.23/0.52	thf(f1095,plain,(
0.23/0.52	  ~spl13_3 | ~spl13_8 | ~spl13_12 | ~spl13_17),
0.23/0.52	  inference(avatar_contradiction_clause,[],[f1094])).
0.23/0.52	thf(f1094,plain,(
0.23/0.52	  $false | (~spl13_3 | ~spl13_8 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(subsumption_resolution,[],[f1093,f298])).
0.23/0.52	thf(f298,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) = sK15) | ~spl13_12),
0.23/0.52	  inference(avatar_component_clause,[],[f296])).
0.23/0.52	thf(f296,plain,(
0.23/0.52	  spl13_12 <=> ((cP @ sK17 @ sK16) = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_12])])).
0.23/0.52	thf(f1093,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) != sK15) | (~spl13_3 | ~spl13_8 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(forward_demodulation,[],[f1088,f1050])).
0.23/0.52	thf(f1050,plain,(
0.23/0.52	  (sK17 = sK26) | (~spl13_8 | ~spl13_12)),
0.23/0.52	  inference(forward_demodulation,[],[f1022,f901])).
0.23/0.52	thf(f901,plain,(
0.23/0.52	  (sK17 = (cL @ sK15)) | ~spl13_12),
0.23/0.52	  inference(superposition,[],[f50,f298])).
0.23/0.52	thf(f50,plain,(
0.23/0.52	  ( ! [X10 : a,X11 : a] : (((cL @ (cP @ X11 @ X10)) = X11)) )),
0.23/0.52	  inference(cnf_transformation,[],[f31])).
0.23/0.52	thf(f31,plain,(
0.23/0.52	  (cZ = (cR @ cZ)) & ! [X0 : a] : ((((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0)) & ((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0))) & ! [X1 : a > $o,X2 : a] : ((($true = (sP1 @ X2 @ X1)) | ((cPSI @ X1 @ X2) != $true)) & (((cPSI @ X1 @ X2) = $true) | ($true != (sP1 @ X2 @ X1)))) & ! [X3 : a,X4 : a] : ((cR @ (cP @ X4 @ X3)) = X3) & (cZ = (cL @ cZ)) & ! [X5 : a > $o,X6 : a] : ((((sP0 @ X6 @ X5) = $true) | ($true != (cPHI @ X5 @ X6))) & (($true = (cPHI @ X5 @ X6)) | ((sP0 @ X6 @ X5) != $true))) & ! [X7 : a > $o] : (((X7 @ cZ) = $true) | ! [X8 : a] : ((($true = (X7 @ (sK12 @ X7))) & ($true != (X7 @ (cL @ (sK12 @ X7))))) | ($true != (X7 @ X8)))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & ! [X10 : a,X11 : a] : ((cL @ (cP @ X11 @ X10)) = X11)),
0.23/0.52	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f29,f30])).
0.23/0.52	thf(f30,plain,(
0.23/0.52	  ! [X7 : a > $o] : (? [X9 : a] : (($true = (X7 @ X9)) & ($true != (X7 @ (cL @ X9)))) => (($true = (X7 @ (sK12 @ X7))) & ($true != (X7 @ (cL @ (sK12 @ X7))))))),
0.23/0.52	  introduced(choice_axiom,[])).
0.23/0.52	thf(f29,plain,(
0.23/0.52	  (cZ = (cR @ cZ)) & ! [X0 : a] : ((((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0)) & ((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0))) & ! [X1 : a > $o,X2 : a] : ((($true = (sP1 @ X2 @ X1)) | ((cPSI @ X1 @ X2) != $true)) & (((cPSI @ X1 @ X2) = $true) | ($true != (sP1 @ X2 @ X1)))) & ! [X3 : a,X4 : a] : ((cR @ (cP @ X4 @ X3)) = X3) & (cZ = (cL @ cZ)) & ! [X5 : a > $o,X6 : a] : ((((sP0 @ X6 @ X5) = $true) | ($true != (cPHI @ X5 @ X6))) & (($true = (cPHI @ X5 @ X6)) | ((sP0 @ X6 @ X5) != $true))) & ! [X7 : a > $o] : (((X7 @ cZ) = $true) | ! [X8 : a] : (? [X9 : a] : (($true = (X7 @ X9)) & ($true != (X7 @ (cL @ X9)))) | ($true != (X7 @ X8)))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & ! [X10 : a,X11 : a] : ((cL @ (cP @ X11 @ X10)) = X11)),
0.23/0.52	  inference(rectify,[],[f28])).
0.23/0.52	thf(f28,plain,(
0.23/0.52	  (cZ = (cR @ cZ)) & ! [X21 : a] : ((((cP @ (cL @ X21) @ (cR @ X21)) = X21) | (cZ = X21)) & ((cZ != X21) | ((cP @ (cL @ X21) @ (cR @ X21)) != X21))) & ! [X4 : a > $o,X5 : a] : ((($true = (sP1 @ X5 @ X4)) | ((cPSI @ X4 @ X5) != $true)) & (((cPSI @ X4 @ X5) = $true) | ($true != (sP1 @ X5 @ X4)))) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & (cZ = (cL @ cZ)) & ! [X14 : a > $o,X15 : a] : ((((sP0 @ X15 @ X14) = $true) | ((cPHI @ X14 @ X15) != $true)) & (((cPHI @ X14 @ X15) = $true) | ((sP0 @ X15 @ X14) != $true))) & ! [X11 : a > $o] : (((X11 @ cZ) = $true) | ! [X12 : a] : (? [X13 : a] : (((X11 @ X13) = $true) & ($true != (X11 @ (cL @ X13)))) | ((X11 @ X12) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1)),
0.23/0.52	  inference(nnf_transformation,[],[f11])).
0.23/0.52	thf(f11,plain,(
0.23/0.52	  (cZ = (cR @ cZ)) & ! [X21 : a] : (((cP @ (cL @ X21) @ (cR @ X21)) = X21) <=> (cZ != X21)) & ! [X4 : a > $o,X5 : a] : (($true = (sP1 @ X5 @ X4)) <=> ((cPSI @ X4 @ X5) = $true)) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & (cZ = (cL @ cZ)) & ! [X14 : a > $o,X15 : a] : (((sP0 @ X15 @ X14) = $true) <=> ((cPHI @ X14 @ X15) = $true)) & ! [X11 : a > $o] : (((X11 @ cZ) = $true) | ! [X12 : a] : (? [X13 : a] : (((X11 @ X13) = $true) & ($true != (X11 @ (cL @ X13)))) | ((X11 @ X12) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1)),
0.23/0.52	  inference(definition_folding,[],[f8,f10,f9])).
0.23/0.52	thf(f9,plain,(
0.23/0.52	  ! [X14 : a > $o,X15 : a] : (((sP0 @ X15 @ X14) = $true) <=> ? [X16 : a] : (! [X17 : a] : (? [X18 : a > $o] : (! [X20 : a] : (($true != (X18 @ X20)) | ((cR @ X20) != X17)) & ! [X19 : a] : (($true = (X18 @ (cL @ X19))) | ($true != (X18 @ X19))) & ($true = (X18 @ X16))) | ($true = (X14 @ X17))) & ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X15))))),
0.23/0.52	  introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
0.23/0.52	thf(f10,plain,(
0.23/0.52	  ! [X4 : a > $o,X5 : a] : (($true = (sP1 @ X5 @ X4)) <=> ? [X6 : a] : (! [X7 : a] : (? [X8 : a > $o] : (! [X10 : a] : (((cR @ X10) != X7) | ($true != (X8 @ X10))) & ! [X9 : a] : (($true != (X8 @ X9)) | ($true = (X8 @ (cL @ X9)))) & ($true = (X8 @ X6))) | ((X4 @ X7) = $true)) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X6) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X5))))),
0.23/0.52	  introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
0.23/0.52	thf(f8,plain,(
0.23/0.52	  (cZ = (cR @ cZ)) & ! [X21 : a] : (((cP @ (cL @ X21) @ (cR @ X21)) = X21) <=> (cZ != X21)) & ! [X4 : a > $o,X5 : a] : (? [X6 : a] : (! [X7 : a] : (? [X8 : a > $o] : (! [X10 : a] : (((cR @ X10) != X7) | ($true != (X8 @ X10))) & ! [X9 : a] : (($true != (X8 @ X9)) | ($true = (X8 @ (cL @ X9)))) & ($true = (X8 @ X6))) | ((X4 @ X7) = $true)) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X6) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X5))) <=> ((cPSI @ X4 @ X5) = $true)) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & (cZ = (cL @ cZ)) & ! [X14 : a > $o,X15 : a] : (? [X16 : a] : (! [X17 : a] : (? [X18 : a > $o] : (! [X20 : a] : (($true != (X18 @ X20)) | ((cR @ X20) != X17)) & ! [X19 : a] : (($true = (X18 @ (cL @ X19))) | ($true != (X18 @ X19))) & ($true = (X18 @ X16))) | ($true = (X14 @ X17))) & ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X15))) <=> ((cPHI @ X14 @ X15) = $true)) & ! [X11 : a > $o] : (((X11 @ cZ) = $true) | ! [X12 : a] : (? [X13 : a] : (((X11 @ X13) = $true) & ($true != (X11 @ (cL @ X13)))) | ((X11 @ X12) != $true))) & ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1)),
0.23/0.52	  inference(flattening,[],[f7])).
0.23/0.52	thf(f7,plain,(
0.23/0.52	  ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))) & (! [X4 : a > $o,X5 : a] : (? [X6 : a] : (! [X7 : a] : (((X4 @ X7) = $true) | ? [X8 : a > $o] : (! [X10 : a] : (((cR @ X10) != X7) | ($true != (X8 @ X10))) & (($true = (X8 @ X6)) & ! [X9 : a] : (($true != (X8 @ X9)) | ($true = (X8 @ (cL @ X9))))))) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X6) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X5))) <=> ((cPSI @ X4 @ X5) = $true)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & (cZ = (cL @ cZ)) & ! [X21 : a] : (((cP @ (cL @ X21) @ (cR @ X21)) = X21) <=> (cZ != X21)) & (cZ = (cR @ cZ)) & ! [X14 : a > $o,X15 : a] : (((cPHI @ X14 @ X15) = $true) <=> ? [X16 : a] : (($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X15)) & ! [X17 : a] : (($true = (X14 @ X17)) | ? [X18 : a > $o] : (! [X20 : a] : (($true != (X18 @ X20)) | ((cR @ X20) != X17)) & (! [X19 : a] : (($true = (X18 @ (cL @ X19))) | ($true != (X18 @ X19))) & ($true = (X18 @ X16))))))) & ! [X11 : a > $o] : (((X11 @ cZ) = $true) | ! [X12 : a] : (? [X13 : a] : (((X11 @ X13) = $true) & ($true != (X11 @ (cL @ X13)))) | ((X11 @ X12) != $true))))),
0.23/0.52	  inference(ennf_transformation,[],[f6])).
0.23/0.52	thf(f6,plain,(
0.23/0.52	  ~((! [X4 : a > $o,X5 : a] : (? [X6 : a] : (! [X7 : a] : (! [X8 : a > $o] : ((($true = (X8 @ X6)) & ! [X9 : a] : (($true = (X8 @ X9)) => ($true = (X8 @ (cL @ X9))))) => ? [X10 : a] : (((cR @ X10) = X7) & ($true = (X8 @ X10)))) => ((X4 @ X7) = $true)) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X6) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X5))) <=> ((cPSI @ X4 @ X5) = $true)) & ! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & (cZ = (cL @ cZ)) & ! [X21 : a] : (((cP @ (cL @ X21) @ (cR @ X21)) = X21) <=> (cZ != X21)) & (cZ = (cR @ cZ)) & ! [X14 : a > $o,X15 : a] : (((cPHI @ X14 @ X15) = $true) <=> ? [X16 : a] : (($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X16) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X15)) & ! [X17 : a] : (! [X18 : a > $o] : ((! [X19 : a] : (($true = (X18 @ X19)) => ($true = (X18 @ (cL @ X19)))) & ($true = (X18 @ X16))) => ? [X20 : a] : (((cR @ X20) = X17) & ($true = (X18 @ X20)))) => ($true = (X14 @ X17))))) & ! [X11 : a > $o] : (? [X12 : a] : (! [X13 : a] : (((X11 @ X13) = $true) => ($true = (X11 @ (cL @ X13)))) & ((X11 @ X12) = $true)) => ((X11 @ cZ) = $true))) => ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) = (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))))),
0.23/0.52	  inference(rectify,[],[f5])).
0.23/0.52	thf(f5,plain,(
0.23/0.52	  ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & ! [X4 : a > $o,X5 : a] : (? [X6 : a] : (! [X7 : a] : (! [X8 : a > $o] : ((($true = (X8 @ X6)) & ! [X9 : a] : (($true = (X8 @ X9)) => ($true = (X8 @ (cL @ X9))))) => ? [X10 : a] : (((cR @ X10) = X7) & ($true = (X8 @ X10)))) => ((X4 @ X7) = $true)) & ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X6) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: (((cR @ Y2) = Y0) & (Y1 @ Y2)))))))) @ X5))) <=> ((cPSI @ X4 @ X5) = $true)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X15 : a > $o] : (? [X16 : a] : (! [X17 : a] : (((X15 @ X17) = $true) => ($true = (X15 @ (cL @ X17)))) & ((X15 @ X16) = $true)) => ((X15 @ cZ) = $true)) & ! [X18 : a > $o,X19 : a] : (($true = (cPHI @ X18 @ X19)) <=> ? [X20 : a] : (! [X21 : a] : (! [X22 : a > $o] : ((($true = (X22 @ X20)) & ! [X23 : a] : (((X22 @ X23) = $true) => ((X22 @ (cL @ X23)) = $true))) => ? [X24 : a] : (((X22 @ X24) = $true) & ((cR @ X24) = X21))) => ((X18 @ X21) = $true)) & ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X20) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X19)))) & ! [X29 : a] : ((cZ != X29) <=> ((cP @ (cL @ X29) @ (cR @ X29)) = X29))) => ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) = (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0)))))),
0.23/0.52	  inference(fool_elimination,[],[f4])).
0.23/0.52	thf(f4,plain,(
0.23/0.52	  ~((! [X0 : a,X1 : a] : ((cL @ (cP @ X1 @ X0)) = X1) & ! [X2 : a,X3 : a] : ((cR @ (cP @ X3 @ X2)) = X2) & ! [X4 : a > $o,X5 : a] : (? [X6 : a] : (! [X7 : a] : (! [X8 : a > $o] : (((X8 @ X6) & ! [X9 : a] : ((X8 @ X9) => (X8 @ (cL @ X9)))) => ? [X10 : a] : ((X8 @ X10) & ((cR @ X10) = X7))) => (X4 @ X7)) & (cPSI @ (^[X11 : a] : (! [X12 : a > $o] : ((! [X13 : a] : ((X12 @ X13) => (X12 @ (cL @ X13))) & (X12 @ X6)) => ? [X14 : a] : ((X12 @ X14) & ((cR @ X14) = X11))))) @ X5)) <=> (cPSI @ X4 @ X5)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X15 : a > $o] : (? [X16 : a] : (! [X17 : a] : ((X15 @ X17) => (X15 @ (cL @ X17))) & (X15 @ X16)) => (X15 @ cZ)) & ! [X18 : a > $o,X19 : a] : ((cPHI @ X18 @ X19) <=> ? [X20 : a] : (! [X21 : a] : (! [X22 : a > $o] : (((X22 @ X20) & ! [X23 : a] : ((X22 @ X23) => (X22 @ (cL @ X23)))) => ? [X24 : a] : ((X22 @ X24) & ((cR @ X24) = X21))) => (X18 @ X21)) & (cPHI @ (^[X25 : a] : (! [X26 : a > $o] : ((! [X27 : a] : ((X26 @ X27) => (X26 @ (cL @ X27))) & (X26 @ X20)) => ? [X28 : a] : (((cR @ X28) = X25) & (X26 @ X28))))) @ X19))) & ! [X29 : a] : ((cZ != X29) <=> ((cP @ (cL @ X29) @ (cR @ X29)) = X29))) => ((^[X30 : a] : ((cZ = X30) | ? [X31 : a,X32 : a] : (((cP @ X31 @ X32) = X30) & (cPHI @ (^[X33 : a] : (! [X34 : a > $o] : ((! [X35 : a] : ((X34 @ X35) => (X34 @ (cL @ X35))) & (X34 @ X31)) => ? [X36 : a] : (((cR @ X36) = X33) & (X34 @ X36))))) @ X32)) | ? [X37 : a,X38 : a] : ((cPSI @ (^[X39 : a] : (! [X40 : a > $o] : (((X40 @ X37) & ! [X41 : a] : ((X40 @ X41) => (X40 @ (cL @ X41)))) => ? [X42 : a] : (((cR @ X42) = X39) & (X40 @ X42))))) @ X38) & ((cP @ X37 @ X38) = X30)) | (cZ = X30))) = (^[X43 : a] : ((cZ = X43) | ? [X44 : a,X45 : a] : (((cPSI @ (^[X46 : a] : (! [X47 : a > $o] : (((X47 @ X44) & ! [X48 : a] : ((X47 @ X48) => (X47 @ (cL @ X48)))) => ? [X49 : a] : (((cR @ X49) = X46) & (X47 @ X49))))) @ X45) | (cPHI @ (^[X50 : a] : (! [X51 : a > $o] : ((! [X52 : a] : ((X51 @ X52) => (X51 @ (cL @ X52))) & (X51 @ X44)) => ? [X53 : a] : (((cR @ X53) = X50) & (X51 @ X53))))) @ X45)) & ((cP @ X44 @ X45) = X43))))))),
0.23/0.52	  inference(rectify,[],[f2])).
0.23/0.52	thf(f2,negated_conjecture,(
0.23/0.52	  ~((! [X2 : a,X1 : a] : ((cL @ (cP @ X1 @ X2)) = X1) & ! [X2 : a,X1 : a] : ((cR @ (cP @ X1 @ X2)) = X2) & ! [X4 : a > $o,X5 : a] : (? [X1 : a] : (! [X11 : a] : (! [X9 : a > $o] : (((X9 @ X1) & ! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7)))) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X11))) => (X4 @ X11)) & (cPSI @ (^[X2 : a] : (! [X9 : a > $o] : ((! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7))) & (X9 @ X1)) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X2))))) @ X5)) <=> (cPSI @ X4 @ X5)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X4 : a > $o] : (? [X8 : a] : (! [X0 : a] : ((X4 @ X0) => (X4 @ (cL @ X0))) & (X4 @ X8)) => (X4 @ cZ)) & ! [X4 : a > $o,X5 : a] : ((cPHI @ X4 @ X5) <=> ? [X1 : a] : (! [X10 : a] : (! [X9 : a > $o] : (((X9 @ X1) & ! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7)))) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X10))) => (X4 @ X10)) & (cPHI @ (^[X2 : a] : (! [X9 : a > $o] : ((! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7))) & (X9 @ X1)) => ? [X6 : a] : (((cR @ X6) = X2) & (X9 @ X6))))) @ X5))) & ! [X8 : a] : ((cZ != X8) <=> ((cP @ (cL @ X8) @ (cR @ X8)) = X8))) => ((^[X5 : a] : ((cZ = X5) | ? [X1 : a,X2 : a] : (((cP @ X1 @ X2) = X5) & (cPHI @ (^[X3 : a] : (! [X4 : a > $o] : ((! [X7 : a] : ((X4 @ X7) => (X4 @ (cL @ X7))) & (X4 @ X1)) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2)) | ? [X1 : a,X2 : a] : ((cPSI @ (^[X3 : a] : (! [X4 : a > $o] : (((X4 @ X1) & ! [X7 : a] : ((X4 @ X7) => (X4 @ (cL @ X7)))) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2) & ((cP @ X1 @ X2) = X5)) | (cZ = X5))) = (^[X0 : a] : ((cZ = X0) | ? [X1 : a,X2 : a] : (((cPSI @ (^[X3 : a] : (! [X4 : a > $o] : (((X4 @ X1) & ! [X5 : a] : ((X4 @ X5) => (X4 @ (cL @ X5)))) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2) | (cPHI @ (^[X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : ((X4 @ X5) => (X4 @ (cL @ X5))) & (X4 @ X1)) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2)) & ((cP @ X1 @ X2) = X0))))))),
0.23/0.52	  inference(negated_conjecture,[],[f1])).
0.23/0.52	thf(f1,conjecture,(
0.23/0.52	  (! [X2 : a,X1 : a] : ((cL @ (cP @ X1 @ X2)) = X1) & ! [X2 : a,X1 : a] : ((cR @ (cP @ X1 @ X2)) = X2) & ! [X4 : a > $o,X5 : a] : (? [X1 : a] : (! [X11 : a] : (! [X9 : a > $o] : (((X9 @ X1) & ! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7)))) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X11))) => (X4 @ X11)) & (cPSI @ (^[X2 : a] : (! [X9 : a > $o] : ((! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7))) & (X9 @ X1)) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X2))))) @ X5)) <=> (cPSI @ X4 @ X5)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X4 : a > $o] : (? [X8 : a] : (! [X0 : a] : ((X4 @ X0) => (X4 @ (cL @ X0))) & (X4 @ X8)) => (X4 @ cZ)) & ! [X4 : a > $o,X5 : a] : ((cPHI @ X4 @ X5) <=> ? [X1 : a] : (! [X10 : a] : (! [X9 : a > $o] : (((X9 @ X1) & ! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7)))) => ? [X6 : a] : ((X9 @ X6) & ((cR @ X6) = X10))) => (X4 @ X10)) & (cPHI @ (^[X2 : a] : (! [X9 : a > $o] : ((! [X7 : a] : ((X9 @ X7) => (X9 @ (cL @ X7))) & (X9 @ X1)) => ? [X6 : a] : (((cR @ X6) = X2) & (X9 @ X6))))) @ X5))) & ! [X8 : a] : ((cZ != X8) <=> ((cP @ (cL @ X8) @ (cR @ X8)) = X8))) => ((^[X5 : a] : ((cZ = X5) | ? [X1 : a,X2 : a] : (((cP @ X1 @ X2) = X5) & (cPHI @ (^[X3 : a] : (! [X4 : a > $o] : ((! [X7 : a] : ((X4 @ X7) => (X4 @ (cL @ X7))) & (X4 @ X1)) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2)) | ? [X1 : a,X2 : a] : ((cPSI @ (^[X3 : a] : (! [X4 : a > $o] : (((X4 @ X1) & ! [X7 : a] : ((X4 @ X7) => (X4 @ (cL @ X7)))) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2) & ((cP @ X1 @ X2) = X5)) | (cZ = X5))) = (^[X0 : a] : ((cZ = X0) | ? [X1 : a,X2 : a] : (((cPSI @ (^[X3 : a] : (! [X4 : a > $o] : (((X4 @ X1) & ! [X5 : a] : ((X4 @ X5) => (X4 @ (cL @ X5)))) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2) | (cPHI @ (^[X3 : a] : (! [X4 : a > $o] : ((! [X5 : a] : ((X4 @ X5) => (X4 @ (cL @ X5))) & (X4 @ X1)) => ? [X6 : a] : (((cR @ X6) = X3) & (X4 @ X6))))) @ X2)) & ((cP @ X1 @ X2) = X0)))))),
0.23/0.52	  file('/export/starexec/sandbox/tmp/tmp.fHMY77o5nw/Vampire---4.8_31691',cPU_X2310B_pme)).
0.23/0.52	thf(f1022,plain,(
0.23/0.52	  (sK26 = (cL @ sK15)) | ~spl13_8),
0.23/0.52	  inference(superposition,[],[f50,f279])).
0.23/0.52	thf(f279,plain,(
0.23/0.52	  ((cP @ sK26 @ sK25) = sK15) | ~spl13_8),
0.23/0.52	  inference(avatar_component_clause,[],[f277])).
0.23/0.52	thf(f277,plain,(
0.23/0.52	  spl13_8 <=> ((cP @ sK26 @ sK25) = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_8])])).
0.23/0.52	thf(f1088,plain,(
0.23/0.52	  ((cP @ sK26 @ sK16) != sK15) | (~spl13_3 | ~spl13_8 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f1087])).
0.23/0.52	thf(f1087,plain,(
0.23/0.52	  ((cP @ sK26 @ sK16) != sK15) | ($false = $true) | (~spl13_3 | ~spl13_8 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(superposition,[],[f322,f1054])).
0.23/0.52	thf(f1054,plain,(
0.23/0.52	  ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK26)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) = $true) | (~spl13_3 | ~spl13_8 | ~spl13_12)),
0.23/0.52	  inference(backward_demodulation,[],[f258,f1052])).
0.23/0.52	thf(f1052,plain,(
0.23/0.52	  (sK16 = sK25) | (~spl13_8 | ~spl13_12)),
0.23/0.52	  inference(forward_demodulation,[],[f1023,f902])).
0.23/0.52	thf(f902,plain,(
0.23/0.52	  (sK16 = (cR @ sK15)) | ~spl13_12),
0.23/0.52	  inference(superposition,[],[f57,f298])).
0.23/0.52	thf(f57,plain,(
0.23/0.52	  ( ! [X3 : a,X4 : a] : (((cR @ (cP @ X4 @ X3)) = X3)) )),
0.23/0.52	  inference(cnf_transformation,[],[f31])).
0.23/0.52	thf(f1023,plain,(
0.23/0.52	  ((cR @ sK15) = sK25) | ~spl13_8),
0.23/0.52	  inference(superposition,[],[f57,f279])).
0.23/0.52	thf(f258,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK26)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25)) | ~spl13_3),
0.23/0.52	  inference(avatar_component_clause,[],[f256])).
0.23/0.52	thf(f256,plain,(
0.23/0.52	  spl13_3 <=> ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK26)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_3])])).
0.23/0.52	thf(f322,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15)) ) | ~spl13_17),
0.23/0.52	  inference(avatar_component_clause,[],[f321])).
0.23/0.52	thf(f321,plain,(
0.23/0.52	  spl13_17 <=> ! [X2 : a,X1 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_17])])).
0.23/0.52	thf(f1012,plain,(
0.23/0.52	  ~spl13_9 | ~spl13_11 | ~spl13_12 | ~spl13_17),
0.23/0.52	  inference(avatar_contradiction_clause,[],[f1011])).
0.23/0.52	thf(f1011,plain,(
0.23/0.52	  $false | (~spl13_9 | ~spl13_11 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(subsumption_resolution,[],[f1010,f298])).
0.23/0.52	thf(f1010,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) != sK15) | (~spl13_9 | ~spl13_11 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(forward_demodulation,[],[f1005,f976])).
0.23/0.52	thf(f976,plain,(
0.23/0.52	  (sK17 = sK24) | (~spl13_11 | ~spl13_12)),
0.23/0.52	  inference(forward_demodulation,[],[f963,f901])).
0.23/0.52	thf(f963,plain,(
0.23/0.52	  ((cL @ sK15) = sK24) | ~spl13_11),
0.23/0.52	  inference(superposition,[],[f50,f293])).
0.23/0.52	thf(f293,plain,(
0.23/0.52	  ((cP @ sK24 @ sK23) = sK15) | ~spl13_11),
0.23/0.52	  inference(avatar_component_clause,[],[f291])).
0.23/0.52	thf(f291,plain,(
0.23/0.52	  spl13_11 <=> ((cP @ sK24 @ sK23) = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_11])])).
0.23/0.52	thf(f1005,plain,(
0.23/0.52	  ((cP @ sK24 @ sK16) != sK15) | (~spl13_9 | ~spl13_11 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f1004])).
0.23/0.52	thf(f1004,plain,(
0.23/0.52	  ((cP @ sK24 @ sK16) != sK15) | ($false = $true) | (~spl13_9 | ~spl13_11 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(superposition,[],[f322,f980])).
0.23/0.52	thf(f980,plain,(
0.23/0.52	  ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK24)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) = $true) | (~spl13_9 | ~spl13_11 | ~spl13_12)),
0.23/0.52	  inference(backward_demodulation,[],[f284,f978])).
0.23/0.52	thf(f978,plain,(
0.23/0.52	  (sK16 = sK23) | (~spl13_11 | ~spl13_12)),
0.23/0.52	  inference(forward_demodulation,[],[f964,f902])).
0.23/0.52	thf(f964,plain,(
0.23/0.52	  ((cR @ sK15) = sK23) | ~spl13_11),
0.23/0.52	  inference(superposition,[],[f57,f293])).
0.23/0.52	thf(f284,plain,(
0.23/0.52	  ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK24)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true) | ~spl13_9),
0.23/0.52	  inference(avatar_component_clause,[],[f282])).
0.23/0.52	thf(f282,plain,(
0.23/0.52	  spl13_9 <=> ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK24)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_9])])).
0.23/0.52	thf(f947,plain,(
0.23/0.52	  ~spl13_6 | ~spl13_12 | ~spl13_17),
0.23/0.52	  inference(avatar_contradiction_clause,[],[f946])).
0.23/0.52	thf(f946,plain,(
0.23/0.52	  $false | (~spl13_6 | ~spl13_12 | ~spl13_17)),
0.23/0.52	  inference(subsumption_resolution,[],[f942,f298])).
0.23/0.52	thf(f942,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) != sK15) | (~spl13_6 | ~spl13_17)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f940])).
0.23/0.52	thf(f940,plain,(
0.23/0.52	  ($false = $true) | ((cP @ sK17 @ sK16) != sK15) | (~spl13_6 | ~spl13_17)),
0.23/0.52	  inference(superposition,[],[f270,f322])).
0.23/0.52	thf(f270,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ~spl13_6),
0.23/0.52	  inference(avatar_component_clause,[],[f268])).
0.23/0.52	thf(f268,plain,(
0.23/0.52	  spl13_6 <=> ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_6])])).
0.23/0.52	thf(f862,plain,(
0.23/0.52	  ~spl13_14 | ~spl13_16 | ~spl13_17),
0.23/0.52	  inference(avatar_contradiction_clause,[],[f861])).
0.23/0.52	thf(f861,plain,(
0.23/0.52	  $false | (~spl13_14 | ~spl13_16 | ~spl13_17)),
0.23/0.52	  inference(subsumption_resolution,[],[f857,f316])).
0.23/0.52	thf(f316,plain,(
0.23/0.52	  (sK15 = (cP @ sK20 @ sK19)) | ~spl13_16),
0.23/0.52	  inference(avatar_component_clause,[],[f314])).
0.23/0.52	thf(f314,plain,(
0.23/0.52	  spl13_16 <=> (sK15 = (cP @ sK20 @ sK19))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_16])])).
0.23/0.52	thf(f857,plain,(
0.23/0.52	  (sK15 != (cP @ sK20 @ sK19)) | (~spl13_14 | ~spl13_17)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f856])).
0.23/0.52	thf(f856,plain,(
0.23/0.52	  (sK15 != (cP @ sK20 @ sK19)) | ($false = $true) | (~spl13_14 | ~spl13_17)),
0.23/0.52	  inference(superposition,[],[f322,f306])).
0.23/0.52	thf(f306,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19)) | ~spl13_14),
0.23/0.52	  inference(avatar_component_clause,[],[f304])).
0.23/0.52	thf(f304,plain,(
0.23/0.52	  spl13_14 <=> ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_14])])).
0.23/0.52	thf(f813,plain,(
0.23/0.52	  ~spl13_13 | ~spl13_15 | ~spl13_18),
0.23/0.52	  inference(avatar_split_clause,[],[f807,f325,f309,f300])).
0.23/0.52	thf(f300,plain,(
0.23/0.52	  spl13_13 <=> ((cP @ sK21 @ sK18) = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_13])])).
0.23/0.52	thf(f309,plain,(
0.23/0.52	  spl13_15 <=> ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_15])])).
0.23/0.52	thf(f807,plain,(
0.23/0.52	  ((cP @ sK21 @ sK18) != sK15) | (~spl13_15 | ~spl13_18)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f805])).
0.23/0.52	thf(f805,plain,(
0.23/0.52	  ($false = $true) | ((cP @ sK21 @ sK18) != sK15) | (~spl13_15 | ~spl13_18)),
0.23/0.52	  inference(superposition,[],[f326,f311])).
0.23/0.52	thf(f311,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18)) | ~spl13_15),
0.23/0.52	  inference(avatar_component_clause,[],[f309])).
0.23/0.52	thf(f762,plain,(
0.23/0.52	  ~spl13_4 | ~spl13_12 | ~spl13_18),
0.23/0.52	  inference(avatar_contradiction_clause,[],[f761])).
0.23/0.52	thf(f761,plain,(
0.23/0.52	  $false | (~spl13_4 | ~spl13_12 | ~spl13_18)),
0.23/0.52	  inference(subsumption_resolution,[],[f751,f298])).
0.23/0.52	thf(f751,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) != sK15) | (~spl13_4 | ~spl13_18)),
0.23/0.52	  inference(trivial_inequality_removal,[],[f743])).
0.23/0.52	thf(f743,plain,(
0.23/0.52	  ($false = $true) | ((cP @ sK17 @ sK16) != sK15) | (~spl13_4 | ~spl13_18)),
0.23/0.52	  inference(superposition,[],[f262,f326])).
0.23/0.52	thf(f262,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ~spl13_4),
0.23/0.52	  inference(avatar_component_clause,[],[f260])).
0.23/0.52	thf(f260,plain,(
0.23/0.52	  spl13_4 <=> ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_4])])).
0.23/0.52	thf(f334,plain,(
0.23/0.52	  ~spl13_5),
0.23/0.52	  inference(avatar_split_clause,[],[f142,f264])).
0.23/0.52	thf(f264,plain,(
0.23/0.52	  spl13_5 <=> (cZ = sK15)),
0.23/0.52	  introduced(avatar_definition,[new_symbols(naming,[spl13_5])])).
0.23/0.52	thf(f142,plain,(
0.23/0.52	  (cZ != sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f141])).
0.23/0.52	thf(f141,plain,(
0.23/0.52	  ($false = (cZ = sK15))),
0.23/0.52	  inference(duplicate_literal_removal,[],[f129])).
0.23/0.52	thf(f129,plain,(
0.23/0.52	  ($false = (cZ = sK15)) | ($false = (cZ = sK15))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f128])).
0.23/0.52	thf(f128,plain,(
0.23/0.52	  ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | ($false = (cZ = sK15))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f126])).
0.23/0.52	thf(f126,plain,(
0.23/0.52	  (((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f124])).
0.23/0.52	thf(f124,plain,(
0.23/0.52	  ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) = $false) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f122])).
0.23/0.52	thf(f122,plain,(
0.23/0.52	  (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $false) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f120])).
0.23/0.52	thf(f120,plain,(
0.23/0.52	  (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) != ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(beta_eta_normalization,[],[f119])).
0.23/0.52	thf(f119,plain,(
0.23/0.52	  (((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) @ sK15) != ((^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0))) @ sK15))),
0.23/0.52	  inference(negative_extensionality,[],[f51])).
0.23/0.52	thf(f51,plain,(
0.23/0.52	  ((^[Y0 : a]: ((((cZ = Y0) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) & ((cP @ Y2 @ Y1) = Y0))))))) | (cZ = Y0))) != (^[Y0 : a]: ((?? @ a @ (^[Y1 : a]: (?? @ a @ (^[Y2 : a]: (((cP @ Y2 @ Y1) = Y0) & ((cPHI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((Y4 @ Y2) & (!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5)))))) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1) | (cPSI @ (^[Y3 : a]: (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: ((Y4 @ Y5) => (Y4 @ (cL @ Y5))))) & (Y4 @ Y2)) => (?? @ a @ (^[Y5 : a]: ((Y4 @ Y5) & ((cR @ Y5) = Y3)))))))) @ Y1))))))) | (cZ = Y0))))),
0.23/0.52	  inference(cnf_transformation,[],[f31])).
0.23/0.52	thf(f332,plain,(
0.23/0.52	  spl13_17 | spl13_17),
0.23/0.52	  inference(avatar_split_clause,[],[f159,f321,f321])).
0.23/0.52	thf(f159,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X2 @ X1) != sK15) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3)) | ((cP @ X4 @ X3) != sK15) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(equality_proxy_clausification,[],[f156])).
0.23/0.52	thf(f156,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X2 @ X1) != sK15) | (((cP @ X4 @ X3) = sK15) = $false) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3)) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f155])).
0.23/0.52	thf(f155,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15) | ($false = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3))) | (((cP @ X4 @ X3) = sK15) = $false)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f154])).
0.23/0.52	thf(f154,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15) | ((((cP @ X4 @ X3) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3))) = $false)) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f153])).
0.23/0.52	thf(f153,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15) | ($false = ((^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3)))) @ X4))) )),
0.23/0.52	  inference(pi_clausification,[],[f152])).
0.23/0.52	thf(f152,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X2 @ X1) != sK15) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ($false = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3))))))) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f151])).
0.23/0.52	thf(f151,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a] : ((((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) @ X3) = $false) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15)) )),
0.23/0.52	  inference(pi_clausification,[],[f150])).
0.23/0.52	thf(f150,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (((cP @ X2 @ X1) != sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(equality_proxy_clausification,[],[f149])).
0.23/0.52	thf(f149,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : ((((cP @ X2 @ X1) = sK15) = $false) | ($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f147])).
0.23/0.52	thf(f147,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | (((cP @ X2 @ X1) = sK15) = $false)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f146])).
0.23/0.52	thf(f146,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = (((cP @ X2 @ X1) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X2)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f145])).
0.23/0.52	thf(f145,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | ($false = ((^[Y0 : a]: (((cP @ Y0 @ X1) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X1))) @ X2))) )),
0.23/0.52	  inference(pi_clausification,[],[f144])).
0.23/0.52	thf(f144,plain,(
0.23/0.52	  ( ! [X1 : a] : (($false = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ X1) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X1))))) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f143])).
0.23/0.52	thf(f143,plain,(
0.23/0.52	  ( ! [X1 : a] : (($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | ($false = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))) @ X1))) )),
0.23/0.52	  inference(pi_clausification,[],[f127])).
0.23/0.52	thf(f127,plain,(
0.23/0.52	  ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $false) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f126])).
0.23/0.52	thf(f330,plain,(
0.23/0.52	  spl13_18 | spl13_18),
0.23/0.52	  inference(avatar_split_clause,[],[f177,f325,f325])).
0.23/0.52	thf(f177,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) = $false) | ((cP @ X2 @ X1) != sK15) | ((cP @ X4 @ X3) != sK15)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f175])).
0.23/0.52	thf(f175,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X2 @ X1) != sK15) | ((cP @ X4 @ X3) != sK15) | ($false = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3))) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(equality_proxy_clausification,[],[f174])).
0.23/0.52	thf(f174,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | (((cP @ X4 @ X3) = sK15) = $false) | ($false = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3))) | ((cP @ X2 @ X1) != sK15)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f173])).
0.23/0.52	thf(f173,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (((cP @ X2 @ X1) != sK15) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((((cP @ X4 @ X3) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X4) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ X4)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X3))) = $false)) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f172])).
0.23/0.52	thf(f172,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a,X4 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | ((cP @ X2 @ X1) != sK15) | ($false = ((^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3)))) @ X4))) )),
0.23/0.52	  inference(pi_clausification,[],[f171])).
0.23/0.52	thf(f171,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a] : (((cP @ X2 @ X1) != sK15) | ($false = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3)))))) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(equality_proxy_clausification,[],[f170])).
0.23/0.52	thf(f170,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a] : (($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | (((cP @ X2 @ X1) = sK15) = $false) | ($false = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ X3) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X3))))))) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f169])).
0.23/0.52	thf(f169,plain,(
0.23/0.52	  ( ! [X2 : a,X3 : a,X1 : a] : ((((cP @ X2 @ X1) = sK15) = $false) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1)) | (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) @ X3) = $false)) )),
0.23/0.52	  inference(pi_clausification,[],[f168])).
0.23/0.52	thf(f168,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false) | (((cP @ X2 @ X1) = sK15) = $false) | ($false = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1))) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f167])).
0.23/0.52	thf(f167,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (($false = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ X2) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ X1) & ((cP @ X2 @ X1) = sK15))) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false)) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f166])).
0.23/0.52	thf(f166,plain,(
0.23/0.52	  ( ! [X2 : a,X1 : a] : (((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false) | (((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X1) & ((cP @ Y0 @ X1) = sK15))) @ X2) = $false)) )),
0.23/0.52	  inference(pi_clausification,[],[f165])).
0.23/0.52	thf(f165,plain,(
0.23/0.52	  ( ! [X1 : a] : (((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X1) & ((cP @ Y0 @ X1) = sK15)))) = $false) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $false)) )),
0.23/0.52	  inference(binary_proxy_clausification,[],[f163])).
0.23/0.52	thf(f163,plain,(
0.23/0.52	  ( ! [X1 : a] : (($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | ((?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ X1) & ((cP @ Y0 @ X1) = sK15)))) = $false)) )),
0.23/0.52	  inference(beta_eta_normalization,[],[f162])).
0.23/0.52	thf(f162,plain,(
0.23/0.52	  ( ! [X1 : a] : (($false = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))) @ X1)) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))) )),
0.23/0.52	  inference(pi_clausification,[],[f125])).
0.23/0.52	thf(f125,plain,(
0.23/0.52	  ($false = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | ($false = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f124])).
0.23/0.52	thf(f318,plain,(
0.23/0.52	  spl13_5 | spl13_12 | spl13_15 | spl13_16),
0.23/0.52	  inference(avatar_split_clause,[],[f224,f314,f309,f296,f264])).
0.23/0.52	thf(f224,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) = sK15) | (sK15 = (cP @ sK20 @ sK19)) | (cZ = sK15) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18))),
0.23/0.52	  inference(equality_proxy_clausification,[],[f223])).
0.23/0.52	thf(f223,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18)) | ((cP @ sK17 @ sK16) = sK15) | (((cP @ sK20 @ sK19) = sK15) = $true) | (cZ = sK15)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f221])).
0.23/0.52	thf(f221,plain,(
0.23/0.52	  (cZ = sK15) | ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) & ((cP @ sK21 @ sK18) = sK15))) | ((cP @ sK17 @ sK16) = sK15) | (((cP @ sK20 @ sK19) = sK15) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f219])).
0.23/0.52	thf(f219,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (((cP @ sK20 @ sK19) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19))) | ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) & ((cP @ sK21 @ sK18) = sK15))) | ((cP @ sK17 @ sK16) = sK15)),
0.23/0.52	  inference(beta_eta_normalization,[],[f218])).
0.23/0.52	thf(f218,plain,(
0.23/0.52	  ($true = ((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))) @ sK21)) | (cZ = sK15) | ($true = (((cP @ sK20 @ sK19) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19))) | ((cP @ sK17 @ sK16) = sK15)),
0.23/0.52	  inference(sigma_clausification,[],[f217])).
0.23/0.52	thf(f217,plain,(
0.23/0.52	  ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | ($true = (((cP @ sK20 @ sK19) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19))) | ((cP @ sK17 @ sK16) = sK15) | (cZ = sK15)),
0.23/0.52	  inference(beta_eta_normalization,[],[f216])).
0.23/0.52	thf(f216,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) = sK15) | ($true = ((^[Y0 : a]: (((cP @ Y0 @ sK19) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK19))) @ sK20)) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | (cZ = sK15)),
0.23/0.52	  inference(sigma_clausification,[],[f215])).
0.23/0.52	thf(f215,plain,(
0.23/0.52	  ($true = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK19) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK19))))) | ((cP @ sK17 @ sK16) = sK15) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | (cZ = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f214])).
0.23/0.52	thf(f214,plain,(
0.23/0.52	  (cZ = sK15) | ($true = ((cP @ sK17 @ sK16) = sK15)) | ($true = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK19) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK19))))) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15)))))),
0.23/0.52	  inference(beta_eta_normalization,[],[f213])).
0.23/0.52	thf(f213,plain,(
0.23/0.52	  ($true = ((cP @ sK17 @ sK16) = sK15)) | (cZ = sK15) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))) @ sK19)) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15)))))),
0.23/0.52	  inference(sigma_clausification,[],[f212])).
0.23/0.52	thf(f212,plain,(
0.23/0.52	  ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | ($true = ((cP @ sK17 @ sK16) = sK15)) | (cZ = sK15)),
0.23/0.52	  inference(duplicate_literal_removal,[],[f211])).
0.23/0.52	thf(f211,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | (cZ = sK15) | ($true = ((cP @ sK17 @ sK16) = sK15)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f210])).
0.23/0.52	thf(f210,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (cZ = sK15)) | ($true = ((cP @ sK17 @ sK16) = sK15)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15)))))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f208])).
0.23/0.52	thf(f208,plain,(
0.23/0.52	  ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | ($true = (cZ = sK15)) | (cZ = sK15) | ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15)))))),
0.23/0.52	  inference(beta_eta_normalization,[],[f207])).
0.23/0.52	thf(f207,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (cZ = sK15)) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))) @ sK18)) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true)),
0.23/0.52	  inference(sigma_clausification,[],[f206])).
0.23/0.52	thf(f206,plain,(
0.23/0.52	  ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | (cZ = sK15) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | ($true = (cZ = sK15))),
0.23/0.52	  inference(duplicate_literal_removal,[],[f205])).
0.23/0.52	thf(f205,plain,(
0.23/0.52	  ($true = (cZ = sK15)) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | ($true = (cZ = sK15))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f204])).
0.23/0.52	thf(f204,plain,(
0.23/0.52	  (((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $true) | (cZ = sK15) | ($true = (cZ = sK15)) | ($true = (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f203])).
0.23/0.52	thf(f203,plain,(
0.23/0.52	  ((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) = $true) | (cZ = sK15) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | ($true = (cZ = sK15))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f202])).
0.23/0.52	thf(f202,plain,(
0.23/0.52	  (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)))) | (cZ = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f201])).
0.23/0.52	thf(f201,plain,(
0.23/0.52	  ($true = (cZ = sK15)) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true) | ($true = (((cP @ sK17 @ sK16) = sK15) & ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))))),
0.23/0.52	  inference(beta_eta_normalization,[],[f200])).
0.23/0.52	thf(f200,plain,(
0.23/0.52	  ($true = (cZ = sK15)) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true) | ($true = ((^[Y0 : a]: (((cP @ Y0 @ sK16) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK16) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK16)))) @ sK17))),
0.23/0.52	  inference(sigma_clausification,[],[f199])).
0.23/0.52	thf(f199,plain,(
0.23/0.52	  ((?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK16) = sK15) & ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK16) | (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK16))))) = $true) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true) | ($true = (cZ = sK15))),
0.23/0.52	  inference(beta_eta_normalization,[],[f198])).
0.23/0.52	thf(f198,plain,(
0.23/0.52	  (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true) | (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) @ sK16) = $true) | ($true = (cZ = sK15))),
0.23/0.52	  inference(sigma_clausification,[],[f197])).
0.23/0.52	thf(f197,plain,(
0.23/0.52	  ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) = $true) | ($true = (cZ = sK15)) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f121])).
0.23/0.52	thf(f121,plain,(
0.23/0.52	  ($true = ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) | (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (cZ = sK15))) | (((((cZ = sK15) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))))) | (?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: ((cPHI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((Y3 @ Y1) & (!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4)))))) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0) & ((cP @ Y1 @ Y0) = sK15))))))) | (cZ = sK15)) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f120])).
0.23/0.52	thf(f317,plain,(
0.23/0.52	  spl13_12 | spl13_5 | spl13_16 | spl13_13),
0.23/0.52	  inference(avatar_split_clause,[],[f226,f300,f314,f264,f296])).
0.23/0.52	thf(f226,plain,(
0.23/0.52	  ((cP @ sK17 @ sK16) = sK15) | (sK15 = (cP @ sK20 @ sK19)) | ((cP @ sK21 @ sK18) = sK15) | (cZ = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f225])).
0.23/0.52	thf(f225,plain,(
0.23/0.52	  (((cP @ sK20 @ sK19) = sK15) = $true) | (cZ = sK15) | ((cP @ sK17 @ sK16) = sK15) | ((cP @ sK21 @ sK18) = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f222])).
0.23/0.52	thf(f222,plain,(
0.23/0.52	  ($true = ((cP @ sK21 @ sK18) = sK15)) | (cZ = sK15) | (((cP @ sK20 @ sK19) = sK15) = $true) | ((cP @ sK17 @ sK16) = sK15)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f221])).
0.23/0.52	thf(f312,plain,(
0.23/0.52	  spl13_5 | spl13_15 | spl13_12 | spl13_14),
0.23/0.52	  inference(avatar_split_clause,[],[f228,f304,f296,f309,f264])).
0.23/0.52	thf(f228,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19)) | (cZ = sK15) | ((cP @ sK17 @ sK16) = sK15)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f220])).
0.23/0.52	thf(f220,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19)) | ((cP @ sK17 @ sK16) = sK15) | (cZ = sK15) | ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK21) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) & ((cP @ sK21 @ sK18) = sK15)))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f219])).
0.23/0.52	thf(f307,plain,(
0.23/0.52	  spl13_12 | spl13_13 | spl13_14 | spl13_5),
0.23/0.52	  inference(avatar_split_clause,[],[f229,f264,f304,f300,f296])).
0.23/0.52	thf(f229,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19)) | ((cP @ sK17 @ sK16) = sK15) | (cZ = sK15) | ((cP @ sK21 @ sK18) = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f227])).
0.23/0.52	thf(f227,plain,(
0.23/0.52	  ($true = ((cP @ sK21 @ sK18) = sK15)) | ((cP @ sK17 @ sK16) = sK15) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK20)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK19))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f220])).
0.23/0.52	thf(f294,plain,(
0.23/0.52	  spl13_6 | spl13_4 | spl13_5 | spl13_11 | spl13_10),
0.23/0.52	  inference(avatar_split_clause,[],[f243,f286,f291,f264,f260,f268])).
0.23/0.52	thf(f243,plain,(
0.23/0.52	  ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ((cP @ sK24 @ sK23) = sK15) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (cZ = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f242])).
0.23/0.52	thf(f242,plain,(
0.23/0.52	  ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (cZ = sK15) | ($true = ((cP @ sK24 @ sK23) = sK15)) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f240])).
0.23/0.52	thf(f240,plain,(
0.23/0.52	  ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (((cP @ sK24 @ sK23) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK24)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23)))),
0.23/0.52	  inference(beta_eta_normalization,[],[f239])).
0.23/0.52	thf(f239,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (((^[Y0 : a]: (((cP @ Y0 @ sK23) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK23))) @ sK24) = $true) | (cZ = sK15)),
0.23/0.52	  inference(sigma_clausification,[],[f238])).
0.23/0.52	thf(f238,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ((?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK23) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK23)))) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f237])).
0.23/0.52	thf(f237,plain,(
0.23/0.52	  ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK23) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK23)))) = $true) | (cZ = sK15)),
0.23/0.52	  inference(duplicate_literal_removal,[],[f236])).
0.23/0.52	thf(f236,plain,(
0.23/0.52	  (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK23) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK23)))) = $true) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (cZ = sK15)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f235])).
0.23/0.52	thf(f235,plain,(
0.23/0.52	  ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ($true = (cZ = sK15)) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK23) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK23)))) = $true) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(beta_eta_normalization,[],[f234])).
0.23/0.52	thf(f234,plain,(
0.23/0.52	  (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | ($true = ((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))) @ sK23)) | ($true = (cZ = sK15)) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(sigma_clausification,[],[f233])).
0.23/0.52	thf(f233,plain,(
0.23/0.52	  ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true) | (cZ = sK15) | ($true = (cZ = sK15)) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f231])).
0.23/0.52	thf(f231,plain,(
0.23/0.52	  (cZ = sK15) | ($true = ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) & ((cP @ sK22 @ sK18) = sK15))) | ($true = (cZ = sK15)) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true)),
0.23/0.52	  inference(beta_eta_normalization,[],[f230])).
0.23/0.52	thf(f230,plain,(
0.23/0.52	  (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ($true = (cZ = sK15)) | (((^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))) @ sK22) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | (cZ = sK15)),
0.23/0.52	  inference(sigma_clausification,[],[f209])).
0.23/0.52	thf(f209,plain,(
0.23/0.52	  ($true = (?? @ a @ (^[Y0 : a]: ((cPHI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((Y2 @ Y0) & (!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3)))))) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK18) & ((cP @ Y0 @ sK18) = sK15))))) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | (cZ = sK15) | ($true = (cZ = sK15)) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f208])).
0.23/0.52	thf(f289,plain,(
0.23/0.52	  spl13_5 | spl13_4 | spl13_6 | spl13_9 | spl13_10),
0.23/0.52	  inference(avatar_split_clause,[],[f241,f286,f282,f268,f260,f264])).
0.23/0.52	thf(f241,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK24)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK23) = $true) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (cZ = sK15) | ((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK22) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK18) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f240])).
0.23/0.52	thf(f280,plain,(
0.23/0.52	  spl13_6 | spl13_7 | spl13_4 | spl13_8 | spl13_5),
0.23/0.52	  inference(avatar_split_clause,[],[f254,f264,f277,f260,f272,f268])).
0.23/0.52	thf(f254,plain,(
0.23/0.52	  ((cP @ sK26 @ sK25) = sK15) | ((cP @ sK22 @ sK18) = sK15) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  inference(equality_proxy_clausification,[],[f253])).
0.23/0.52	thf(f253,plain,(
0.23/0.52	  ($true = ((cP @ sK26 @ sK25) = sK15)) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cP @ sK22 @ sK18) = sK15) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f251])).
0.23/0.52	thf(f251,plain,(
0.23/0.52	  ((cP @ sK22 @ sK18) = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (((cP @ sK26 @ sK25) = sK15) & (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK26)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25))) | (cZ = sK15)),
0.23/0.52	  inference(beta_eta_normalization,[],[f250])).
0.23/0.52	thf(f250,plain,(
0.23/0.52	  (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (((^[Y0 : a]: (((cP @ Y0 @ sK25) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK25))) @ sK26) = $true) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cP @ sK22 @ sK18) = sK15)),
0.23/0.52	  inference(sigma_clausification,[],[f249])).
0.23/0.52	thf(f249,plain,(
0.23/0.52	  ($true = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK25) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK25))))) | ((cP @ sK22 @ sK18) = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | (cZ = sK15) | ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f248])).
0.23/0.52	thf(f248,plain,(
0.23/0.52	  (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | (cZ = sK15) | ($true = (?? @ a @ (^[Y0 : a]: (((cP @ Y0 @ sK25) = sK15) & (cPSI @ (^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: ((Y2 @ Y3) => (Y2 @ (cL @ Y3))))) & (Y2 @ Y0)) => (?? @ a @ (^[Y3 : a]: ((Y2 @ Y3) & ((cR @ Y3) = Y1)))))))) @ sK25))))) | ((cP @ sK22 @ sK18) = sK15)),
0.23/0.52	  inference(beta_eta_normalization,[],[f247])).
0.23/0.52	thf(f247,plain,(
0.23/0.52	  (((^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0))))) @ sK25) = $true) | ((cP @ sK22 @ sK18) = sK15) | (cZ = sK15) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(sigma_clausification,[],[f246])).
0.23/0.52	thf(f246,plain,(
0.23/0.52	  (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((cP @ sK22 @ sK18) = sK15)),
0.23/0.52	  inference(duplicate_literal_removal,[],[f245])).
0.23/0.52	thf(f245,plain,(
0.23/0.52	  ((cP @ sK22 @ sK18) = sK15) | (cZ = sK15) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true) | (cZ = sK15) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f244])).
0.23/0.52	thf(f244,plain,(
0.23/0.52	  ((cP @ sK22 @ sK18) = sK15) | ($true = (cZ = sK15)) | (cZ = sK15) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true)),
0.23/0.52	  inference(equality_proxy_clausification,[],[f232])).
0.23/0.52	thf(f232,plain,(
0.23/0.52	  ($true = ((cP @ sK22 @ sK18) = sK15)) | (cZ = sK15) | ($true = (cZ = sK15)) | (((cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16) | (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) = $true) | ((?? @ a @ (^[Y0 : a]: (?? @ a @ (^[Y1 : a]: (((cP @ Y1 @ Y0) = sK15) & (cPSI @ (^[Y2 : a]: (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: ((Y3 @ Y4) => (Y3 @ (cL @ Y4))))) & (Y3 @ Y1)) => (?? @ a @ (^[Y4 : a]: ((Y3 @ Y4) & ((cR @ Y4) = Y2)))))))) @ Y0)))))) = $true)),
0.23/0.52	  inference(binary_proxy_clausification,[],[f231])).
0.23/0.52	thf(f275,plain,(
0.23/0.52	  spl13_3 | spl13_4 | spl13_5 | spl13_6 | spl13_7),
0.23/0.52	  inference(avatar_split_clause,[],[f252,f272,f268,f264,f260,f256])).
0.23/0.52	thf(f252,plain,(
0.23/0.52	  ($true = (cPHI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((Y1 @ sK17) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2)))))) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ((cP @ sK22 @ sK18) = sK15) | (cZ = sK15) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK17)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK16)) | ($true = (cPSI @ (^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (Y1 @ (cL @ Y2))))) & (Y1 @ sK26)) => (?? @ a @ (^[Y2 : a]: ((Y1 @ Y2) & ((cR @ Y2) = Y0)))))))) @ sK25))),
0.23/0.52	  inference(binary_proxy_clausification,[],[f251])).
0.23/0.52	% SZS output end Proof for Vampire---4
0.23/0.52	% (31940)------------------------------
0.23/0.52	% (31940)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.23/0.52	% (31940)Termination reason: Refutation
0.23/0.52	
0.23/0.52	% (31940)Memory used [KB]: 6652
0.23/0.52	% (31940)Time elapsed: 0.133 s
0.23/0.52	% (31940)Instructions burned: 199 (million)
0.23/0.52	% (31940)------------------------------
0.23/0.52	% (31940)------------------------------
0.23/0.52	% (31936)Success in time 0.137 s
0.23/0.52	% Vampire---4.8 exiting
0.23/0.52	EOF