0.00/0.02	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.36	% Computer : n015.cluster.edu
0.11/0.36	% Model    : x86_64 x86_64
0.11/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.36	% Memory   : 8046.5625MB
0.11/0.36	% OS       : Linux 6.8.0-71-generic
0.11/0.36	% CPULimit : 1440
0.11/0.36	% WCLimit  : 180
0.11/0.36	% DateTime : Mon Jul 27 09:02:35 UTC 2026
0.11/0.36	% CPUTime  : 
0.14/0.36	Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.14/0.39	Running higher-order theorem proving
0.14/0.40	Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.27/0.48	% (790791)Detected a higher-order problem, will run a greedy HOL sequence.
0.27/0.48	% (790796)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4192544740:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.27/0.48	% (790797)lrs+10_16_si=on:nwc=1.5:random_seed=2792371120:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi)
0.27/0.48	% (790798)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=726186087:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi)
0.27/0.48	% (790799)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2677561549:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi)
0.27/0.48	% (790798)Refutation not found, incomplete strategy
0.27/0.48	% (790798)------------------------------
0.27/0.48	% (790798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790798)CaDiCaL version: 2.1.3
0.27/0.48	% (790798)Termination reason: Refutation not found, incomplete strategy
0.27/0.48	% (790798)Time elapsed: 0.001 s
0.27/0.48	% (790798)Peak memory usage: 12 MB
0.27/0.48	% (790798)Instructions burned: 1 (million)
0.27/0.48	% (790798)------------------------------
0.27/0.48	% (790798)------------------------------
0.27/0.48	% (790800)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3274682917:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi)
0.27/0.48	% (790802)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
0.27/0.48	% (790802)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
0.27/0.48	% (790797)Instruction limit reached! 
0.27/0.48	% (790797)------------------------------
0.27/0.48	% (790797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790797)CaDiCaL version: 2.1.3
0.27/0.48	% (790797)Termination reason: Instruction limit
0.27/0.48	% (790797)Termination phase: Saturation
0.27/0.48	% (790797)Time elapsed: 0.011 s
0.27/0.48	% (790797)Peak memory usage: 12 MB
0.27/0.48	% (790797)Instructions burned: 18 (million)
0.27/0.48	% (790801)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=444854622:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi)
0.27/0.48	% (790802)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1716855803:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi)
0.27/0.48	% (790796)Instruction limit reached! 
0.27/0.48	% (790796)------------------------------
0.27/0.48	% (790796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790796)CaDiCaL version: 2.1.3
0.27/0.48	% (790796)Termination reason: Instruction limit
0.27/0.48	% (790796)Termination phase: Saturation
0.27/0.48	% (790796)Time elapsed: 0.022 s
0.27/0.48	% (790796)Peak memory usage: 12 MB
0.27/0.48	% (790796)Instructions burned: 88 (million)
0.27/0.48	% (790800)Instruction limit reached! 
0.27/0.48	% (790800)------------------------------
0.27/0.48	% (790800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790800)CaDiCaL version: 2.1.3
0.27/0.48	% (790800)Termination reason: Instruction limit
0.27/0.48	% (790800)Termination phase: Saturation
0.27/0.48	% (790800)Time elapsed: 0.013 s
0.27/0.48	% (790800)Peak memory usage: 11 MB
0.27/0.48	% (790800)Instructions burned: 25 (million)
0.27/0.48	% (790812)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
0.27/0.48	% (790799) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-790791-790799"...
0.27/0.48	% (790812)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=18041119:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_1799 on theBenchmark for (1799ds/7Mi)
0.27/0.48	% (790809)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2313354835:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_1799 on theBenchmark for (1799ds/5Mi)
0.27/0.48	% (790812)Instruction limit reached! 
0.27/0.48	% (790812)------------------------------
0.27/0.48	% (790812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790812)CaDiCaL version: 2.1.3
0.27/0.48	% (790812)Termination reason: Instruction limit
0.27/0.48	% (790812)Termination phase: Saturation
0.27/0.48	% (790812)Time elapsed: 0.003 s
0.27/0.48	% (790812)Peak memory usage: 12 MB
0.27/0.48	% (790812)Instructions burned: 11 (million)
0.27/0.48	% (790807)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2208900871:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi)
0.27/0.48	% (790809)Instruction limit reached! 
0.27/0.48	% (790809)------------------------------
0.27/0.48	% (790809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790809)CaDiCaL version: 2.1.3
0.27/0.48	% (790809)Termination reason: Instruction limit
0.27/0.48	% (790809)Termination phase: Saturation
0.27/0.48	% (790809)Time elapsed: 0.003 s
0.27/0.48	% (790809)Peak memory usage: 11 MB
0.27/0.48	% (790809)Instructions burned: 5 (million)
0.27/0.48	% (790799)...printing done.
0.27/0.48	% (790807)Instruction limit reached! 
0.27/0.48	% (790807)------------------------------
0.27/0.48	% (790807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.48	% (790807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.48	% (790807)CaDiCaL version: 2.1.3
0.27/0.48	% (790807)Termination reason: Instruction limit
0.27/0.48	% (790807)Termination phase: Saturation
0.27/0.48	% (790807)Time elapsed: 0.002 s
0.27/0.48	% (790807)Peak memory usage: 12 MB
0.27/0.48	% (790807)Instructions burned: 3 (million)
0.27/0.48	% (790799)Refutation found. Thanks to Tanya!
0.27/0.48	% SZS status Theorem for theBenchmark
0.27/0.48	% SZS output start Proof for theBenchmark
0.27/0.48	thf(type_def_5, type, a: $tType).
0.27/0.48	thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
0.27/0.48	thf(func_def_0, type, cX: (a > $o)).
0.27/0.48	thf(func_def_2, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
0.27/0.48	thf(func_def_3, type, vAND: ($o > $o > $o)).
0.27/0.48	thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.27/0.48	thf(func_def_5, type, vIMP: ($o > $o > $o)).
0.27/0.48	thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
0.27/0.48	thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.27/0.48	thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
0.27/0.48	thf(func_def_11, type, db3: !>[X0: $tType]:(X0)).
0.27/0.48	thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
0.27/0.48	thf(func_def_13, type, vOR: ($o > $o > $o)).
0.27/0.48	thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.27/0.48	thf(func_def_15, type, vNOT: ($o > $o)).
0.27/0.48	thf(func_def_17, type, sK1: a).
0.27/0.48	thf(func_def_18, type, sK2: ((a > $o) > a)).
0.27/0.48	thf(func_def_19, type, sK3: ((a > $o) > (a > $o) > $o)).
0.27/0.48	thf(func_def_20, type, sK4: (a > $o)).
0.27/0.48	thf(func_def_21, type, sK5: (((a > $o) > $o) > a > $o)).
0.27/0.48	thf(func_def_22, type, sK6: (((a > $o) > $o) > a)).
0.27/0.48	thf(f1,conjecture,(
0.27/0.48	  ((^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => (cX @ X3)) & ! [X2 : ((a > $o) > $o)] : ((! [X3 : (a > $o)] : ((X2 @ X3) => ! [X4 : a] : ((X1 @ X4) => (X2 @ (^[X5 : a] : ((X3 @ X5) | (X4 = X5)))))) & (X2 @ (^[X6 : a] : ($false)))) => (X2 @ X1))))) = cX)),
0.27/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA3_pme)).
0.27/0.48	thf(f2,negated_conjecture,(
0.27/0.48	  ~ ((^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => (cX @ X3)) & ! [X2 : ((a > $o) > $o)] : ((! [X3 : (a > $o)] : ((X2 @ X3) => ! [X4 : a] : ((X1 @ X4) => (X2 @ (^[X5 : a] : ((X3 @ X5) | (X4 = X5)))))) & (X2 @ (^[X6 : a] : ($false)))) => (X2 @ X1))))) = cX)),
0.27/0.48	  inference(negated_conjecture,[status(cth)],[f1])).
0.27/0.48	thf(f3,plain,(
0.27/0.48	  ~ ((^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => (cX @ X2)) & ! [X3 : ((a > $o) > $o)] : ((! [X4 : (a > $o)] : ((X3 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X3 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6)))))) & (X3 @ (^[X7 : a] : ($false)))) => (X3 @ X1))))) = cX)),
0.27/0.48	  inference(rectify,[],[f2])).
0.27/0.48	thf(f4,plain,(
0.27/0.48	  ~ (cX = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))))),
0.27/0.48	  inference(fool_elimination,[],[f3])).
0.27/0.48	thf(f5,plain,(
0.27/0.48	  (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))))),
0.27/0.48	  inference(flattening,[],[f4])).
0.27/0.48	thf(f6,plain,(
0.27/0.48	  (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))))),
0.27/0.48	  inference(cnf_transformation,[],[f5])).
0.27/0.48	thf(f9,definition,(
0.27/0.48	  spl0_1 <=> (cX = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))))),
0.27/0.48	  introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
0.27/0.48	thf(f11,plain,(
0.27/0.48	  (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0)))))) | spl0_1),
0.27/0.48	  inference(avatar_component_clause,[],[f9])).
0.27/0.48	thf(f12,plain,(
0.27/0.48	  ~spl0_1),
0.27/0.48	  inference(avatar_split_clause,[],[f6,f9])).
0.27/0.48	thf(f13,plain,(
0.27/0.48	  (((cX @ sK1)) != (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))) @ sK1))) | spl0_1),
0.27/0.48	  inference(negative_extensionality,[],[f11])).
0.27/0.48	thf(f14,plain,(
0.27/0.48	  ($true = ((cX @ sK1))) | ($true = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))) @ sK1))) | spl0_1),
0.27/0.48	  inference(xor_proxy_clausification,[],[f13])).
0.27/0.48	thf(f15,plain,(
0.27/0.48	  ($false = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((Y2 @ (^[Y3 : a]: ($false))) & (!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5))))))))))) => (Y2 @ Y1)))) & (!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2))))) & (Y1 @ Y0))))) @ sK1))) | ($false = ((cX @ sK1))) | spl0_1),
0.27/0.48	  inference(xor_proxy_clausification,[],[f13])).
0.27/0.48	thf(f16,plain,(
0.27/0.48	  ($false = ((cX @ sK1))) | ($false = ((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))) & (Y0 @ sK1)))))) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f15])).
0.27/0.48	thf(f17,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (((((^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))) & (Y0 @ sK1))) @ X1)) = $false) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(pi_proxy_clausification,[],[f16])).
0.27/0.48	thf(f18,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = ((cX @ sK1))) | ($false = ((((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))))) & (X1 @ sK1))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f17])).
0.27/0.48	thf(f19,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1)))) & (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))))))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f18])).
0.27/0.48	thf(f20,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($false = ((cX @ sK1))) | ($false = ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0)))))) | ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))))))) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f19])).
0.27/0.48	thf(f21,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ((((^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))) @ (sK2 @ X1))) = $false) | ($false = ((cX @ sK1))) | ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))))))) ) | spl0_1),
0.27/0.48	  inference(sigma_proxy_clausification,[],[f20])).
0.27/0.48	thf(f22,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ((((^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))) @ (sK2 @ X1))) = $false) | ($false = ((cX @ sK1))) | ($false = (((^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ X1))) @ (sK3 @ X1))))) ) | spl0_1),
0.27/0.48	  inference(sigma_proxy_clausification,[],[f21])).
0.27/0.48	thf(f23,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($false = (((X1 @ (sK2 @ X1)) => (cX @ (sK2 @ X1))))) | ($false = ((cX @ sK1))) | ($false = ((((sK3 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) => (sK3 @ X1 @ X1))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f22])).
0.27/0.48	thf(f24,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = ((cX @ sK1))) | ($false = ((cX @ (sK2 @ X1)))) | (((X1 @ sK1)) = $false) | ($false = ((((sK3 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) => (sK3 @ X1 @ X1))))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f23])).
0.27/0.48	thf(f25,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false) | ($false = ((((sK3 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) => (sK3 @ X1 @ X1)))) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f23])).
0.27/0.48	thf(f26,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = ((cX @ sK1))) | (((X1 @ sK1)) = $false) | (((sK3 @ X1 @ X1)) = $false) | (((X1 @ (sK2 @ X1))) = $true)) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f25])).
0.27/0.48	thf(f27,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($true = (((sK3 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))))) | (((X1 @ (sK2 @ X1))) = $true) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f25])).
0.27/0.48	thf(f28,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) = $true) | (((X1 @ sK1)) = $false) | ($false = ((cX @ sK1))) | (((X1 @ (sK2 @ X1))) = $true)) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f27])).
0.27/0.48	thf(f29,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f27])).
0.27/0.48	thf(f30,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($true = (((^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2))) | (((X1 @ (sK2 @ X1))) = $true) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(pi_proxy_clausification,[],[f28])).
0.27/0.48	thf(f31,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | ($false = ((cX @ sK1))) | ($true = (((sK3 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f30])).
0.27/0.48	thf(f32,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((sK3 @ X1 @ X2)) = $false) | ($false = ((cX @ sK1))) | (((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false) | ($true = ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))))))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f31])).
0.27/0.48	thf(f33,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | ($false = ((cX @ sK1))) | (((sK3 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3)))) ) | spl0_1),
0.27/0.48	  inference(pi_proxy_clausification,[],[f32])).
0.27/0.48	thf(f34,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($false = ((cX @ sK1))) | (((sK3 @ X1 @ X2)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | ($true = (((X1 @ X3) => (sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f33])).
0.27/0.48	thf(f35,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((X1 @ X3)) = $false) | ($false = ((cX @ sK1))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((sK3 @ X1 @ X2)) = $false) | (((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true)) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f34])).
0.27/0.48	thf(f36,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = ((cX @ (sK2 @ X1)))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ sK1))) | (((sK3 @ X1 @ X1)) = $false)) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f24])).
0.27/0.48	thf(f37,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($true = (((sK3 @ X1 @ (^[Y0 : a]: ($false))) & (!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f24])).
0.27/0.48	thf(f38,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($false = ((cX @ sK1))) | ($false = ((cX @ (sK2 @ X1)))) | (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) = $true)) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f37])).
0.27/0.48	thf(f39,plain,(
0.27/0.48	  ( ! [X1 : (a > $o)] : (($false = ((cX @ sK1))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false)))))) ) | spl0_1),
0.27/0.48	  inference(and_proxy_clausification,[],[f37])).
0.27/0.48	thf(f40,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : (($false = ((cX @ sK1))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | ($true = (((^[Y0 : a > $o]: ((sK3 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK3 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2)))) ) | spl0_1),
0.27/0.48	  inference(pi_proxy_clausification,[],[f38])).
0.27/0.48	thf(f41,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | ($false = ((cX @ sK1))) | ($true = (((sK3 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f40])).
0.27/0.48	thf(f42,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X1 : (a > $o)] : (($false = ((cX @ (sK2 @ X1)))) | ($false = ((cX @ sK1))) | (((sK3 @ X1 @ X2)) = $false) | ($true = ((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))) | (((X1 @ sK1)) = $false)) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f41])).
0.27/0.48	thf(f43,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((sK3 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : a]: ((X1 @ Y0) => (sK3 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(pi_proxy_clausification,[],[f42])).
0.27/0.48	thf(f44,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((sK3 @ X1 @ X2)) = $false) | ($false = ((cX @ sK1))) | ($false = ((cX @ (sK2 @ X1)))) | (((X1 @ sK1)) = $false) | ($true = (((X1 @ X3) => (sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))))) ) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f43])).
0.27/0.48	thf(f45,plain,(
0.27/0.48	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((sK3 @ X1 @ X2)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | (((X1 @ X3)) = $false) | (((X1 @ sK1)) = $false) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | ($false = ((cX @ sK1)))) ) | spl0_1),
0.27/0.48	  inference(imp_proxy_clausification,[],[f44])).
0.27/0.48	thf(f46,plain,(
0.27/0.48	  ($true = ((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))) & (Y0 @ sK1)))))) | ($true = ((cX @ sK1))) | spl0_1),
0.27/0.48	  inference(beta-eta_normalization,[],[f14])).
0.27/0.48	thf(f47,plain,(
0.27/0.48	  ($true = ((cX @ sK1))) | ($true = (((^[Y0 : a > $o]: (((!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((Y1 @ (^[Y2 : a]: ($false))) & (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4))))))))))) => (Y1 @ Y0)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1))))) & (Y0 @ sK1))) @ sK4))) | spl0_1),
0.27/0.49	  inference(sigma_proxy_clausification,[],[f46])).
0.27/0.49	thf(f48,plain,(
0.27/0.49	  ($true = ((cX @ sK1))) | ($true = ((((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ sK4)))) & (!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0))))) & (sK4 @ sK1)))) | spl0_1),
0.27/0.49	  inference(beta-eta_normalization,[],[f47])).
0.27/0.49	thf(f49,plain,(
0.27/0.49	  (((sK4 @ sK1)) = $true) | ($true = ((cX @ sK1))) | spl0_1),
0.27/0.49	  inference(and_proxy_clausification,[],[f48])).
0.27/0.49	thf(f50,plain,(
0.27/0.49	  ($true = ((cX @ sK1))) | ($true = (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((Y0 @ (^[Y1 : a]: ($false))) & (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3))))))))))) => (Y0 @ sK4)))) & (!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0))))))) | spl0_1),
0.27/0.49	  inference(and_proxy_clausification,[],[f48])).
0.27/0.49	thf(f51,plain,(
0.27/0.49	  ($true = ((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0)))))) | ($true = ((cX @ sK1))) | spl0_1),
0.27/0.49	  inference(and_proxy_clausification,[],[f50])).
0.27/0.49	thf(f65,plain,(
0.27/0.49	  ( ! [X1 : a] : (($true = (((^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0))) @ X1))) | ($true = ((cX @ sK1)))) ) | spl0_1),
0.27/0.49	  inference(pi_proxy_clausification,[],[f51])).
0.27/0.49	thf(f66,plain,(
0.27/0.49	  ( ! [X1 : a] : (($true = ((cX @ sK1))) | ($true = (((sK4 @ X1) => (cX @ X1))))) ) | spl0_1),
0.27/0.49	  inference(beta-eta_normalization,[],[f65])).
0.27/0.49	thf(f67,plain,(
0.27/0.49	  ( ! [X1 : a] : (($true = ((cX @ X1))) | ($true = ((cX @ sK1))) | ($false = ((sK4 @ X1)))) ) | spl0_1),
0.27/0.49	  inference(imp_proxy_clausification,[],[f66])).
0.27/0.49	thf(f69,definition,(
0.27/0.49	  spl0_2 <=> ! [X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
0.27/0.49	thf(f70,plain,(
0.27/0.49	  ( ! [X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true)) ) | ~spl0_2),
0.27/0.49	  inference(avatar_component_clause,[],[f69])).
0.27/0.49	thf(f72,definition,(
0.27/0.49	  spl0_3 <=> ($false = ((cX @ sK1)))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
0.27/0.49	thf(f74,plain,(
0.27/0.49	  ($false = ((cX @ sK1))) | ~spl0_3),
0.27/0.49	  inference(avatar_component_clause,[],[f72])).
0.27/0.49	thf(f75,plain,(
0.27/0.49	  spl0_2 | spl0_3 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f29,f9,f72,f69])).
0.27/0.49	thf(f77,definition,(
0.27/0.49	  spl0_4 <=> ! [X2 : (a > $o),X1 : (a > $o),X3 : a] : ((((X1 @ X3)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false) | (((sK3 @ X1 @ X2)) = $false) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
0.27/0.49	thf(f78,plain,(
0.27/0.49	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((sK3 @ X1 @ X2)) = $false) | (((X1 @ X3)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false)) ) | ~spl0_4),
0.27/0.49	  inference(avatar_component_clause,[],[f77])).
0.27/0.49	thf(f79,plain,(
0.27/0.49	  spl0_4 | spl0_3 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f35,f9,f72,f77])).
0.27/0.49	thf(f81,definition,(
0.27/0.49	  spl0_5 <=> ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | (((sK3 @ X1 @ X1)) = $false))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
0.27/0.49	thf(f82,plain,(
0.27/0.49	  ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) = $false) | (((X1 @ (sK2 @ X1))) = $true) | (((X1 @ sK1)) = $false)) ) | ~spl0_5),
0.27/0.49	  inference(avatar_component_clause,[],[f81])).
0.27/0.49	thf(f83,plain,(
0.27/0.49	  spl0_5 | spl0_3 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f26,f9,f72,f81])).
0.27/0.49	thf(f85,definition,(
0.27/0.49	  spl0_6 <=> ! [X1 : (a > $o)] : ((((X1 @ sK1)) = $false) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false))))) | ($false = ((cX @ (sK2 @ X1)))))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
0.27/0.49	thf(f86,plain,(
0.27/0.49	  ( ! [X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ sK1)) = $false) | ($false = ((cX @ (sK2 @ X1))))) ) | ~spl0_6),
0.27/0.49	  inference(avatar_component_clause,[],[f85])).
0.27/0.49	thf(f87,plain,(
0.27/0.49	  spl0_3 | spl0_6 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f39,f9,f85,f72])).
0.27/0.49	thf(f89,definition,(
0.27/0.49	  spl0_7 <=> ! [X2 : (a > $o),X1 : (a > $o),X3 : a] : ((((sK3 @ X1 @ X2)) = $false) | ($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((X1 @ sK1)) = $false) | (((X1 @ X3)) = $false) | ($false = ((cX @ (sK2 @ X1)))))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
0.27/0.49	thf(f90,plain,(
0.27/0.49	  ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((X1 @ sK1)) = $false) | (((sK3 @ X1 @ X2)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | (((X1 @ X3)) = $false)) ) | ~spl0_7),
0.27/0.49	  inference(avatar_component_clause,[],[f89])).
0.27/0.49	thf(f91,plain,(
0.27/0.49	  spl0_3 | spl0_7 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f45,f9,f89,f72])).
0.27/0.49	thf(f93,definition,(
0.27/0.49	  spl0_8 <=> ! [X1 : (a > $o)] : (($false = ((cX @ (sK2 @ X1)))) | (((sK3 @ X1 @ X1)) = $false) | (((X1 @ sK1)) = $false))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
0.27/0.49	thf(f94,plain,(
0.27/0.49	  ( ! [X1 : (a > $o)] : ((((sK3 @ X1 @ X1)) = $false) | ($false = ((cX @ (sK2 @ X1)))) | (((X1 @ sK1)) = $false)) ) | ~spl0_8),
0.27/0.49	  inference(avatar_component_clause,[],[f93])).
0.27/0.49	thf(f95,plain,(
0.27/0.49	  spl0_8 | spl0_3 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f36,f9,f72,f93])).
0.27/0.49	thf(f97,definition,(
0.27/0.49	  spl0_9 <=> ($true = ((cX @ sK1)))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
0.27/0.49	thf(f99,plain,(
0.27/0.49	  ($true = ((cX @ sK1))) | ~spl0_9),
0.27/0.49	  inference(avatar_component_clause,[],[f97])).
0.27/0.49	thf(f113,definition,(
0.27/0.49	  spl0_13 <=> ! [X1 : a] : (($true = ((cX @ X1))) | ($false = ((sK4 @ X1))))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
0.27/0.49	thf(f114,plain,(
0.27/0.49	  ( ! [X1 : a] : (($true = ((cX @ X1))) | ($false = ((sK4 @ X1)))) ) | ~spl0_13),
0.27/0.49	  inference(avatar_component_clause,[],[f113])).
0.27/0.49	thf(f115,plain,(
0.27/0.49	  spl0_13 | spl0_9 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f67,f9,f97,f113])).
0.27/0.49	thf(f117,definition,(
0.27/0.49	  spl0_14 <=> (((sK4 @ sK1)) = $true)),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
0.27/0.49	thf(f119,plain,(
0.27/0.49	  (((sK4 @ sK1)) = $true) | ~spl0_14),
0.27/0.49	  inference(avatar_component_clause,[],[f117])).
0.27/0.49	thf(f120,plain,(
0.27/0.49	  spl0_14 | spl0_9 | spl0_1),
0.27/0.49	  inference(avatar_split_clause,[],[f49,f9,f97,f117])).
0.27/0.49	thf(f121,plain,(
0.27/0.49	  ($true = $false) | (~spl0_3 | ~spl0_9)),
0.27/0.49	  inference(forward_demodulation,[],[f99,f74])).
0.27/0.49	thf(f122,plain,(
0.27/0.49	  $false | (~spl0_3 | ~spl0_9)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f121])).
0.27/0.49	thf(f123,plain,(
0.27/0.49	  ~spl0_3 | ~spl0_9),
0.27/0.49	  inference(avatar_contradiction_clause,[],[f122])).
0.27/0.49	thf(f126,plain,(
0.27/0.49	  (((sK4 @ sK1)) = $false) | ($true = $false) | (~spl0_3 | ~spl0_13)),
0.27/0.49	  inference(superposition,[],[f74,f114])).
0.27/0.49	thf(f127,plain,(
0.27/0.49	  (((sK4 @ sK1)) = $false) | (~spl0_3 | ~spl0_13)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f126])).
0.27/0.49	thf(f130,definition,(
0.27/0.49	  spl0_15 <=> (((sK4 @ sK1)) = $false)),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
0.27/0.49	thf(f132,plain,(
0.27/0.49	  (((sK4 @ sK1)) = $false) | ~spl0_15),
0.27/0.49	  inference(avatar_component_clause,[],[f130])).
0.27/0.49	thf(f133,plain,(
0.27/0.49	  spl0_15 | ~spl0_3 | ~spl0_13),
0.27/0.49	  inference(avatar_split_clause,[],[f127,f113,f72,f130])).
0.27/0.49	thf(f136,plain,(
0.27/0.49	  ($true = $false) | (~spl0_14 | ~spl0_15)),
0.27/0.49	  inference(superposition,[],[f119,f132])).
0.27/0.49	thf(f139,plain,(
0.27/0.49	  $false | (~spl0_14 | ~spl0_15)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f136])).
0.27/0.49	thf(f140,plain,(
0.27/0.49	  ~spl0_14 | ~spl0_15),
0.27/0.49	  inference(avatar_contradiction_clause,[],[f139])).
0.27/0.49	thf(f148,definition,(
0.27/0.49	  spl0_17 <=> (sK1 = ((sK2 @ (= @ sK1))))),
0.27/0.49	  introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
0.27/0.49	thf(f149,plain,(
0.27/0.49	  (sK1 != ((sK2 @ (= @ sK1)))) | spl0_17),
0.27/0.49	  inference(avatar_component_clause,[],[f148])).
0.27/0.49	thf(f150,plain,(
0.27/0.49	  (sK1 = ((sK2 @ (= @ sK1)))) | ~spl0_17),
0.27/0.49	  inference(avatar_component_clause,[],[f148])).
0.27/0.49	thf(f212,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($true = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(superposition,[],[f82,f78])).
0.27/0.49	thf(f233,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($true = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f212])).
0.27/0.49	thf(f234,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f233])).
0.27/0.49	thf(f235,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = (((X0 = sK1) | (X1 @ sK1)))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) | ((((X0 = X0) | (X1 @ X0))) = $false)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(beta-eta_normalization,[],[f234])).
0.27/0.49	thf(f237,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = ((X0 = sK1))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) | ((((X0 = X0) | (X1 @ X0))) = $false)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(or_proxy_clausification,[],[f235])).
0.27/0.49	thf(f238,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (((((X0 = X0) | (X1 @ X0))) = $false) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f237])).
0.27/0.49	thf(f240,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (((X0 = X0)) = $false) | (sK1 != X0) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))))) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(or_proxy_clausification,[],[f238])).
0.27/0.49	thf(f241,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((sK1 != X0) | (X0 != X0) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f240])).
0.27/0.49	thf(f242,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($true = ((X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(or_proxy_clausification,[],[f241])).
0.27/0.49	thf(f243,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0) | ($true = ((X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f242])).
0.27/0.49	thf(f244,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($true = ((X1 @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0)) ) | (~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f243])).
0.27/0.49	thf(f302,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($true = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(superposition,[],[f90,f94])).
0.27/0.49	thf(f306,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($true = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f302])).
0.27/0.49	thf(f307,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1)))) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f306])).
0.27/0.49	thf(f308,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ((((X0 = X0) | (X1 @ X0))) = $false) | ($false = (((X0 = sK1) | (X1 @ sK1)))) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(beta-eta_normalization,[],[f307])).
0.27/0.49	thf(f310,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = (((X0 = sK1) | (X1 @ sK1)))) | (((X0 = X0)) = $false) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(or_proxy_clausification,[],[f308])).
0.27/0.49	thf(f312,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : (($false = ((X0 = sK1))) | (((X0 = X0)) = $false) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(or_proxy_clausification,[],[f310])).
0.27/0.49	thf(f313,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((sK1 != X0) | (((X0 = X0)) = $false) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f312])).
0.27/0.49	thf(f314,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((sK1 != X0) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (X0 != X0)) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f313])).
0.27/0.49	thf(f315,plain,(
0.27/0.49	  ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (sK1 != X0) | ($false = ((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))))) ) | (~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f314])).
0.27/0.49	thf(f375,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $false) | (sK1 != X0) | ($true = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | (((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $false)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(superposition,[],[f315,f86])).
0.27/0.49	thf(f591,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | (sK1 != X0) | ($true = $false)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f375])).
0.27/0.49	thf(f592,plain,(
0.27/0.49	  ( ! [X0 : a] : (($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | (((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $false) | (sK1 != X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f591])).
0.27/0.49	thf(f593,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | ($false = (((X0 = sK1) | $false))) | (((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(beta-eta_normalization,[],[f592])).
0.27/0.49	thf(f595,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | ($false = ((X0 = sK1))) | (((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(or_proxy_clausification,[],[f593])).
0.27/0.49	thf(f596,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | (((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false) | (sK1 != X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f595])).
0.27/0.49	thf(f597,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((cX @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false) | (sK1 != X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f596])).
0.27/0.49	thf(f598,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((cX @ (sK2 @ (^[Y0 : a]: (X0 = Y0))))) = $false) | (sK1 != X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(boolean_simplification,[],[f597])).
0.27/0.49	thf(f599,plain,(
0.27/0.49	  ( ! [X0 : a] : (($false = ((cX @ (sK2 @ (= @ X0))))) | (sK1 != X0)) ) | (~spl0_6 | ~spl0_7 | ~spl0_8)),
0.27/0.49	  inference(beta-eta_normalization,[],[f598])).
0.27/0.49	thf(f622,plain,(
0.27/0.49	  ($false = ((cX @ sK1))) | (sK1 != sK1) | (~spl0_6 | ~spl0_7 | ~spl0_8 | ~spl0_17)),
0.27/0.49	  inference(superposition,[],[f599,f150])).
0.27/0.49	thf(f627,plain,(
0.27/0.49	  ($false = ((cX @ sK1))) | (~spl0_6 | ~spl0_7 | ~spl0_8 | ~spl0_17)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f622])).
0.27/0.49	thf(f628,plain,(
0.27/0.49	  spl0_3 | ~spl0_6 | ~spl0_7 | ~spl0_8 | ~spl0_17),
0.27/0.49	  inference(avatar_split_clause,[],[f627,f148,f93,f89,f85,f72])).
0.27/0.49	thf(f923,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | ($true = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))) = X0) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | ($true = (((^[Y0 : a]: ($false)) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | ($true = $false)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(superposition,[],[f70,f244])).
0.27/0.49	thf(f937,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))) = X0) | ($true = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | ($true = (((^[Y0 : a]: ($false)) @ (sK2 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))))) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f923])).
0.27/0.49	thf(f938,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (sK1 != X0) | ($true = (((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) | $false))) | ($false = (((X0 = sK1) | $false))) | ($true = $false)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(beta-eta_normalization,[],[f937])).
0.27/0.49	thf(f939,plain,(
0.27/0.49	  ( ! [X0 : a] : (($false = (((X0 = sK1) | $false))) | ($true = $false) | ($true = $false) | (sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($true = ((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false))))))) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(or_proxy_clausification,[],[f938])).
0.27/0.49	thf(f941,plain,(
0.27/0.49	  ( ! [X0 : a] : (($true = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($false = ((X0 = sK1))) | ($true = ((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))))) | (sK1 != X0) | ($true = $false)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(or_proxy_clausification,[],[f939])).
0.27/0.49	thf(f942,plain,(
0.27/0.49	  ( ! [X0 : a] : (($true = ((X0 = (sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))))) | (sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($true = $false) | ($true = $false) | (sK1 != X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f941])).
0.27/0.49	thf(f943,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($true = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (sK1 != X0) | ($true = $false) | (sK1 != X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(equality_proxy_clausification,[],[f942])).
0.27/0.49	thf(f944,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (sK1 != X0) | ($true = $false)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f943])).
0.27/0.49	thf(f945,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f944])).
0.27/0.49	thf(f946,plain,(
0.27/0.49	  ( ! [X0 : a] : ((sK1 != X0) | (((sK2 @ (^[Y0 : a]: (X0 = Y0)))) = X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(boolean_simplification,[],[f945])).
0.27/0.49	thf(f947,plain,(
0.27/0.49	  ( ! [X0 : a] : ((((sK2 @ (= @ X0))) = X0) | (sK1 != X0)) ) | (~spl0_2 | ~spl0_4 | ~spl0_5)),
0.27/0.49	  inference(beta-eta_normalization,[],[f946])).
0.27/0.49	thf(f1209,plain,(
0.27/0.49	  (sK1 != sK1) | (sK1 != sK1) | (~spl0_2 | ~spl0_4 | ~spl0_5 | spl0_17)),
0.27/0.49	  inference(superposition,[],[f149,f947])).
0.27/0.49	thf(f1211,plain,(
0.27/0.49	  (sK1 != sK1) | (~spl0_2 | ~spl0_4 | ~spl0_5 | spl0_17)),
0.27/0.49	  inference(duplicate_literal_removal,[],[f1209])).
0.27/0.49	thf(f1212,plain,(
0.27/0.49	  $false | (~spl0_2 | ~spl0_4 | ~spl0_5 | spl0_17)),
0.27/0.49	  inference(trivial_inequality_removal,[],[f1211])).
0.27/0.49	thf(f1213,plain,(
0.27/0.49	  ~spl0_2 | ~spl0_4 | ~spl0_5 | spl0_17),
0.27/0.49	  inference(avatar_contradiction_clause,[],[f1212])).
0.27/0.49	cnf(s1, plain, ~spl0_1, inference(sat_conversion,[],[f12])).
0.27/0.49	cnf(s2, plain, spl0_1 | spl0_2 | spl0_3, inference(sat_conversion,[],[f75])).
0.27/0.49	cnf(s3, plain, spl0_1 | spl0_3 | spl0_4, inference(sat_conversion,[],[f79])).
0.27/0.49	cnf(s4, plain, spl0_1 | spl0_3 | spl0_5, inference(sat_conversion,[],[f83])).
0.27/0.49	cnf(s5, plain, spl0_1 | spl0_3 | spl0_6, inference(sat_conversion,[],[f87])).
0.27/0.49	cnf(s6, plain, spl0_1 | spl0_3 | spl0_7, inference(sat_conversion,[],[f91])).
0.27/0.49	cnf(s7, plain, spl0_1 | spl0_3 | spl0_8, inference(sat_conversion,[],[f95])).
0.27/0.49	cnf(s11, plain, spl0_1 | spl0_9 | spl0_13, inference(sat_conversion,[],[f115])).
0.27/0.49	cnf(s12, plain, spl0_1 | spl0_9 | spl0_14, inference(sat_conversion,[],[f120])).
0.27/0.49	cnf(s13, plain, ~spl0_3 | ~spl0_9, inference(sat_conversion,[],[f123])).
0.27/0.49	cnf(s14, plain, ~spl0_3 | ~spl0_13 | spl0_15, inference(sat_conversion,[],[f133])).
0.27/0.49	cnf(s18, plain, ~spl0_14 | ~spl0_15, inference(sat_conversion,[],[f140])).
0.27/0.49	cnf(s21, plain, spl0_3 | ~spl0_6 | ~spl0_7 | ~spl0_8 | ~spl0_17, inference(sat_conversion,[],[f628])).
0.27/0.49	cnf(s23, plain, ~spl0_2 | ~spl0_4 | ~spl0_5 | spl0_17, inference(sat_conversion,[],[f1213])).
0.27/0.49	cnf(s24, plain, ~spl0_3, inference(rat,[],[s14,s18,s11,s12,s13,s1])).
0.27/0.49	cnf(s25, plain, spl0_8, inference(rat,[],[s7,s1,s24])).
0.27/0.49	cnf(s26, plain, spl0_7, inference(rat,[],[s6,s1,s24])).
0.27/0.49	cnf(s27, plain, spl0_6, inference(rat,[],[s5,s1,s24])).
0.27/0.49	cnf(s28, plain, spl0_5, inference(rat,[],[s4,s1,s24])).
0.27/0.49	cnf(s29, plain, spl0_4, inference(rat,[],[s3,s1,s24])).
0.27/0.49	cnf(s30, plain, spl0_2, inference(rat,[],[s2,s1,s24])).
0.27/0.49	cnf(s31, plain, ~spl0_17, inference(rat,[],[s21,s26,s25,s24,s27])).
0.27/0.49	cnf(s33, plain, $false, inference(rat,[],[s23,s31,s30,s28,s29])).
0.27/0.49	thf(f1214,plain,(
0.27/0.49	  $false),
0.27/0.49	  inference(avatar_sat_refutation,[],[s33])).
0.27/0.49	% SZS output end Proof for theBenchmark
0.27/0.49	% (790799)------------------------------
0.27/0.49	% (790799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.27/0.49	% (790799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.27/0.49	% (790799)CaDiCaL version: 2.1.3
0.27/0.49	% (790799)Termination reason: Refutation
0.27/0.49	% (790799)Time elapsed: 0.032 s
0.27/0.49	% (790799)Peak memory usage: 13 MB
0.27/0.49	% (790799)Instructions burned: 65 (million)
0.27/0.49	% (790791)Success in time 0.076 s
0.27/0.49	% Vampire exiting
0.27/0.49	EOF