%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU874^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:51 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU874^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n005.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:41:58 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (1755251)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (1755259)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=1901627105: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (1755262)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (1755262)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
% 0.19/0.27 % (1755260)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2466882520:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (1755256)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2688758162:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (1755257)lrs+10_16_si=on:nwc=1.5:random_seed=3130588371:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (1755258)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3185115913:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (1755261)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2123943957:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (1755262)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=1798186730:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (1755258)Refutation not found, incomplete strategy
% 0.19/0.27 % (1755258)------------------------------
% 0.19/0.27 % (1755258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1755258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1755258)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1755258)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (1755258)Time elapsed: 0.001 s
% 0.19/0.27 % (1755258)Peak memory usage: 12 MB
% 0.19/0.27 % (1755258)Instructions burned: 1 (million)
% 0.19/0.27 % (1755258)------------------------------
% 0.19/0.27 % (1755258)------------------------------
% 0.19/0.27 % (1755259) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1755251-1755259"...
% 0.19/0.27 % (1755259)...printing done.
% 0.19/0.27 % (1755257)Instruction limit reached!
% 0.19/0.27 % (1755257)------------------------------
% 0.19/0.27 % (1755257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1755257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1755257)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1755257)Termination reason: Instruction limit
% 0.19/0.27 % (1755257)Termination phase: Saturation
% 0.19/0.27 % (1755257)Time elapsed: 0.012 s
% 0.19/0.27 % (1755257)Peak memory usage: 12 MB
% 0.19/0.27 % (1755257)Instructions burned: 20 (million)
% 0.19/0.27 % (1755259)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, a: $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, cX: (a > $o)).
% 0.19/0.27 thf(func_def_2, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_3, type, vAND: ($o > $o > $o)).
% 0.19/0.27 thf(func_def_4, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.27 thf(func_def_5, type, vIMP: ($o > $o > $o)).
% 0.19/0.27 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(func_def_9, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.19/0.27 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.27 thf(func_def_15, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(func_def_17, type, sK1: a).
% 0.19/0.27 thf(func_def_18, type, sK2: ((a > $o) > (a > $o) > $o)).
% 0.19/0.27 thf(func_def_19, type, sK3: ((a > $o) > a)).
% 0.19/0.27 thf(func_def_20, type, sK4: (a > $o)).
% 0.19/0.27 thf(func_def_21, type, sK5: (((a > $o) > $o) > a > $o)).
% 0.19/0.27 thf(func_def_22, type, sK6: (((a > $o) > $o) > a)).
% 0.19/0.27 thf(f1,conjecture,(
% 0.19/0.27 (cX = (^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : ((a > $o) > $o)] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6))))))) => (X2 @ X1)) & ! [X4 : a] : ((X1 @ X4) => (cX @ X4))))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA3_pme)).
% 0.19/0.27 thf(f2,negated_conjecture,(
% 0.19/0.27 ~ (cX = (^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : ((a > $o) > $o)] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6))))))) => (X2 @ X1)) & ! [X4 : a] : ((X1 @ X4) => (cX @ X4))))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.27 thf(f3,plain,(
% 0.19/0.27 ~ (cX = (^[X0 : a] : (? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : ((a > $o) > $o)] : (((X2 @ (^[X3 : a] : ($false))) & ! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X4 @ X6) | (X5 = X6))))))) => (X2 @ X1)) & ! [X7 : a] : ((X1 @ X7) => (cX @ X7))))))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f4,plain,(
% 0.19/0.27 ~ (cX = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))))),
% 0.19/0.27 inference(fool_elimination,[],[f3])).
% 0.19/0.27 thf(f5,plain,(
% 0.19/0.27 (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))))),
% 0.19/0.27 inference(flattening,[],[f4])).
% 0.19/0.27 thf(f6,plain,(
% 0.19/0.27 (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))))),
% 0.19/0.27 inference(cnf_transformation,[],[f5])).
% 0.19/0.27 thf(f9,definition,(
% 0.19/0.27 spl0_1 <=> (cX = (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 (cX != (^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0)))))) | spl0_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f9])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 ~spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f6,f9])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 (((cX @ sK1)) != (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))) @ sK1))) | spl0_1),
% 0.19/0.27 inference(negative_extensionality,[],[f11])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 (((cX @ sK1)) = $true) | ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))) @ sK1)) = $true) | spl0_1),
% 0.19/0.27 inference(xor_proxy_clausification,[],[f13])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 (((cX @ sK1)) = $false) | ($false = (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: ((Y1 @ Y2) => (cX @ Y2)))) & (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: ((Y2 @ Y3) => (!! @ a @ (^[Y4 : a]: ((Y1 @ Y4) => (Y2 @ (^[Y5 : a]: ((Y4 = Y5) | (Y3 @ Y5)))))))))) & (Y2 @ (^[Y3 : a]: ($false)))) => (Y2 @ Y1))))) & (Y1 @ Y0))))) @ sK1))) | spl0_1),
% 0.19/0.27 inference(xor_proxy_clausification,[],[f13])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 (((cX @ sK1)) = $false) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))) & (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4)))))))))) & (Y1 @ (^[Y2 : a]: ($false)))) => (Y1 @ Y0))))) & (Y0 @ sK1))))) = $false) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((cX @ sK1)) = $false) | ($false = (((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))) & (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4)))))))))) & (Y1 @ (^[Y2 : a]: ($false)))) => (Y1 @ Y0))))) & (Y0 @ sK1))) @ X1)))) ) | spl0_1),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f16])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ X1))))) & (X1 @ sK1))) = $false) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f17])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ((((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ X1)))))) = $false) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f18])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((cX @ sK1)) = $false) | ($false = ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ X1)))))) | (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))))) = $false) | ($false = ((X1 @ sK1)))) ) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f19])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ((((^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ X1))) @ (sK2 @ X1))) = $false) | (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))))) = $false)) ) | spl0_1),
% 0.19/0.27 inference(sigma_proxy_clausification,[],[f20])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ($false = (((^[Y0 : a]: ((X1 @ Y0) => (cX @ Y0))) @ (sK3 @ X1)))) | ((((^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((X1 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ X1))) @ (sK2 @ X1))) = $false)) ) | spl0_1),
% 0.19/0.27 inference(sigma_proxy_clausification,[],[f21])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((((!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2)))))))))) & (sK2 @ X1 @ (^[Y0 : a]: ($false)))) => (sK2 @ X1 @ X1)))) | ($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1)))))) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f22])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1))))) | (((sK2 @ X1 @ X1)) = $false) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f23])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2)))))))))) & (sK2 @ X1 @ (^[Y0 : a]: ($false)))))) | ($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1)))))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f23])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1))))) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | ($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f25])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((!! @ (a > $o) @ (^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))))) = $true) | ($false = ((X1 @ sK1))) | ($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1))))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f25])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((cX @ sK1)) = $false) | ($true = (((^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2))) | ($false = ((X1 @ sK1))) | ($false = (((X1 @ (sK3 @ X1)) => (cX @ (sK3 @ X1)))))) ) | spl0_1),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f27])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : (($false = ((cX @ (sK3 @ X1)))) | ($true = (((^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2))) | (((cX @ sK1)) = $false) | ($false = ((X1 @ sK1)))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f28])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((cX @ sK1)) = $false) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1))) | ($true = (((^[Y0 : a > $o]: ((sK2 @ X1 @ Y0) => (!! @ a @ (^[Y1 : a]: ((X1 @ Y1) => (sK2 @ X1 @ (^[Y2 : a]: ((Y1 = Y2) | (Y0 @ Y2))))))))) @ X2)))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f28])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ((((sK2 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))) = $true)) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f30])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : (($false = ((X1 @ sK1))) | (((sK2 @ X1 @ X2)) = $false) | (((X1 @ (sK3 @ X1))) = $true) | (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))))) = $true) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f31])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((X1 @ (sK3 @ X1))) = $true) | (((sK2 @ X1 @ X2)) = $false) | ($false = ((X1 @ sK1))) | ((((^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3)) = $true) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f32])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((sK2 @ X1 @ X2)) = $false) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1))) | (((cX @ sK1)) = $false) | ((((X1 @ X3) => (sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) = $true)) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f33])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : ((((cX @ sK1)) = $false) | (((sK2 @ X1 @ X2)) = $false) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ X3))) | ($false = ((X1 @ sK1)))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f34])).
% 0.19/0.27 thf(f36,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false) | ((((sK2 @ X1 @ X2) => (!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1))))))))) = $true)) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f29])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X1 : (a > $o)] : ((((sK2 @ X1 @ X2)) = $false) | (((!! @ a @ (^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))))) = $true) | ($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f36])).
% 0.19/0.27 thf(f38,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (((((^[Y0 : a]: ((X1 @ Y0) => (sK2 @ X1 @ (^[Y1 : a]: ((Y0 = Y1) | (X2 @ Y1)))))) @ X3)) = $true) | (((sK2 @ X1 @ X2)) = $false) | ($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f37])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (((((X1 @ X3) => (sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) = $true) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false) | (((sK2 @ X1 @ X2)) = $false) | ($false = ((X1 @ sK1)))) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f38])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false) | ($false = ((X1 @ sK1))) | ($false = ((X1 @ X3))) | (((sK2 @ X1 @ X2)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f39])).
% 0.19/0.27 thf(f41,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | ($false = ((cX @ (sK3 @ X1)))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f26])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | (((X1 @ (sK3 @ X1))) = $true) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | (((cX @ sK1)) = $false)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f26])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | (((cX @ sK1)) = $false) | ($false = ((cX @ (sK3 @ X1)))) | ($false = ((X1 @ sK1)))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f24])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | (((cX @ sK1)) = $false) | ($false = ((X1 @ sK1))) | (((X1 @ (sK3 @ X1))) = $true)) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f24])).
% 0.19/0.27 thf(f45,plain,(
% 0.19/0.27 (((cX @ sK1)) = $true) | (((?? @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))) & (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4)))))))))) & (Y1 @ (^[Y2 : a]: ($false)))) => (Y1 @ Y0))))) & (Y0 @ sK1))))) = $true) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f14])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 (((cX @ sK1)) = $true) | ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cX @ Y1)))) & (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) => (!! @ a @ (^[Y3 : a]: ((Y0 @ Y3) => (Y1 @ (^[Y4 : a]: ((Y3 = Y4) | (Y2 @ Y4)))))))))) & (Y1 @ (^[Y2 : a]: ($false)))) => (Y1 @ Y0))))) & (Y0 @ sK1))) @ sK4)) = $true) | spl0_1),
% 0.19/0.27 inference(sigma_proxy_clausification,[],[f45])).
% 0.19/0.27 thf(f47,plain,(
% 0.19/0.27 (((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ sK4))))) & (sK4 @ sK1))) = $true) | (((cX @ sK1)) = $true) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f46])).
% 0.19/0.27 thf(f48,plain,(
% 0.19/0.27 (((cX @ sK1)) = $true) | (((sK4 @ sK1)) = $true) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f47])).
% 0.19/0.27 thf(f49,plain,(
% 0.19/0.27 ((((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0)))) & (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) => (!! @ a @ (^[Y2 : a]: ((sK4 @ Y2) => (Y0 @ (^[Y3 : a]: ((Y2 = Y3) | (Y1 @ Y3)))))))))) & (Y0 @ (^[Y1 : a]: ($false)))) => (Y0 @ sK4)))))) = $true) | (((cX @ sK1)) = $true) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f47])).
% 0.19/0.27 thf(f51,plain,(
% 0.19/0.27 (((!! @ a @ (^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0))))) = $true) | (((cX @ sK1)) = $true) | spl0_1),
% 0.19/0.27 inference(and_proxy_clausification,[],[f49])).
% 0.19/0.27 thf(f52,plain,(
% 0.19/0.27 ( ! [X1 : a] : ((((cX @ sK1)) = $true) | ((((^[Y0 : a]: ((sK4 @ Y0) => (cX @ Y0))) @ X1)) = $true)) ) | spl0_1),
% 0.19/0.27 inference(pi_proxy_clausification,[],[f51])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 ( ! [X1 : a] : ((((cX @ sK1)) = $true) | ((((sK4 @ X1) => (cX @ X1))) = $true)) ) | spl0_1),
% 0.19/0.27 inference(beta-eta_normalization,[],[f52])).
% 0.19/0.27 thf(f54,plain,(
% 0.19/0.27 ( ! [X1 : a] : ((((sK4 @ X1)) = $false) | (((cX @ sK1)) = $true) | ($true = ((cX @ X1)))) ) | spl0_1),
% 0.19/0.27 inference(imp_proxy_clausification,[],[f53])).
% 0.19/0.27 thf(f68,definition,(
% 0.19/0.27 spl0_2 <=> (((cX @ sK1)) = $false)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.19/0.27 thf(f70,plain,(
% 0.19/0.27 (((cX @ sK1)) = $false) | ~spl0_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f68])).
% 0.19/0.27 thf(f72,definition,(
% 0.19/0.27 spl0_3 <=> ! [X2 : (a > $o),X1 : (a > $o),X3 : a] : ((((sK2 @ X1 @ X2)) = $false) | ($false = ((X1 @ sK1))) | ($false = ((X1 @ X3))) | (((X1 @ (sK3 @ X1))) = $true) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.19/0.27 thf(f73,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((sK2 @ X1 @ X2)) = $false) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1))) | ($false = ((X1 @ X3)))) ) | ~spl0_3),
% 0.19/0.27 inference(avatar_component_clause,[],[f72])).
% 0.19/0.27 thf(f74,plain,(
% 0.19/0.27 spl0_2 | spl0_3 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f35,f9,f72,f68])).
% 0.19/0.27 thf(f76,definition,(
% 0.19/0.27 spl0_4 <=> ! [X2 : (a > $o),X1 : (a > $o),X3 : a] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((sK2 @ X1 @ X2)) = $false) | ($false = ((X1 @ X3))) | ($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.19/0.27 thf(f77,plain,(
% 0.19/0.27 ( ! [X2 : (a > $o),X3 : a,X1 : (a > $o)] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ((X3 = Y0) | (X2 @ Y0)))))) | (((sK2 @ X1 @ X2)) = $false) | ($false = ((cX @ (sK3 @ X1)))) | ($false = ((X1 @ X3))) | ($false = ((X1 @ sK1)))) ) | ~spl0_4),
% 0.19/0.27 inference(avatar_component_clause,[],[f76])).
% 0.19/0.27 thf(f78,plain,(
% 0.19/0.27 spl0_4 | spl0_2 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f40,f9,f68,f76])).
% 0.19/0.27 thf(f80,definition,(
% 0.19/0.27 spl0_5 <=> ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ (sK3 @ X1))) = $true))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.19/0.27 thf(f81,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1)))) ) | ~spl0_5),
% 0.19/0.27 inference(avatar_component_clause,[],[f80])).
% 0.19/0.27 thf(f82,plain,(
% 0.19/0.27 spl0_2 | spl0_5 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f42,f9,f80,f68])).
% 0.19/0.27 thf(f84,definition,(
% 0.19/0.27 spl0_6 <=> ! [X1 : (a > $o)] : (($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))) | ($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.19/0.27 thf(f85,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : (($true = ((sK2 @ X1 @ (^[Y0 : a]: ($false))))) | ($false = ((cX @ (sK3 @ X1)))) | ($false = ((X1 @ sK1)))) ) | ~spl0_6),
% 0.19/0.27 inference(avatar_component_clause,[],[f84])).
% 0.19/0.27 thf(f86,plain,(
% 0.19/0.27 spl0_2 | spl0_6 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f41,f9,f84,f68])).
% 0.19/0.27 thf(f88,definition,(
% 0.19/0.27 spl0_7 <=> ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | (((X1 @ (sK3 @ X1))) = $true) | ($false = ((X1 @ sK1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.19/0.27 thf(f89,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | ($false = ((X1 @ sK1))) | (((X1 @ (sK3 @ X1))) = $true)) ) | ~spl0_7),
% 0.19/0.27 inference(avatar_component_clause,[],[f88])).
% 0.19/0.27 thf(f90,plain,(
% 0.19/0.27 spl0_7 | spl0_2 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f44,f9,f68,f88])).
% 0.19/0.27 thf(f92,definition,(
% 0.19/0.27 spl0_8 <=> ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | ($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1)))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.19/0.27 thf(f93,plain,(
% 0.19/0.27 ( ! [X1 : (a > $o)] : ((((sK2 @ X1 @ X1)) = $false) | ($false = ((X1 @ sK1))) | ($false = ((cX @ (sK3 @ X1))))) ) | ~spl0_8),
% 0.19/0.27 inference(avatar_component_clause,[],[f92])).
% 0.19/0.27 thf(f94,plain,(
% 0.19/0.27 spl0_2 | spl0_8 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f43,f9,f92,f68])).
% 0.19/0.27 thf(f96,definition,(
% 0.19/0.27 spl0_9 <=> (((cX @ sK1)) = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.19/0.27 thf(f97,plain,(
% 0.19/0.27 (((cX @ sK1)) != $true) | spl0_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f96])).
% 0.19/0.27 thf(f98,plain,(
% 0.19/0.27 (((cX @ sK1)) = $true) | ~spl0_9),
% 0.19/0.27 inference(avatar_component_clause,[],[f96])).
% 0.19/0.27 thf(f100,definition,(
% 0.19/0.27 spl0_10 <=> ! [X1 : a] : ((((sK4 @ X1)) = $false) | ($true = ((cX @ X1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.19/0.27 thf(f101,plain,(
% 0.19/0.27 ( ! [X1 : a] : (($true = ((cX @ X1))) | (((sK4 @ X1)) = $false)) ) | ~spl0_10),
% 0.19/0.27 inference(avatar_component_clause,[],[f100])).
% 0.19/0.27 thf(f102,plain,(
% 0.19/0.27 spl0_9 | spl0_10 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f54,f9,f100,f96])).
% 0.19/0.27 thf(f116,definition,(
% 0.19/0.27 spl0_14 <=> (((sK4 @ sK1)) = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 0.19/0.27 thf(f119,plain,(
% 0.19/0.27 spl0_9 | spl0_14 | spl0_1),
% 0.19/0.27 inference(avatar_split_clause,[],[f48,f9,f116,f96])).
% 0.19/0.27 thf(f126,definition,(
% 0.19/0.27 spl0_16 <=> (sK1 = ((sK3 @ (= @ sK1))))),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition])).
% 0.19/0.27 thf(f127,plain,(
% 0.19/0.27 (sK1 != ((sK3 @ (= @ sK1)))) | spl0_16),
% 0.19/0.27 inference(avatar_component_clause,[],[f126])).
% 0.19/0.27 thf(f128,plain,(
% 0.19/0.27 (sK1 = ((sK3 @ (= @ sK1)))) | ~spl0_16),
% 0.19/0.27 inference(avatar_component_clause,[],[f126])).
% 0.19/0.27 thf(f131,plain,(
% 0.19/0.27 ($false = $true) | (~spl0_2 | ~spl0_9)),
% 0.19/0.27 inference(superposition,[],[f98,f70])).
% 0.19/0.27 thf(f134,plain,(
% 0.19/0.27 $false | (~spl0_2 | ~spl0_9)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f131])).
% 0.19/0.27 thf(f135,plain,(
% 0.19/0.27 ~spl0_2 | ~spl0_9),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f134])).
% 0.19/0.27 thf(f180,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = $true) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0)))) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(superposition,[],[f89,f73])).
% 0.19/0.27 thf(f181,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f180])).
% 0.19/0.27 thf(f182,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ((((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f181])).
% 0.19/0.27 thf(f183,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = (((X0 = X0) | (X1 @ X0)))) | ((((X0 = sK1) | (X1 @ sK1))) = $false) | ((((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) = $true) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f182])).
% 0.19/0.27 thf(f185,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = ((X0 = X0))) | ((((X0 = sK1) | (X1 @ sK1))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ((((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) = $true)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f183])).
% 0.19/0.27 thf(f186,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | ((((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) | (X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) = $true) | ((((X0 = sK1) | (X1 @ sK1))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f185])).
% 0.19/0.27 thf(f187,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($true = ((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))))) | (((X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (X0 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ((((X0 = sK1) | (X1 @ sK1))) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f186])).
% 0.19/0.27 thf(f188,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0) | (((X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (X0 != X0) | ((((X0 = sK1) | (X1 @ sK1))) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f187])).
% 0.19/0.27 thf(f190,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0) | (((X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (((X0 = sK1)) = $false)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f188])).
% 0.19/0.27 thf(f191,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (((X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0) | (sK1 != X0)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f190])).
% 0.19/0.27 thf(f192,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (((X1 @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $true) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))))) = X0)) ) | (~spl0_3 | ~spl0_7)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f191])).
% 0.19/0.27 thf(f259,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(superposition,[],[f93,f77])).
% 0.19/0.27 thf(f261,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = $true) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f259])).
% 0.19/0.27 thf(f262,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ sK1))) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | ($false = (((^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X0))) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f261])).
% 0.19/0.27 thf(f263,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : (((((X0 = sK1) | (X1 @ sK1))) = $false) | ($false = (((X0 = X0) | (X1 @ X0)))) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f262])).
% 0.19/0.27 thf(f265,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((X0 = sK1)) = $false) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = (((X0 = X0) | (X1 @ X0))))) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f263])).
% 0.19/0.27 thf(f266,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | (sK1 != X0) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | ($false = (((X0 = X0) | (X1 @ X0))))) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f265])).
% 0.19/0.27 thf(f268,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | ($false = ((X0 = X0)))) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f266])).
% 0.19/0.27 thf(f269,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((X0 != X0) | (sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false) | (((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f268])).
% 0.19/0.27 thf(f270,plain,(
% 0.19/0.27 ( ! [X0 : a,X1 : (a > $o)] : ((((sK2 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0))) @ X1)) = $false) | (sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | (X1 @ Y0)))))) = $false)) ) | (~spl0_4 | ~spl0_8)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f269])).
% 0.19/0.27 thf(f333,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | ($false = ((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | ($false = $true) | ($false = ((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))))) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(superposition,[],[f85,f270])).
% 0.19/0.27 thf(f450,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($false = ((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | (sK1 != X0) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | ($false = $true)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f333])).
% 0.19/0.27 thf(f451,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | ($false = ((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))))) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1)))) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f450])).
% 0.19/0.27 thf(f452,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | ($false = (((X0 = sK1) | $false))) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f451])).
% 0.19/0.27 thf(f454,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((X0 = sK1)) = $false) | (sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f452])).
% 0.19/0.27 thf(f455,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false) | (sK1 != X0)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f454])).
% 0.19/0.27 thf(f456,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((cX @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $false) | (sK1 != X0)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f455])).
% 0.19/0.27 thf(f457,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | (((cX @ (sK3 @ (^[Y0 : a]: (X0 = Y0))))) = $false)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(boolean_simplification,[],[f456])).
% 0.19/0.27 thf(f458,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((cX @ (sK3 @ (= @ X0)))) = $false) | (sK1 != X0)) ) | (~spl0_4 | ~spl0_6 | ~spl0_8)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f457])).
% 0.19/0.27 thf(f566,plain,(
% 0.19/0.27 (sK1 != sK1) | (((cX @ sK1)) = $false) | (~spl0_4 | ~spl0_6 | ~spl0_8 | ~spl0_16)),
% 0.19/0.27 inference(superposition,[],[f458,f128])).
% 0.19/0.27 thf(f567,plain,(
% 0.19/0.27 (((cX @ sK1)) = $false) | (~spl0_4 | ~spl0_6 | ~spl0_8 | ~spl0_16)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f566])).
% 0.19/0.27 thf(f568,plain,(
% 0.19/0.27 spl0_2 | ~spl0_4 | ~spl0_6 | ~spl0_8 | ~spl0_16),
% 0.19/0.27 inference(avatar_split_clause,[],[f567,f126,f92,f84,f76,f68])).
% 0.19/0.27 thf(f904,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | ((((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))) = X0) | ((((^[Y0 : a]: ($false)) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | ($false = $true)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(superposition,[],[f192,f81])).
% 0.19/0.27 thf(f1111,plain,(
% 0.19/0.27 ( ! [X0 : a] : (((((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $true) | ((((^[Y0 : a]: ($false)) @ (sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0)))))) = $true) | ($false = (((^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))) @ sK1))) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | ((^[Y1 : a]: ($false)) @ Y0))))) = X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f904])).
% 0.19/0.27 thf(f1112,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | ($false = $true) | ((((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) | $false)) = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($false = (((X0 = sK1) | $false)))) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f1111])).
% 0.19/0.27 thf(f1113,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($false = $true) | (sK1 != X0) | (((X0 = (sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false))))) = $true) | ($false = (((X0 = sK1) | $false))) | ($false = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f1112])).
% 0.19/0.27 thf(f1114,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($false = (((X0 = sK1) | $false))) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($false = $true) | ($false = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f1113])).
% 0.19/0.27 thf(f1116,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($false = $true) | ($false = $true) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (((X0 = sK1)) = $false)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(or_proxy_clausification,[],[f1114])).
% 0.19/0.27 thf(f1117,plain,(
% 0.19/0.27 ( ! [X0 : a] : (($false = $true) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($false = $true) | (sK1 != X0) | (((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(equality_proxy_clausification,[],[f1116])).
% 0.19/0.27 thf(f1118,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | ($false = $true) | (sK1 != X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f1117])).
% 0.19/0.27 thf(f1119,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((sK3 @ (^[Y0 : a]: ((X0 = Y0) | $false)))) = X0) | (sK1 != X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f1118])).
% 0.19/0.27 thf(f1120,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((sK1 != X0) | (((sK3 @ (^[Y0 : a]: (X0 = Y0)))) = X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(boolean_simplification,[],[f1119])).
% 0.19/0.27 thf(f1121,plain,(
% 0.19/0.27 ( ! [X0 : a] : ((((sK3 @ (= @ X0))) = X0) | (sK1 != X0)) ) | (~spl0_3 | ~spl0_5 | ~spl0_7)),
% 0.19/0.27 inference(beta-eta_normalization,[],[f1120])).
% 0.19/0.27 thf(f1148,plain,(
% 0.19/0.27 (sK1 != sK1) | (sK1 != sK1) | (~spl0_3 | ~spl0_5 | ~spl0_7 | spl0_16)),
% 0.19/0.27 inference(superposition,[],[f127,f1121])).
% 0.19/0.27 thf(f1149,plain,(
% 0.19/0.27 (sK1 != sK1) | (~spl0_3 | ~spl0_5 | ~spl0_7 | spl0_16)),
% 0.19/0.27 inference(duplicate_literal_removal,[],[f1148])).
% 0.19/0.27 thf(f1150,plain,(
% 0.19/0.27 $false | (~spl0_3 | ~spl0_5 | ~spl0_7 | spl0_16)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f1149])).
% 0.19/0.27 thf(f1151,plain,(
% 0.19/0.27 ~spl0_3 | ~spl0_5 | ~spl0_7 | spl0_16),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f1150])).
% 0.19/0.27 thf(f1154,plain,(
% 0.19/0.27 ($true != $true) | (((sK4 @ sK1)) = $false) | (spl0_9 | ~spl0_10)),
% 0.19/0.27 inference(superposition,[],[f97,f101])).
% 0.19/0.27 thf(f1157,plain,(
% 0.19/0.27 (((sK4 @ sK1)) = $false) | (spl0_9 | ~spl0_10)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f1154])).
% 0.19/0.27 thf(f1160,definition,(
% 0.19/0.27 spl0_19 <=> (((sK4 @ sK1)) = $false)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])).
% 0.19/0.27 thf(f1163,plain,(
% 0.19/0.27 spl0_19 | spl0_9 | ~spl0_10),
% 0.19/0.27 inference(avatar_split_clause,[],[f1157,f100,f96,f1160])).
% 0.19/0.27 thf(f1164,definition,(
% 0.19/0.27 (((sK4 @ sK1)) != $true) | (((sK4 @ sK1)) != $false) | (((cX @ sK1)) != $false) | (((cX @ sK1)) = $true)),
% 0.19/0.27 introduced(theory,[theory_tautology_sat_conflict])).
% 0.19/0.27 cnf(s1, plain, ~spl0_1, inference(sat_conversion,[],[f12])).
% 0.19/0.27 cnf(s2, plain, spl0_1 | spl0_2 | spl0_3, inference(sat_conversion,[],[f74])).
% 0.19/0.27 cnf(s3, plain, spl0_1 | spl0_2 | spl0_4, inference(sat_conversion,[],[f78])).
% 0.19/0.27 cnf(s4, plain, spl0_1 | spl0_2 | spl0_5, inference(sat_conversion,[],[f82])).
% 0.19/0.27 cnf(s5, plain, spl0_1 | spl0_2 | spl0_6, inference(sat_conversion,[],[f86])).
% 0.19/0.27 cnf(s6, plain, spl0_1 | spl0_2 | spl0_7, inference(sat_conversion,[],[f90])).
% 0.19/0.27 cnf(s7, plain, spl0_1 | spl0_2 | spl0_8, inference(sat_conversion,[],[f94])).
% 0.19/0.27 cnf(s8, plain, spl0_1 | spl0_9 | spl0_10, inference(sat_conversion,[],[f102])).
% 0.19/0.27 cnf(s12, plain, spl0_1 | spl0_9 | spl0_14, inference(sat_conversion,[],[f119])).
% 0.19/0.27 cnf(s15, plain, ~spl0_2 | ~spl0_9, inference(sat_conversion,[],[f135])).
% 0.19/0.27 cnf(s17, plain, spl0_2 | ~spl0_4 | ~spl0_6 | ~spl0_8 | ~spl0_16, inference(sat_conversion,[],[f568])).
% 0.19/0.27 cnf(s19, plain, ~spl0_3 | ~spl0_5 | ~spl0_7 | spl0_16, inference(sat_conversion,[],[f1151])).
% 0.19/0.27 cnf(s20, plain, spl0_9 | ~spl0_10 | spl0_19, inference(sat_conversion,[],[f1163])).
% 0.19/0.27 cnf(s21, plain, ~spl0_2 | spl0_9 | ~spl0_14 | ~spl0_19, inference(sat_conversion,[],[f1164])).
% 0.19/0.27 cnf(s22, plain, spl0_2, inference(rat,[],[s19,s17,s2,s3,s4,s5,s6,s7,s1])).
% 0.19/0.27 cnf(s23, plain, ~spl0_9, inference(rat,[],[s15,s22])).
% 0.19/0.27 cnf(s24, plain, spl0_14, inference(rat,[],[s12,s1,s23])).
% 0.19/0.27 cnf(s28, plain, spl0_10, inference(rat,[],[s8,s1,s23])).
% 0.19/0.27 cnf(s29, plain, ~spl0_19, inference(rat,[],[s21,s23,s22,s24])).
% 0.19/0.27 cnf(s30, plain, $false, inference(rat,[],[s20,s23,s29,s28])).
% 0.19/0.27 thf(f1165,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s30])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (1755259)------------------------------
% 0.19/0.27 % (1755259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1755259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1755259)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1755259)Termination reason: Refutation
% 0.19/0.27 % (1755259)Time elapsed: 0.017 s
% 0.19/0.27 % (1755259)Peak memory usage: 13 MB
% 0.19/0.27 % (1755259)Instructions burned: 65 (million)
% 0.19/0.27 % (1755251)Success in time 0.045 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------