%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO515^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:48:10 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO515^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:12:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (3450240)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3450251)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3450251)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
% 0.20/0.28 % (3450247)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=436812208:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (3450246)lrs+10_16_si=on:nwc=1.5:random_seed=3346141686:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (3450245)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3961054849:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3450249)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3382945226:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (3450248)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=2506357160: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)
% 0.20/0.28 % (3450251)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=2984698426:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (3450247)Refutation not found, incomplete strategy
% 0.20/0.28 % (3450247)------------------------------
% 0.20/0.28 % (3450247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450245)Refutation not found, incomplete strategy
% 0.20/0.28 % (3450245)------------------------------
% 0.20/0.28 % (3450245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450245)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450247)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450247)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3450247)Time elapsed: 0.001 s
% 0.20/0.28 % (3450245)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3450245)Time elapsed: 0.001 s
% 0.20/0.28 % (3450247)Peak memory usage: 11 MB
% 0.20/0.28 % (3450245)Peak memory usage: 12 MB
% 0.20/0.28 % (3450247)Instructions burned: 1 (million)
% 0.20/0.28 % (3450245)Instructions burned: 1 (million)
% 0.20/0.28 % (3450245)------------------------------
% 0.20/0.28 % (3450245)------------------------------
% 0.20/0.28 % (3450247)------------------------------
% 0.20/0.28 % (3450247)------------------------------
% 0.20/0.28 % (3450248)Refutation not found, incomplete strategy
% 0.20/0.28 % (3450248)------------------------------
% 0.20/0.28 % (3450248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450248)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450248)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3450248)Time elapsed: 0.003 s
% 0.20/0.28 % (3450248)Peak memory usage: 12 MB
% 0.20/0.28 % (3450248)Instructions burned: 4 (million)
% 0.20/0.28 % (3450250)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1635588450:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3450248)------------------------------
% 0.20/0.28 % (3450248)------------------------------
% 0.20/0.28 % (3450251)Refutation not found, incomplete strategy
% 0.20/0.28 % (3450251)------------------------------
% 0.20/0.28 % (3450251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450251)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450251)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3450251)Time elapsed: 0.004 s
% 0.20/0.28 % (3450251)Peak memory usage: 12 MB
% 0.20/0.28 % (3450251)Instructions burned: 2 (million)
% 0.20/0.28 % (3450251)------------------------------
% 0.20/0.28 % (3450251)------------------------------
% 0.20/0.28 % (3450246)Refutation not found, incomplete strategy
% 0.20/0.28 % (3450246)------------------------------
% 0.20/0.28 % (3450246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450246)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450246)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3450246)Time elapsed: 0.010 s
% 0.20/0.28 % (3450246)Peak memory usage: 12 MB
% 0.20/0.28 % (3450246)Instructions burned: 15 (million)
% 0.20/0.28 % (3450246)------------------------------
% 0.20/0.28 % (3450246)------------------------------
% 0.20/0.28 % (3450250) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3450240-3450250"...
% 0.20/0.28 % (3450249)Instruction limit reached!
% 0.20/0.28 % (3450249)------------------------------
% 0.20/0.28 % (3450249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450249)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450249)Termination reason: Instruction limit
% 0.20/0.28 % (3450249)Termination phase: Saturation
% 0.20/0.28 % (3450249)Time elapsed: 0.012 s
% 0.20/0.28 % (3450249)Peak memory usage: 11 MB
% 0.20/0.28 % (3450249)Instructions burned: 25 (million)
% 0.20/0.28 % (3450250)...printing done.
% 0.20/0.28 % (3450250)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, t: ((($o > $o) > $o) > $o > $o)).
% 0.20/0.28 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_8, type, vOR: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(func_def_11, type, sK0: (($o > $o) > $o)).
% 0.20/0.28 thf(func_def_12, type, sK1: ($o > $o)).
% 0.20/0.28 thf(func_def_13, type, sK2: $o).
% 0.20/0.28 thf(func_def_15, type, sK4: $o).
% 0.20/0.28 thf(func_def_16, type, sK5: $o).
% 0.20/0.28 thf(func_def_17, type, sK6: $o).
% 0.20/0.28 thf(func_def_18, type, sK7: $o).
% 0.20/0.28 thf(func_def_19, type, sK8: $o).
% 0.20/0.28 thf(func_def_20, type, sK9: $o).
% 0.20/0.28 thf(func_def_21, type, sK10: $o).
% 0.20/0.28 thf(func_def_22, type, sK11: $o).
% 0.20/0.28 thf(func_def_23, type, sK12: $o).
% 0.20/0.28 thf(func_def_24, type, sK13: $o).
% 0.20/0.28 thf(func_def_25, type, sK14: $o).
% 0.20/0.28 thf(func_def_26, type, sK15: $o).
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 (t = (^[X0 : (($o > $o) > $o), X1 : $o] : (((~X1 = ((X0 @ (^[X1 : $o] : (~X1))))) | (X0 @ (^[X1 : $o] : ($true)))) & ~(X0 @ (^[X1 : $o] : ($false))))))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',t)).
% 0.20/0.28 thf(f2,conjecture,(
% 0.20/0.28 ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (X0 @ X1) => (X0 @ (t @ X0)))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceoo1)).
% 0.20/0.28 thf(f3,negated_conjecture,(
% 0.20/0.28 ~ ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (X0 @ X1) => (X0 @ (t @ X0)))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (X0 @ X1) => (X0 @ (t @ X0)))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ~ ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (((X0 @ X1)) = $true) => (((X0 @ (t @ X0))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 (t = (^[X0 : (($o > $o) > $o), X1 : $o] : (((~X1 = ((X0 @ (^[X2 : $o] : (~X2))))) | (X0 @ (^[X3 : $o] : ($true)))) & ~(X0 @ (^[X4 : $o] : ($false))))))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 (t = (^[Y0 : ($o > $o) > $o]: ((^[Y1 : $o]: ((~ (Y0 @ (^[Y2 : $o]: ($false)))) & ((Y0 @ (^[Y2 : $o]: ($true))) | ((~ Y1) = (Y0 @ (^[Y2 : $o]: (~ Y2))))))))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ? [X0 : (($o > $o) > $o)] : ((((X0 @ (t @ X0))) != $true) & ? [X1 : ($o > $o)] : (((X0 @ X1)) = $true))),
% 0.20/0.28 inference(ennf_transformation,[],[f5])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 (((sK0 @ (t @ sK0))) != $true) & ($true = ((sK0 @ sK1)))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 (t = (^[Y0 : ($o > $o) > $o]: ((^[Y1 : $o]: ((~ (Y0 @ (^[Y2 : $o]: ($false)))) & ((Y0 @ (^[Y2 : $o]: ($true))) | ((~ Y1) = (Y0 @ (^[Y2 : $o]: (~ Y2))))))))))),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ($true = ((sK0 @ sK1)))),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 (((sK0 @ (t @ sK0))) != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f14,definition,(
% 0.20/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ($true != ((sK0 @ ((^[Y0 : ($o > $o) > $o]: ((^[Y1 : $o]: ((~ (Y0 @ (^[Y2 : $o]: ($false)))) & ((Y0 @ (^[Y2 : $o]: ($true))) | ((~ Y1) = (Y0 @ (^[Y2 : $o]: (~ Y2))))))))) @ sK0))))),
% 0.20/0.28 inference(definition_unfolding,[],[f12,f10])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))))) != $true)),
% 0.20/0.28 inference(beta-eta_normalization,[],[f15])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 (sK1 != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~)))))) | ($true != $true)),
% 0.20/0.28 inference(constrained_superposition,[],[f16,f11])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 (sK1 != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))))),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK2)) != ((sK1 @ sK2)))),
% 0.20/0.28 inference(negative_extensionality,[],[f18])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 ($true = ((sK1 @ sK2))) | ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK2)) = $true)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f19])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 (((sK1 @ sK2)) = $false) | ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK2)) = $false)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f19])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ($false = (((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK2) = (sK0 @ ~)))))) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(beta-eta_normalization,[],[f21])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | (((sK1 @ sK2)) = $false) | ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK2) = (sK0 @ ~)))) = $false)),
% 0.20/0.28 inference(and_proxy_clausification,[],[f22])).
% 0.20/0.28 thf(f24,plain,(
% 0.20/0.28 ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK2) = (sK0 @ ~)))) = $false) | (((sK1 @ sK2)) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true)),
% 0.20/0.28 inference(not_proxy_clausification,[],[f23])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 ((((~ sK2) = (sK0 @ ~))) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(or_proxy_clausification,[],[f24])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(or_proxy_clausification,[],[f24])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 (((~ sK2)) != ((sK0 @ ~))) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f25])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 (((~ sK2)) = $true) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) = $true) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) = $false) | (((sK1 @ sK2)) = $false) | (((~ sK2)) = $false)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f27])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 (((sK1 @ sK2)) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) = $false) | ($true = sK2)),
% 0.20/0.28 inference(not_proxy_clausification,[],[f29])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ($false = sK2) | (((sK0 @ ~)) = $true) | (((sK1 @ sK2)) = $false)),
% 0.20/0.28 inference(not_proxy_clausification,[],[f28])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ($true = ((sK1 @ sK2))) | ($true = (((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK2) = (sK0 @ ~))))))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f20])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ($true = ((sK1 @ sK2))) | ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK2) = (sK0 @ ~)))) = $true)),
% 0.20/0.28 inference(and_proxy_clausification,[],[f32])).
% 0.20/0.28 thf(f34,plain,(
% 0.20/0.28 ($true = ((~ (sK0 @ (^[Y0 : $o]: ($false)))))) | ($true = ((sK1 @ sK2)))),
% 0.20/0.28 inference(and_proxy_clausification,[],[f32])).
% 0.20/0.28 thf(f35,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $false) | ($true = ((sK1 @ sK2)))),
% 0.20/0.28 inference(not_proxy_clausification,[],[f34])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 ((((~ sK2) = (sK0 @ ~))) = $true) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ($true = ((sK1 @ sK2)))),
% 0.20/0.28 inference(or_proxy_clausification,[],[f33])).
% 0.20/0.28 thf(f37,plain,(
% 0.20/0.28 (((~ sK2)) = ((sK0 @ ~))) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ($true = ((sK1 @ sK2)))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f36])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ($true = ((sK1 @ sK2))) | (((sK0 @ ~)) = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (((~ sK2)) = $true)),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f37])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $true) | (((~ sK2)) = $false) | ($true = ((sK1 @ sK2))) | ($true = ((sK0 @ (^[Y0 : $o]: ($true)))))),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f37])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ($true = sK2) | ($true = ((sK1 @ sK2))) | (((sK0 @ ~)) = $true)),
% 0.20/0.28 inference(not_proxy_clausification,[],[f39])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ($true = ((sK1 @ sK2))) | ($false = sK2)),
% 0.20/0.28 inference(not_proxy_clausification,[],[f38])).
% 0.20/0.28 thf(f43,definition,(
% 0.20/0.28 spl3_1 <=> (((sK0 @ (^[Y0 : $o]: ($false)))) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ~spl3_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f43])).
% 0.20/0.28 thf(f46,definition,(
% 0.20/0.28 spl3_2 <=> (((sK0 @ (^[Y0 : $o]: ($true)))) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.20/0.28 thf(f47,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | ~spl3_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f46])).
% 0.20/0.28 thf(f49,definition,(
% 0.20/0.28 spl3_3 <=> (((sK1 @ sK2)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.20/0.28 thf(f50,plain,(
% 0.20/0.28 (((sK1 @ sK2)) = $false) | ~spl3_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f49])).
% 0.20/0.28 thf(f51,plain,(
% 0.20/0.28 spl3_1 | spl3_2 | spl3_3),
% 0.20/0.28 inference(avatar_split_clause,[],[f26,f49,f46,f43])).
% 0.20/0.28 thf(f53,definition,(
% 0.20/0.28 spl3_4 <=> ($true = sK2)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.20/0.28 thf(f54,plain,(
% 0.20/0.28 ($true = sK2) | ~spl3_4),
% 0.20/0.28 inference(avatar_component_clause,[],[f53])).
% 0.20/0.28 thf(f56,definition,(
% 0.20/0.28 spl3_5 <=> (((sK0 @ ~)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.20/0.28 thf(f57,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | ~spl3_5),
% 0.20/0.28 inference(avatar_component_clause,[],[f56])).
% 0.20/0.28 thf(f58,plain,(
% 0.20/0.28 spl3_4 | spl3_3 | spl3_5 | spl3_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f30,f43,f56,f49,f53])).
% 0.20/0.28 thf(f60,definition,(
% 0.20/0.28 spl3_6 <=> ($false = sK2)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition])).
% 0.20/0.28 thf(f61,plain,(
% 0.20/0.28 ($false = sK2) | ~spl3_6),
% 0.20/0.28 inference(avatar_component_clause,[],[f60])).
% 0.20/0.28 thf(f63,definition,(
% 0.20/0.28 spl3_7 <=> (((sK0 @ ~)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition])).
% 0.20/0.28 thf(f64,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $true) | ~spl3_7),
% 0.20/0.28 inference(avatar_component_clause,[],[f63])).
% 0.20/0.28 thf(f65,plain,(
% 0.20/0.28 spl3_1 | spl3_6 | spl3_3 | spl3_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f31,f63,f49,f60,f43])).
% 0.20/0.28 thf(f67,definition,(
% 0.20/0.28 spl3_8 <=> (((sK0 @ (^[Y0 : $o]: ($false)))) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition])).
% 0.20/0.28 thf(f68,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $false) | ~spl3_8),
% 0.20/0.28 inference(avatar_component_clause,[],[f67])).
% 0.20/0.28 thf(f70,definition,(
% 0.20/0.28 spl3_9 <=> ($true = ((sK1 @ sK2)))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.20/0.28 thf(f71,plain,(
% 0.20/0.28 ($true = ((sK1 @ sK2))) | ~spl3_9),
% 0.20/0.28 inference(avatar_component_clause,[],[f70])).
% 0.20/0.28 thf(f72,plain,(
% 0.20/0.28 spl3_8 | spl3_9),
% 0.20/0.28 inference(avatar_split_clause,[],[f35,f70,f67])).
% 0.20/0.28 thf(f74,definition,(
% 0.20/0.28 spl3_10 <=> ($true = ((sK0 @ (^[Y0 : $o]: ($true)))))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.20/0.28 thf(f75,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ~spl3_10),
% 0.20/0.28 inference(avatar_component_clause,[],[f74])).
% 0.20/0.28 thf(f76,plain,(
% 0.20/0.28 spl3_7 | spl3_9 | spl3_4 | spl3_10),
% 0.20/0.28 inference(avatar_split_clause,[],[f40,f74,f53,f70,f63])).
% 0.20/0.28 thf(f77,plain,(
% 0.20/0.28 spl3_9 | spl3_10 | spl3_5 | spl3_6),
% 0.20/0.28 inference(avatar_split_clause,[],[f41,f60,f56,f74,f70])).
% 0.20/0.28 thf(f78,plain,(
% 0.20/0.28 (((sK1 @ $true)) = $false) | (~spl3_3 | ~spl3_4)),
% 0.20/0.28 inference(forward_demodulation,[],[f50,f54])).
% 0.20/0.28 thf(f79,plain,(
% 0.20/0.28 (sK1 != ~) | ($true = $false) | ~spl3_5),
% 0.20/0.28 inference(constrained_superposition,[],[f57,f11])).
% 0.20/0.28 thf(f82,plain,(
% 0.20/0.28 (sK1 != ~) | ~spl3_5),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.28 thf(f84,plain,(
% 0.20/0.28 ($true = $false) | (sK1 != (^[Y0 : $o]: ($false))) | ~spl3_8),
% 0.20/0.28 inference(constrained_superposition,[],[f68,f11])).
% 0.20/0.28 thf(f87,plain,(
% 0.20/0.28 (sK1 != (^[Y0 : $o]: ($false))) | ~spl3_8),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f84])).
% 0.20/0.28 thf(f89,plain,(
% 0.20/0.28 (((sK1 @ sK4)) != ((~ sK4))) | ~spl3_5),
% 0.20/0.28 inference(negative_extensionality,[],[f82])).
% 0.20/0.28 thf(f90,plain,(
% 0.20/0.28 ($true = ((~ sK4))) | (((sK1 @ sK4)) = $true) | ~spl3_5),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f89])).
% 0.20/0.28 thf(f91,plain,(
% 0.20/0.28 ($false = ((~ sK4))) | (((sK1 @ sK4)) = $false) | ~spl3_5),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f89])).
% 0.20/0.28 thf(f92,plain,(
% 0.20/0.28 (((sK1 @ sK4)) = $false) | (sK4 = $true) | ~spl3_5),
% 0.20/0.28 inference(not_proxy_clausification,[],[f91])).
% 0.20/0.28 thf(f93,plain,(
% 0.20/0.28 (((sK1 @ sK4)) = $true) | (sK4 = $false) | ~spl3_5),
% 0.20/0.28 inference(not_proxy_clausification,[],[f90])).
% 0.20/0.28 thf(f95,definition,(
% 0.20/0.28 spl3_11 <=> (sK4 = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition])).
% 0.20/0.28 thf(f96,plain,(
% 0.20/0.28 (sK4 = $true) | ~spl3_11),
% 0.20/0.28 inference(avatar_component_clause,[],[f95])).
% 0.20/0.28 thf(f98,definition,(
% 0.20/0.28 spl3_12 <=> (((sK1 @ sK4)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition])).
% 0.20/0.28 thf(f99,plain,(
% 0.20/0.28 (((sK1 @ sK4)) = $false) | ~spl3_12),
% 0.20/0.28 inference(avatar_component_clause,[],[f98])).
% 0.20/0.28 thf(f100,plain,(
% 0.20/0.28 spl3_11 | spl3_12 | ~spl3_5),
% 0.20/0.28 inference(avatar_split_clause,[],[f92,f56,f98,f95])).
% 0.20/0.28 thf(f102,definition,(
% 0.20/0.28 spl3_13 <=> (sK4 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition])).
% 0.20/0.28 thf(f103,plain,(
% 0.20/0.28 (sK4 = $false) | ~spl3_13),
% 0.20/0.28 inference(avatar_component_clause,[],[f102])).
% 0.20/0.28 thf(f105,definition,(
% 0.20/0.28 spl3_14 <=> (((sK1 @ sK4)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition])).
% 0.20/0.28 thf(f106,plain,(
% 0.20/0.28 (((sK1 @ sK4)) = $true) | ~spl3_14),
% 0.20/0.28 inference(avatar_component_clause,[],[f105])).
% 0.20/0.28 thf(f107,plain,(
% 0.20/0.28 spl3_13 | spl3_14 | ~spl3_5),
% 0.20/0.28 inference(avatar_split_clause,[],[f93,f56,f105,f102])).
% 0.20/0.28 thf(f108,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_4 | ~spl3_6)),
% 0.20/0.28 inference(backward_demodulation,[],[f54,f61])).
% 0.20/0.28 thf(f109,plain,(
% 0.20/0.28 $false | (~spl3_4 | ~spl3_6)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f108])).
% 0.20/0.28 thf(f110,plain,(
% 0.20/0.28 ~spl3_4 | ~spl3_6),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f109])).
% 0.20/0.28 thf(f115,plain,(
% 0.20/0.28 (((sK1 @ sK5)) != (((^[Y0 : $o]: ($false)) @ sK5))) | ~spl3_8),
% 0.20/0.28 inference(negative_extensionality,[],[f87])).
% 0.20/0.28 thf(f116,plain,(
% 0.20/0.28 ($true = (((^[Y0 : $o]: ($false)) @ sK5))) | (((sK1 @ sK5)) = $true) | ~spl3_8),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f115])).
% 0.20/0.28 thf(f119,plain,(
% 0.20/0.28 ($true = $false) | (((sK1 @ sK5)) = $true) | ~spl3_8),
% 0.20/0.28 inference(beta-eta_normalization,[],[f116])).
% 0.20/0.28 thf(f120,plain,(
% 0.20/0.28 (((sK1 @ sK5)) = $true) | ~spl3_8),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f119])).
% 0.20/0.28 thf(f122,plain,(
% 0.20/0.28 ($true != $true) | ((^[Y0 : $o]: ($true)) != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~)))))) | ~spl3_10),
% 0.20/0.28 inference(constrained_superposition,[],[f16,f75])).
% 0.20/0.28 thf(f125,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ($true)) != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~)))))) | ~spl3_10),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f122])).
% 0.20/0.28 thf(f135,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))))) = $false) | ($true != $true)),
% 0.20/0.28 inference(constrained_superposition,[],[f16,f14])).
% 0.20/0.28 thf(f138,plain,(
% 0.20/0.28 (((sK1 @ $true)) = $true) | (sK5 = $false) | ~spl3_8),
% 0.20/0.28 inference(constrained_superposition,[],[f120,f14])).
% 0.20/0.28 thf(f146,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))))) = $false)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f135])).
% 0.20/0.28 thf(f147,plain,(
% 0.20/0.28 ($true = $false) | (sK5 = $false) | (~spl3_3 | ~spl3_4 | ~spl3_8)),
% 0.20/0.28 inference(forward_demodulation,[],[f138,f78])).
% 0.20/0.28 thf(f148,plain,(
% 0.20/0.28 (sK5 = $false) | (~spl3_3 | ~spl3_4 | ~spl3_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f147])).
% 0.20/0.28 thf(f151,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ($true)) @ sK7)) != (((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK7))) | ~spl3_10),
% 0.20/0.28 inference(negative_extensionality,[],[f125])).
% 0.20/0.28 thf(f153,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK7)) = $false) | ((((^[Y0 : $o]: ($true)) @ sK7)) = $false) | ~spl3_10),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f151])).
% 0.20/0.28 thf(f154,plain,(
% 0.20/0.28 ($true = $false) | ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK7) = (sK0 @ ~))))) = $false) | ~spl3_10),
% 0.20/0.28 inference(beta-eta_normalization,[],[f153])).
% 0.20/0.28 thf(f155,plain,(
% 0.20/0.28 ($true = $false) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK7) = (sK0 @ ~)))) = $false) | ~spl3_10),
% 0.20/0.28 inference(and_proxy_clausification,[],[f154])).
% 0.20/0.28 thf(f156,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK7) = (sK0 @ ~)))) = $false) | ($true = $false) | ~spl3_10),
% 0.20/0.28 inference(not_proxy_clausification,[],[f155])).
% 0.20/0.28 thf(f158,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ($true = $false) | (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | ~spl3_10),
% 0.20/0.28 inference(or_proxy_clausification,[],[f156])).
% 0.20/0.28 thf(f159,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | ~spl3_10),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f158])).
% 0.20/0.28 thf(f177,plain,(
% 0.20/0.28 ($true = $false) | (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | (~spl3_8 | ~spl3_10)),
% 0.20/0.28 inference(forward_demodulation,[],[f159,f68])).
% 0.20/0.28 thf(f178,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($true)))) = $false) | (~spl3_8 | ~spl3_10)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f177])).
% 0.20/0.28 thf(f183,plain,(
% 0.20/0.28 spl3_2 | ~spl3_8 | ~spl3_10),
% 0.20/0.28 inference(avatar_split_clause,[],[f178,f74,f67,f46])).
% 0.20/0.28 thf(f193,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_1 | ~spl3_8)),
% 0.20/0.28 inference(forward_demodulation,[],[f44,f68])).
% 0.20/0.28 thf(f194,plain,(
% 0.20/0.28 $false | (~spl3_1 | ~spl3_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f193])).
% 0.20/0.28 thf(f195,plain,(
% 0.20/0.28 ~spl3_1 | ~spl3_8),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f194])).
% 0.20/0.28 thf(f200,plain,(
% 0.20/0.28 (((sK1 @ $false)) = $false) | (~spl3_12 | ~spl3_13)),
% 0.20/0.28 inference(forward_demodulation,[],[f99,f103])).
% 0.20/0.28 thf(f205,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_3 | ~spl3_9)),
% 0.20/0.28 inference(forward_demodulation,[],[f71,f50])).
% 0.20/0.28 thf(f206,plain,(
% 0.20/0.28 $false | (~spl3_3 | ~spl3_9)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f205])).
% 0.20/0.28 thf(f207,plain,(
% 0.20/0.28 ~spl3_3 | ~spl3_9),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f206])).
% 0.20/0.28 thf(f212,definition,(
% 0.20/0.28 spl3_18 <=> (sK5 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_18])],[avatar_definition])).
% 0.20/0.28 thf(f213,plain,(
% 0.20/0.28 (sK5 = $false) | ~spl3_18),
% 0.20/0.28 inference(avatar_component_clause,[],[f212])).
% 0.20/0.28 thf(f218,plain,(
% 0.20/0.28 (((sK1 @ $false)) = $true) | (~spl3_8 | ~spl3_18)),
% 0.20/0.28 inference(backward_demodulation,[],[f120,f213])).
% 0.20/0.28 thf(f219,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_8 | ~spl3_12 | ~spl3_13 | ~spl3_18)),
% 0.20/0.28 inference(forward_demodulation,[],[f218,f200])).
% 0.20/0.28 thf(f220,plain,(
% 0.20/0.28 $false | (~spl3_8 | ~spl3_12 | ~spl3_13 | ~spl3_18)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f219])).
% 0.20/0.28 thf(f221,plain,(
% 0.20/0.28 ~spl3_8 | ~spl3_12 | ~spl3_13 | ~spl3_18),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f220])).
% 0.20/0.28 thf(f224,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_12 | ~spl3_14)),
% 0.20/0.28 inference(forward_demodulation,[],[f106,f99])).
% 0.20/0.28 thf(f225,plain,(
% 0.20/0.28 $false | (~spl3_12 | ~spl3_14)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f224])).
% 0.20/0.28 thf(f226,plain,(
% 0.20/0.28 ~spl3_12 | ~spl3_14),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f225])).
% 0.20/0.28 thf(f229,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_2 | ~spl3_10)),
% 0.20/0.28 inference(forward_demodulation,[],[f75,f47])).
% 0.20/0.28 thf(f230,plain,(
% 0.20/0.28 $false | (~spl3_2 | ~spl3_10)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f229])).
% 0.20/0.28 thf(f231,plain,(
% 0.20/0.28 ~spl3_2 | ~spl3_10),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f230])).
% 0.20/0.28 thf(f252,plain,(
% 0.20/0.28 ($true = $false) | ((^[Y0 : $o]: ($false)) != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~)))))) | ~spl3_1),
% 0.20/0.28 inference(constrained_superposition,[],[f146,f44])).
% 0.20/0.28 thf(f260,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ($false)) != (^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~)))))) | ~spl3_1),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f252])).
% 0.20/0.28 thf(f290,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ($false)) @ sK9)) != (((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK9))) | ~spl3_1),
% 0.20/0.28 inference(negative_extensionality,[],[f260])).
% 0.20/0.28 thf(f291,plain,(
% 0.20/0.28 ($true = (((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK9))) | ((((^[Y0 : $o]: ($false)) @ sK9)) = $true) | ~spl3_1),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f290])).
% 0.20/0.28 thf(f305,plain,(
% 0.20/0.28 ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK9) = (sK0 @ ~))))) = $true) | ($true = $false) | ~spl3_1),
% 0.20/0.28 inference(beta-eta_normalization,[],[f291])).
% 0.20/0.28 thf(f307,plain,(
% 0.20/0.28 ($true = $false) | ($true = ((~ (sK0 @ (^[Y0 : $o]: ($false)))))) | ~spl3_1),
% 0.20/0.28 inference(and_proxy_clausification,[],[f305])).
% 0.20/0.28 thf(f308,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $false) | ($true = $false) | ~spl3_1),
% 0.20/0.28 inference(not_proxy_clausification,[],[f307])).
% 0.20/0.28 thf(f309,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $false) | ~spl3_1),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f308])).
% 0.20/0.28 thf(f318,plain,(
% 0.20/0.28 spl3_8 | ~spl3_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f309,f43,f67])).
% 0.20/0.28 thf(f320,plain,(
% 0.20/0.28 (sK1 != (^[Y0 : $o]: ($true))) | ($true = $false) | ~spl3_2),
% 0.20/0.28 inference(constrained_superposition,[],[f47,f11])).
% 0.20/0.28 thf(f323,plain,(
% 0.20/0.28 (sK1 != (^[Y0 : $o]: ($true))) | ~spl3_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f320])).
% 0.20/0.28 thf(f325,plain,(
% 0.20/0.28 (((sK1 @ sK10)) != (((^[Y0 : $o]: ($true)) @ sK10))) | ~spl3_2),
% 0.20/0.28 inference(negative_extensionality,[],[f323])).
% 0.20/0.28 thf(f327,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ($true)) @ sK10)) = $false) | (((sK1 @ sK10)) = $false) | ~spl3_2),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f325])).
% 0.20/0.28 thf(f328,plain,(
% 0.20/0.28 (((sK1 @ sK10)) = $false) | ($true = $false) | ~spl3_2),
% 0.20/0.28 inference(beta-eta_normalization,[],[f327])).
% 0.20/0.28 thf(f329,plain,(
% 0.20/0.28 (((sK1 @ sK10)) = $false) | ~spl3_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f328])).
% 0.20/0.28 thf(f333,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) != ~) | ($true = $false) | ~spl3_7),
% 0.20/0.28 inference(constrained_superposition,[],[f146,f64])).
% 0.20/0.28 thf(f337,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) != ~) | ~spl3_7),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f333])).
% 0.20/0.28 thf(f339,plain,(
% 0.20/0.28 (sK10 = $false) | (((sK1 @ $true)) = $false) | ~spl3_2),
% 0.20/0.28 inference(constrained_superposition,[],[f329,f14])).
% 0.20/0.28 thf(f340,plain,(
% 0.20/0.28 ($true = $false) | (((sK1 @ sK10)) = $false) | ~spl3_2),
% 0.20/0.28 inference(constrained_superposition,[],[f329,f14])).
% 0.20/0.28 thf(f345,plain,(
% 0.20/0.28 (((sK1 @ sK10)) = $false) | ~spl3_2),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f340])).
% 0.20/0.28 thf(f360,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK12)) != ((~ sK12))) | ~spl3_7),
% 0.20/0.28 inference(negative_extensionality,[],[f337])).
% 0.20/0.28 thf(f361,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK12)) = $true) | (((~ sK12)) = $true) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f360])).
% 0.20/0.28 thf(f362,plain,(
% 0.20/0.28 (((~ sK12)) = $false) | ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK12)) = $false) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f360])).
% 0.20/0.28 thf(f363,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK12)) = $false) | (sK12 = $true) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f362])).
% 0.20/0.28 thf(f364,plain,(
% 0.20/0.28 ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK12) = (sK0 @ ~))))) = $false) | (sK12 = $true) | ~spl3_7),
% 0.20/0.28 inference(beta-eta_normalization,[],[f363])).
% 0.20/0.28 thf(f365,plain,(
% 0.20/0.28 (sK12 = $true) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | ($false = (((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK12) = (sK0 @ ~))))) | ~spl3_7),
% 0.20/0.28 inference(and_proxy_clausification,[],[f364])).
% 0.20/0.28 thf(f366,plain,(
% 0.20/0.28 ($false = (((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK12) = (sK0 @ ~))))) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (sK12 = $true) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f365])).
% 0.20/0.28 thf(f367,plain,(
% 0.20/0.28 (sK12 = $true) | ($false = (((~ sK12) = (sK0 @ ~)))) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ~spl3_7),
% 0.20/0.28 inference(or_proxy_clausification,[],[f366])).
% 0.20/0.28 thf(f369,plain,(
% 0.20/0.28 (sK12 = $true) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) != ((~ sK12))) | ~spl3_7),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f367])).
% 0.20/0.28 thf(f371,plain,(
% 0.20/0.28 (sK12 = $true) | (((~ sK12)) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f369])).
% 0.20/0.28 thf(f372,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | (sK12 = $true) | (sK12 = $true) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f371])).
% 0.20/0.28 thf(f373,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | (((sK0 @ ~)) = $false) | (sK12 = $true) | ~spl3_7),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f372])).
% 0.20/0.28 thf(f375,plain,(
% 0.20/0.28 (sK12 = $false) | ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK12)) = $true) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f361])).
% 0.20/0.28 thf(f376,plain,(
% 0.20/0.28 ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK12) = (sK0 @ ~))))) = $true) | (sK12 = $false) | ~spl3_7),
% 0.20/0.28 inference(beta-eta_normalization,[],[f375])).
% 0.20/0.28 thf(f377,plain,(
% 0.20/0.28 (sK12 = $false) | ($true = (((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK12) = (sK0 @ ~))))) | ~spl3_7),
% 0.20/0.28 inference(and_proxy_clausification,[],[f376])).
% 0.20/0.28 thf(f380,plain,(
% 0.20/0.28 (sK12 = $false) | ($true = (((~ sK12) = (sK0 @ ~)))) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ~spl3_7),
% 0.20/0.28 inference(or_proxy_clausification,[],[f377])).
% 0.20/0.28 thf(f381,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (sK12 = $false) | (((sK0 @ ~)) = ((~ sK12))) | ~spl3_7),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f380])).
% 0.20/0.28 thf(f383,plain,(
% 0.20/0.28 (sK12 = $false) | (((sK0 @ ~)) = $false) | (((~ sK12)) = $true) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ~spl3_7),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f381])).
% 0.20/0.28 thf(f384,plain,(
% 0.20/0.28 (sK12 = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (sK12 = $false) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f383])).
% 0.20/0.28 thf(f385,plain,(
% 0.20/0.28 (sK12 = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f384])).
% 0.20/0.28 thf(f387,plain,(
% 0.20/0.28 (sK12 = $true) | ($true = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ~spl3_7),
% 0.20/0.28 inference(forward_demodulation,[],[f373,f64])).
% 0.20/0.28 thf(f388,plain,(
% 0.20/0.28 (sK12 = $true) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ~spl3_7),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f387])).
% 0.20/0.28 thf(f390,definition,(
% 0.20/0.28 spl3_19 <=> (sK12 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition])).
% 0.20/0.28 thf(f391,plain,(
% 0.20/0.28 (sK12 = $false) | ~spl3_19),
% 0.20/0.28 inference(avatar_component_clause,[],[f390])).
% 0.20/0.28 thf(f393,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | ($true = $false) | (sK12 = $false) | (~spl3_2 | ~spl3_7)),
% 0.20/0.28 inference(forward_demodulation,[],[f385,f47])).
% 0.20/0.28 thf(f394,plain,(
% 0.20/0.28 (sK12 = $false) | (((sK0 @ ~)) = $false) | (~spl3_2 | ~spl3_7)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f393])).
% 0.20/0.28 thf(f396,definition,(
% 0.20/0.28 spl3_20 <=> (sK12 = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition])).
% 0.20/0.28 thf(f397,plain,(
% 0.20/0.28 (sK12 = $true) | ~spl3_20),
% 0.20/0.28 inference(avatar_component_clause,[],[f396])).
% 0.20/0.28 thf(f398,plain,(
% 0.20/0.28 spl3_20 | spl3_1 | ~spl3_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f388,f63,f43,f396])).
% 0.20/0.28 thf(f399,plain,(
% 0.20/0.28 ($true = $false) | (sK12 = $false) | (~spl3_2 | ~spl3_7)),
% 0.20/0.28 inference(forward_demodulation,[],[f394,f64])).
% 0.20/0.28 thf(f400,plain,(
% 0.20/0.28 (sK12 = $false) | (~spl3_2 | ~spl3_7)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f399])).
% 0.20/0.28 thf(f401,plain,(
% 0.20/0.28 spl3_19 | ~spl3_2 | ~spl3_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f400,f63,f46,f390])).
% 0.20/0.28 thf(f402,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_19 | ~spl3_20)),
% 0.20/0.28 inference(backward_demodulation,[],[f397,f391])).
% 0.20/0.28 thf(f403,plain,(
% 0.20/0.28 $false | (~spl3_19 | ~spl3_20)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f402])).
% 0.20/0.28 thf(f404,plain,(
% 0.20/0.28 ~spl3_19 | ~spl3_20),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f403])).
% 0.20/0.28 thf(f407,plain,(
% 0.20/0.28 (((sK1 @ $false)) = $true) | (~spl3_6 | ~spl3_9)),
% 0.20/0.28 inference(backward_demodulation,[],[f71,f61])).
% 0.20/0.28 thf(f414,definition,(
% 0.20/0.28 spl3_21 <=> (sK10 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition])).
% 0.20/0.28 thf(f415,plain,(
% 0.20/0.28 (sK10 = $false) | ~spl3_21),
% 0.20/0.28 inference(avatar_component_clause,[],[f414])).
% 0.20/0.28 thf(f417,definition,(
% 0.20/0.28 spl3_22 <=> (((sK1 @ $true)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_22])],[avatar_definition])).
% 0.20/0.28 thf(f418,plain,(
% 0.20/0.28 (((sK1 @ $true)) = $false) | ~spl3_22),
% 0.20/0.28 inference(avatar_component_clause,[],[f417])).
% 0.20/0.28 thf(f419,plain,(
% 0.20/0.28 spl3_21 | spl3_22 | ~spl3_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f339,f46,f417,f414])).
% 0.20/0.28 thf(f420,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_11 | ~spl3_13)),
% 0.20/0.28 inference(backward_demodulation,[],[f96,f103])).
% 0.20/0.28 thf(f421,plain,(
% 0.20/0.28 $false | (~spl3_11 | ~spl3_13)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f420])).
% 0.20/0.28 thf(f422,plain,(
% 0.20/0.28 ~spl3_11 | ~spl3_13),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f421])).
% 0.20/0.28 thf(f423,plain,(
% 0.20/0.28 (((sK1 @ $false)) = $false) | (~spl3_2 | ~spl3_21)),
% 0.20/0.28 inference(backward_demodulation,[],[f345,f415])).
% 0.20/0.28 thf(f424,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_2 | ~spl3_6 | ~spl3_9 | ~spl3_21)),
% 0.20/0.28 inference(backward_demodulation,[],[f407,f423])).
% 0.20/0.28 thf(f425,plain,(
% 0.20/0.28 $false | (~spl3_2 | ~spl3_6 | ~spl3_9 | ~spl3_21)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f424])).
% 0.20/0.28 thf(f426,plain,(
% 0.20/0.28 ~spl3_2 | ~spl3_6 | ~spl3_9 | ~spl3_21),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f425])).
% 0.20/0.28 thf(f436,plain,(
% 0.20/0.28 spl3_18 | ~spl3_3 | ~spl3_4 | ~spl3_8),
% 0.20/0.28 inference(avatar_split_clause,[],[f148,f67,f53,f49,f212])).
% 0.20/0.28 thf(f439,plain,(
% 0.20/0.28 (((sK1 @ $true)) = $true) | (~spl3_11 | ~spl3_14)),
% 0.20/0.28 inference(forward_demodulation,[],[f106,f96])).
% 0.20/0.28 thf(f446,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_11 | ~spl3_14 | ~spl3_22)),
% 0.20/0.28 inference(forward_demodulation,[],[f439,f418])).
% 0.20/0.28 thf(f447,plain,(
% 0.20/0.28 $false | (~spl3_11 | ~spl3_14 | ~spl3_22)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f446])).
% 0.20/0.28 thf(f448,plain,(
% 0.20/0.28 ~spl3_11 | ~spl3_14 | ~spl3_22),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f447])).
% 0.20/0.28 thf(f449,plain,(
% 0.20/0.28 spl3_22 | ~spl3_3 | ~spl3_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f78,f53,f49,f417])).
% 0.20/0.28 thf(f459,plain,(
% 0.20/0.28 (((sK1 @ $false)) = $true) | (~spl3_6 | ~spl3_9)),
% 0.20/0.28 inference(backward_demodulation,[],[f71,f61])).
% 0.20/0.28 thf(f460,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_6 | ~spl3_9 | ~spl3_12 | ~spl3_13)),
% 0.20/0.28 inference(forward_demodulation,[],[f459,f200])).
% 0.20/0.28 thf(f461,plain,(
% 0.20/0.28 $false | (~spl3_6 | ~spl3_9 | ~spl3_12 | ~spl3_13)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f460])).
% 0.20/0.28 thf(f462,plain,(
% 0.20/0.28 ~spl3_6 | ~spl3_9 | ~spl3_12 | ~spl3_13),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f461])).
% 0.20/0.28 thf(f495,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) != ~) | ($true = $false) | ~spl3_7),
% 0.20/0.28 inference(constrained_superposition,[],[f64,f146])).
% 0.20/0.28 thf(f500,plain,(
% 0.20/0.28 ((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) != ~) | ~spl3_7),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f495])).
% 0.20/0.28 thf(f518,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK15)) != ((~ sK15))) | ~spl3_7),
% 0.20/0.28 inference(negative_extensionality,[],[f500])).
% 0.20/0.28 thf(f519,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK15)) = $true) | (((~ sK15)) = $true) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f518])).
% 0.20/0.28 thf(f520,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK15)) = $false) | (((~ sK15)) = $false) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f518])).
% 0.20/0.28 thf(f521,plain,(
% 0.20/0.28 ($true = sK15) | ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK15)) = $false) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f520])).
% 0.20/0.28 thf(f522,plain,(
% 0.20/0.28 ($true = sK15) | ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK15) = (sK0 @ ~))))) = $false) | ~spl3_7),
% 0.20/0.28 inference(beta-eta_normalization,[],[f521])).
% 0.20/0.28 thf(f523,plain,(
% 0.20/0.28 ($true = sK15) | ((((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK15) = (sK0 @ ~)))) = $false) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | ~spl3_7),
% 0.20/0.28 inference(and_proxy_clausification,[],[f522])).
% 0.20/0.28 thf(f524,plain,(
% 0.20/0.28 ((((~ sK15) = (sK0 @ ~))) = $false) | ($true = sK15) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | ~spl3_7),
% 0.20/0.28 inference(or_proxy_clausification,[],[f523])).
% 0.20/0.28 thf(f527,plain,(
% 0.20/0.28 (((sK0 @ ~)) != ((~ sK15))) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | ($true = sK15) | ~spl3_7),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f524])).
% 0.20/0.28 thf(f529,plain,(
% 0.20/0.28 (((~ sK15)) = $false) | ($true = sK15) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f527])).
% 0.20/0.28 thf(f530,plain,(
% 0.20/0.28 ($true = sK15) | ($true = sK15) | (((~ (sK0 @ (^[Y0 : $o]: ($false))))) = $false) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f529])).
% 0.20/0.28 thf(f531,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ($true = sK15) | ($true = sK15) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f530])).
% 0.20/0.28 thf(f532,plain,(
% 0.20/0.28 (((sK0 @ (^[Y0 : $o]: ($false)))) = $true) | ($true = sK15) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f531])).
% 0.20/0.28 thf(f535,plain,(
% 0.20/0.28 ((((^[Y0 : $o]: ((~ (sK0 @ (^[Y1 : $o]: ($false)))) & ((sK0 @ (^[Y1 : $o]: ($true))) | ((~ Y0) = (sK0 @ ~))))) @ sK15)) = $true) | (sK15 = $false) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f519])).
% 0.20/0.28 thf(f536,plain,(
% 0.20/0.28 (sK15 = $false) | ((((~ (sK0 @ (^[Y0 : $o]: ($false)))) & ((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK15) = (sK0 @ ~))))) = $true) | ~spl3_7),
% 0.20/0.28 inference(beta-eta_normalization,[],[f535])).
% 0.20/0.28 thf(f537,plain,(
% 0.20/0.28 ($true = (((sK0 @ (^[Y0 : $o]: ($true))) | ((~ sK15) = (sK0 @ ~))))) | (sK15 = $false) | ~spl3_7),
% 0.20/0.28 inference(and_proxy_clausification,[],[f536])).
% 0.20/0.28 thf(f540,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (sK15 = $false) | ((((~ sK15) = (sK0 @ ~))) = $true) | ~spl3_7),
% 0.20/0.28 inference(or_proxy_clausification,[],[f537])).
% 0.20/0.28 thf(f541,plain,(
% 0.20/0.28 (((sK0 @ ~)) = ((~ sK15))) | (sK15 = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ~spl3_7),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f540])).
% 0.20/0.28 thf(f543,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (((sK0 @ ~)) = $false) | (sK15 = $false) | (((~ sK15)) = $true) | ~spl3_7),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f541])).
% 0.20/0.28 thf(f544,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (((sK0 @ ~)) = $false) | (sK15 = $false) | (sK15 = $false) | ~spl3_7),
% 0.20/0.28 inference(not_proxy_clausification,[],[f543])).
% 0.20/0.28 thf(f545,plain,(
% 0.20/0.28 (sK15 = $false) | ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (((sK0 @ ~)) = $false) | ~spl3_7),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f544])).
% 0.20/0.28 thf(f549,plain,(
% 0.20/0.28 (((sK0 @ ~)) = $false) | ($true = $false) | ($true = sK15) | (~spl3_7 | ~spl3_8)),
% 0.20/0.28 inference(forward_demodulation,[],[f532,f68])).
% 0.20/0.28 thf(f550,plain,(
% 0.20/0.28 ($true = sK15) | (((sK0 @ ~)) = $false) | (~spl3_7 | ~spl3_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f549])).
% 0.20/0.28 thf(f551,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | ($true = $false) | (sK15 = $false) | ~spl3_7),
% 0.20/0.28 inference(forward_demodulation,[],[f545,f64])).
% 0.20/0.28 thf(f552,plain,(
% 0.20/0.28 ($true = ((sK0 @ (^[Y0 : $o]: ($true))))) | (sK15 = $false) | ~spl3_7),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f551])).
% 0.20/0.28 thf(f554,definition,(
% 0.20/0.28 spl3_23 <=> ($true = sK15)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_23])],[avatar_definition])).
% 0.20/0.28 thf(f555,plain,(
% 0.20/0.28 ($true = sK15) | ~spl3_23),
% 0.20/0.28 inference(avatar_component_clause,[],[f554])).
% 0.20/0.28 thf(f557,plain,(
% 0.20/0.28 ($true = $false) | ($true = sK15) | (~spl3_7 | ~spl3_8)),
% 0.20/0.28 inference(forward_demodulation,[],[f550,f64])).
% 0.20/0.28 thf(f558,plain,(
% 0.20/0.28 ($true = sK15) | (~spl3_7 | ~spl3_8)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f557])).
% 0.20/0.28 thf(f560,definition,(
% 0.20/0.28 spl3_24 <=> (sK15 = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl3_24])],[avatar_definition])).
% 0.20/0.28 thf(f561,plain,(
% 0.20/0.28 (sK15 = $false) | ~spl3_24),
% 0.20/0.28 inference(avatar_component_clause,[],[f560])).
% 0.20/0.28 thf(f562,plain,(
% 0.20/0.28 spl3_24 | spl3_10 | ~spl3_7),
% 0.20/0.28 inference(avatar_split_clause,[],[f552,f63,f74,f560])).
% 0.20/0.28 thf(f563,plain,(
% 0.20/0.28 spl3_23 | ~spl3_7 | ~spl3_8),
% 0.20/0.28 inference(avatar_split_clause,[],[f558,f67,f63,f554])).
% 0.20/0.28 thf(f564,plain,(
% 0.20/0.28 ($true = $false) | (~spl3_23 | ~spl3_24)),
% 0.20/0.28 inference(forward_demodulation,[],[f555,f561])).
% 0.20/0.28 thf(f565,plain,(
% 0.20/0.28 $false | (~spl3_23 | ~spl3_24)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f564])).
% 0.20/0.28 thf(f566,plain,(
% 0.20/0.28 ~spl3_23 | ~spl3_24),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f565])).
% 0.20/0.28 cnf(s1, plain, spl3_1 | spl3_2 | spl3_3, inference(sat_conversion,[],[f51])).
% 0.20/0.28 cnf(s2, plain, spl3_1 | spl3_3 | spl3_4 | spl3_5, inference(sat_conversion,[],[f58])).
% 0.20/0.28 cnf(s3, plain, spl3_1 | spl3_3 | spl3_6 | spl3_7, inference(sat_conversion,[],[f65])).
% 0.20/0.28 cnf(s4, plain, spl3_8 | spl3_9, inference(sat_conversion,[],[f72])).
% 0.20/0.28 cnf(s5, plain, spl3_4 | spl3_7 | spl3_9 | spl3_10, inference(sat_conversion,[],[f76])).
% 0.20/0.28 cnf(s6, plain, spl3_5 | spl3_6 | spl3_9 | spl3_10, inference(sat_conversion,[],[f77])).
% 0.20/0.28 cnf(s7, plain, ~spl3_5 | spl3_11 | spl3_12, inference(sat_conversion,[],[f100])).
% 0.20/0.28 cnf(s8, plain, ~spl3_5 | spl3_13 | spl3_14, inference(sat_conversion,[],[f107])).
% 0.20/0.28 cnf(s9, plain, ~spl3_4 | ~spl3_6, inference(sat_conversion,[],[f110])).
% 0.20/0.28 cnf(s11, plain, spl3_2 | ~spl3_8 | ~spl3_10, inference(sat_conversion,[],[f183])).
% 0.20/0.28 cnf(s14, plain, ~spl3_1 | ~spl3_8, inference(sat_conversion,[],[f195])).
% 0.20/0.28 cnf(s16, plain, ~spl3_3 | ~spl3_9, inference(sat_conversion,[],[f207])).
% 0.20/0.28 cnf(s19, plain, ~spl3_8 | ~spl3_12 | ~spl3_13 | ~spl3_18, inference(sat_conversion,[],[f221])).
% 0.20/0.28 cnf(s20, plain, ~spl3_12 | ~spl3_14, inference(sat_conversion,[],[f226])).
% 0.20/0.28 cnf(s22, plain, ~spl3_2 | ~spl3_10, inference(sat_conversion,[],[f231])).
% 0.20/0.28 cnf(s28, plain, ~spl3_1 | spl3_8, inference(sat_conversion,[],[f318])).
% 0.20/0.28 cnf(s30, plain, spl3_1 | ~spl3_7 | spl3_20, inference(sat_conversion,[],[f398])).
% 0.20/0.28 cnf(s31, plain, ~spl3_2 | ~spl3_7 | spl3_19, inference(sat_conversion,[],[f401])).
% 0.20/0.28 cnf(s32, plain, ~spl3_19 | ~spl3_20, inference(sat_conversion,[],[f404])).
% 0.20/0.28 cnf(s35, plain, ~spl3_2 | spl3_21 | spl3_22, inference(sat_conversion,[],[f419])).
% 0.20/0.28 cnf(s36, plain, ~spl3_11 | ~spl3_13, inference(sat_conversion,[],[f422])).
% 0.20/0.28 cnf(s37, plain, ~spl3_2 | ~spl3_6 | ~spl3_9 | ~spl3_21, inference(sat_conversion,[],[f426])).
% 0.20/0.28 cnf(s40, plain, ~spl3_3 | ~spl3_4 | ~spl3_8 | spl3_18, inference(sat_conversion,[],[f436])).
% 0.20/0.28 cnf(s49, plain, ~spl3_11 | ~spl3_14 | ~spl3_22, inference(sat_conversion,[],[f448])).
% 0.20/0.28 cnf(s51, plain, ~spl3_3 | ~spl3_4 | spl3_22, inference(sat_conversion,[],[f449])).
% 0.20/0.28 cnf(s54, plain, ~spl3_6 | ~spl3_9 | ~spl3_12 | ~spl3_13, inference(sat_conversion,[],[f462])).
% 0.20/0.28 cnf(s59, plain, ~spl3_7 | spl3_10 | spl3_24, inference(sat_conversion,[],[f562])).
% 0.20/0.28 cnf(s60, plain, ~spl3_7 | ~spl3_8 | spl3_23, inference(sat_conversion,[],[f563])).
% 0.20/0.28 cnf(s61, plain, ~spl3_23 | ~spl3_24, inference(sat_conversion,[],[f566])).
% 0.20/0.28 cnf(s62, plain, ~spl3_7 | spl3_10 | ~spl3_8, inference(rat,[],[s61,s59,s60])).
% 0.20/0.28 cnf(s63, plain, ~spl3_12 | ~spl3_5 | ~spl3_18 | ~spl3_8, inference(rat,[],[s8,s19,s20])).
% 0.20/0.28 cnf(s64, plain, spl3_2 | spl3_1, inference(rat,[],[s8,s36,s49,s7,s63,s6,s9,s40,s51,s5,s62,s11,s4,s16,s1])).
% 0.20/0.28 cnf(s65, plain, ~spl3_3 | spl3_10, inference(rat,[],[s8,s36,s49,s7,s63,s6,s9,s40,s51,s5,s62,s4,s16])).
% 0.20/0.28 cnf(s66, plain, ~spl3_7 | spl3_1, inference(rat,[],[s32,s30,s31,s64])).
% 0.20/0.28 cnf(s67, plain, ~spl3_11 | spl3_1, inference(rat,[],[s8,s36,s49,s2,s35,s37,s5,s9,s3,s66,s65,s22,s64])).
% 0.20/0.28 cnf(s68, plain, spl3_1, inference(rat,[],[s8,s54,s20,s7,s67,s2,s5,s9,s3,s66,s65,s22,s64])).
% 0.20/0.28 cnf(s69, plain, spl3_8, inference(rat,[],[s28,s68])).
% 0.20/0.28 cnf(s70, plain, $false, inference(rat,[],[s14,s69,s68])).
% 0.20/0.28 thf(f567,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s70])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (3450250)------------------------------
% 0.20/0.28 % (3450250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3450250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3450250)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3450250)Termination reason: Refutation
% 0.20/0.28 % (3450250)Time elapsed: 0.010 s
% 0.20/0.28 % (3450250)Peak memory usage: 13 MB
% 0.20/0.28 % (3450250)Instructions burned: 29 (million)
% 0.20/0.28 % (3450240)Success in time 0.045 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------