%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_7, type, sK4: ($i > $o)).
thf(func_def_8, type, sK5: (($i > $o) > $i)).
thf(func_def_9, type, vNOT: ($o > $o)).
thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(f1,conjecture,(
  ! [X3 : ($i > $o),X0 : $i,X2 : $i,X1 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((X5 @ X0) | (X4 @ X0)) & ((X3 @ X1) | (X5 @ X1)) & (~(X3 @ X2) | (X4 @ X2)) & ! [X6 : $i] : (~(X3 @ X6) <=> (X5 @ X6)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM125C)).
thf(f2,negated_conjecture,(
  ~ ! [X3 : ($i > $o),X0 : $i,X2 : $i,X1 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((X5 @ X0) | (X4 @ X0)) & ((X3 @ X1) | (X5 @ X1)) & (~(X3 @ X2) | (X4 @ X2)) & ! [X6 : $i] : (~(X3 @ X6) <=> (X5 @ X6)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((X5 @ X1) | (X4 @ X1)) & ((X0 @ X3) | (X5 @ X3)) & (~(X0 @ X2) | (X4 @ X2)) & ! [X6 : $i] : (~(X0 @ X6) <=> (X5 @ X6)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : ($i > $o),X1 : $i,X2 : $i,X3 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : (((((X4 @ X1)) = $true) | (((X5 @ X1)) = $true)) & ((((X5 @ X3)) = $true) | (((X0 @ X3)) = $true)) & (~ ($true = ((X0 @ X2))) | (((X4 @ X2)) = $true)) & ! [X6 : $i] : (~ (((X0 @ X6)) = $true) <=> (((X5 @ X6)) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ~ ! [X1 : $i,X3 : $i,X0 : ($i > $o),X2 : $i] : ? [X4 : ($i > $o),X5 : ($i > $o)] : ((($true != ((X0 @ X2))) | (((X4 @ X2)) = $true)) & ((((X4 @ X1)) = $true) | (((X5 @ X1)) = $true)) & ((((X5 @ X3)) = $true) | (((X0 @ X3)) = $true)) & ! [X6 : $i] : ((((X5 @ X6)) = $true) <=> (((X0 @ X6)) != $true)))),
  inference(flattening,[],[f4])).
thf(f6,plain,(
  ? [X2 : $i,X1 : $i,X3 : $i,X0 : ($i > $o)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X0 @ X6)) != $true)) | ((((X5 @ X1)) != $true) & (((X4 @ X1)) != $true)) | (($true = ((X0 @ X2))) & (((X4 @ X2)) != $true)) | ((((X5 @ X3)) != $true) & (((X0 @ X3)) != $true)))),
  inference(ennf_transformation,[],[f5])).
thf(f7,definition,(
  ! [X3 : $i,X5 : ($i > $o),X0 : ($i > $o)] : (((((X5 @ X3)) != $true) & (((X0 @ X3)) != $true)) | ~ (((sP0 @ X0 @ X5 @ X3)) = $true))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f8,plain,(
  ? [X2 : $i,X1 : $i,X3 : $i,X0 : ($i > $o)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : (? [X6 : $i] : ((((X5 @ X6)) = $true) <~> (((X0 @ X6)) != $true)) | ((((X5 @ X1)) != $true) & (((X4 @ X1)) != $true)) | (($true = ((X0 @ X2))) & (((X4 @ X2)) != $true)) | (((sP0 @ X0 @ X5 @ X3)) = $true))),
  inference(definition_folding,[],[f6,f7])).
thf(f9,plain,(
  ! [X3 : $i,X5 : ($i > $o),X0 : ($i > $o)] : (((((X5 @ X3)) != $true) & (((X0 @ X3)) != $true)) | (((sP0 @ X0 @ X5 @ X3)) != $true))),
  inference(nnf_transformation,[],[f7])).
thf(f10,plain,(
  ! [X0 : $i,X1 : ($i > $o),X2 : ($i > $o)] : (((((X1 @ X0)) != $true) & (((X2 @ X0)) != $true)) | ($true != ((sP0 @ X2 @ X1 @ X0))))),
  inference(rectify,[],[f9])).
thf(f11,plain,(
  ? [X2 : $i,X1 : $i,X3 : $i,X0 : ($i > $o)] : ! [X5 : ($i > $o),X4 : ($i > $o)] : (? [X6 : $i] : (((((X0 @ X6)) = $true) | (((X5 @ X6)) != $true)) & ((((X0 @ X6)) != $true) | (((X5 @ X6)) = $true))) | ((((X5 @ X1)) != $true) & (((X4 @ X1)) != $true)) | (($true = ((X0 @ X2))) & (((X4 @ X2)) != $true)) | (((sP0 @ X0 @ X5 @ X3)) = $true))),
  inference(nnf_transformation,[],[f8])).
thf(f12,plain,(
  ? [X0 : $i,X1 : $i,X2 : $i,X3 : ($i > $o)] : ! [X4 : ($i > $o),X5 : ($i > $o)] : (? [X6 : $i] : (((((X3 @ X6)) = $true) | (((X4 @ X6)) != $true)) & ((((X3 @ X6)) != $true) | (((X4 @ X6)) = $true))) | ((((X4 @ X1)) != $true) & (((X5 @ X1)) != $true)) | ((((X3 @ X0)) = $true) & (((X5 @ X0)) != $true)) | ($true = ((sP0 @ X3 @ X4 @ X2))))),
  inference(rectify,[],[f11])).
thf(f13,plain,(
  ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((((sK4 @ (sK5 @ X4))) = $true) | ($true != ((X4 @ (sK5 @ X4))))) & ((((sK4 @ (sK5 @ X4))) != $true) | ($true = ((X4 @ (sK5 @ X4)))))) | (($true != ((X4 @ sK2))) & (((X5 @ sK2)) != $true)) | ((((sK4 @ sK1)) = $true) & ($true != ((X5 @ sK1)))) | (((sP0 @ sK4 @ X4 @ sK3)) = $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,$thf(sK1)),skolemize(X1,$thf(sK2)),skolemize(X2,$thf(sK3)),skolemize(X3,$thf(sK4)),skolemize(X6,$thf(sK5 @ X4))],[f12])).
thf(f14,plain,(
  ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | (((X2 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f15,plain,(
  ( ! [X2 : ($i > $o),X0 : $i,X1 : ($i > $o)] : (($true != ((sP0 @ X2 @ X1 @ X0))) | (((X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f16,plain,(
  ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((X5 @ sK2)) != $true) | (((sP0 @ sK4 @ X4 @ sK3)) = $true) | ($true != ((X5 @ sK1))) | (((sK4 @ (sK5 @ X4))) != $true) | ($true = ((X4 @ (sK5 @ X4))))) )),
  inference(cnf_transformation,[],[f13])).
thf(f20,plain,(
  ( ! [X4 : ($i > $o),X5 : ($i > $o)] : ((((sK4 @ (sK5 @ X4))) = $true) | (((X5 @ sK2)) != $true) | ($true != ((X4 @ (sK5 @ X4)))) | ($true != ((X5 @ sK1))) | (((sP0 @ sK4 @ X4 @ sK3)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f35,definition,(
  spl6_3 <=> ! [X4 : ($i > $o)] : ((((sK4 @ (sK5 @ X4))) = $true) | (((sP0 @ sK4 @ X4 @ sK3)) = $true) | ($true != ((X4 @ (sK5 @ X4)))))),
  introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
thf(f36,plain,(
  ( ! [X4 : ($i > $o)] : (($true != ((X4 @ (sK5 @ X4)))) | (((sP0 @ sK4 @ X4 @ sK3)) = $true) | (((sK4 @ (sK5 @ X4))) = $true)) ) | ~spl6_3),
  inference(avatar_component_clause,[],[f35])).
thf(f38,definition,(
  spl6_4 <=> ! [X5 : ($i > $o)] : ((((X5 @ sK2)) != $true) | ($true != ((X5 @ sK1))))),
  introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
thf(f39,plain,(
  ( ! [X5 : ($i > $o)] : (($true != ((X5 @ sK1))) | (((X5 @ sK2)) != $true)) ) | ~spl6_4),
  inference(avatar_component_clause,[],[f38])).
thf(f40,plain,(
  spl6_3 | spl6_4),
  inference(avatar_split_clause,[],[f20,f38,f35])).
thf(f50,definition,(
  spl6_7 <=> ! [X4 : ($i > $o)] : ((((sP0 @ sK4 @ X4 @ sK3)) = $true) | ($true = ((X4 @ (sK5 @ X4)))) | (((sK4 @ (sK5 @ X4))) != $true))),
  introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
thf(f51,plain,(
  ( ! [X4 : ($i > $o)] : ((((sK4 @ (sK5 @ X4))) != $true) | (((sP0 @ sK4 @ X4 @ sK3)) = $true) | ($true = ((X4 @ (sK5 @ X4))))) ) | ~spl6_7),
  inference(avatar_component_clause,[],[f50])).
thf(f57,plain,(
  spl6_7 | spl6_4),
  inference(avatar_split_clause,[],[f16,f38,f50])).
thf(f77,plain,(
  ((((^[Y0 : $i]: ($true)) @ sK2)) != $true) | ($true != (((^[Y0 : $i]: ($true)) @ sK1))) | ~spl6_4),
  inference(primitive_instantiation,[],[f39])).
thf(f89,plain,(
  ($true != $true) | ($true != $true) | ~spl6_4),
  inference(beta-eta_normalization,[],[f77])).
thf(f90,plain,(
  ($true != $true) | ~spl6_4),
  inference(duplicate_literal_removal,[],[f89])).
thf(f91,plain,(
  $false | ~spl6_4),
  inference(trivial_inequality_removal,[],[f90])).
thf(f92,plain,(
  ~spl6_4),
  inference(avatar_contradiction_clause,[],[f91])).
thf(f98,plain,(
  ( ! [X5 : ($i > $o)] : ((((sP0 @ sK4 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK3)) = $true) | ((((^[Y0 : $i]: (~ (X5 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) != $true) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true)) ) | ~spl6_3),
  inference(primitive_instantiation,[],[f36])).
thf(f105,plain,(
  ( ! [X5 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true) | (((~ (X5 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))) != $true) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK3)) = $true)) ) | ~spl6_3),
  inference(beta-eta_normalization,[],[f98])).
thf(f106,plain,(
  ( ! [X5 : ($i > $o)] : ((((sP0 @ sK4 @ (^[Y0 : $i]: (~ (X5 @ Y0))) @ sK3)) = $true) | ($true = ((X5 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))) = $true)) ) | ~spl6_3),
  inference(not_proxy_clausification,[],[f105])).
thf(f175,plain,(
  ( ! [X0 : ($i > $o)] : ((((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != $true) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != ((sK4 @ sK3)))) ) | ~spl6_3),
  inference(constrained_superposition,[],[f14,f106])).
thf(f180,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != ((sK4 @ sK3))) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_3),
  inference(trivial_inequality_removal,[],[f175])).
thf(f272,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != $true) | ($true != (((^[Y0 : $i]: (~ (X0 @ Y0))) @ sK3))) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_3),
  inference(constrained_superposition,[],[f15,f106])).
thf(f306,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != (((^[Y0 : $i]: (~ (X0 @ Y0))) @ sK3))) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_3),
  inference(trivial_inequality_removal,[],[f272])).
thf(f307,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true != ((~ (X0 @ sK3))))) ) | ~spl6_3),
  inference(beta-eta_normalization,[],[f306])).
thf(f308,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | ($true = ((X0 @ sK3)))) ) | ~spl6_3),
  inference(not_proxy_clausification,[],[f307])).
thf(f319,definition,(
  spl6_15 <=> ($true = ((sK4 @ sK3)))),
  introduced(definition,[new_symbols(definition,[spl6_15])],[avatar_definition])).
thf(f320,plain,(
  ($true = ((sK4 @ sK3))) | ~spl6_15),
  inference(avatar_component_clause,[],[f319])).
thf(f321,plain,(
  ($true != ((sK4 @ sK3))) | spl6_15),
  inference(avatar_component_clause,[],[f319])).
thf(f328,definition,(
  spl6_17 <=> ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true))),
  introduced(definition,[new_symbols(definition,[spl6_17])],[avatar_definition])).
thf(f329,plain,(
  ( ! [X0 : ($i > $o)] : ((((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true) | (((X0 @ (sK5 @ (^[Y0 : $i]: (~ (X0 @ Y0)))))) = $true)) ) | ~spl6_17),
  inference(avatar_component_clause,[],[f328])).
thf(f330,plain,(
  spl6_17 | ~spl6_15 | ~spl6_3),
  inference(avatar_split_clause,[],[f180,f35,f319,f328])).
thf(f397,plain,(
  ($true = ((sK4 @ sK3))) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $true) | ($true != $true) | ~spl6_3),
  inference(equality_factoring,[],[f308])).
thf(f407,plain,(
  (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $true) | ($true = ((sK4 @ sK3))) | ~spl6_3),
  inference(trivial_inequality_removal,[],[f397])).
thf(f422,plain,(
  (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $true) | (~spl6_3 | spl6_15)),
  inference(forward_subsumption_resolution,[],[f407,f321])).
thf(f425,plain,(
  ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | ($true != $true) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(constrained_superposition,[],[f51,f422])).
thf(f430,plain,(
  ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(trivial_inequality_removal,[],[f425])).
thf(f431,plain,(
  (((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) = $true) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(beta-eta_normalization,[],[f430])).
thf(f432,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $false) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(not_proxy_clausification,[],[f431])).
thf(f435,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | ($true = $false) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(forward_demodulation,[],[f432,f422])).
thf(f436,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_3 | ~spl6_7 | spl6_15)),
  inference(trivial_inequality_removal,[],[f435])).
thf(f438,definition,(
  spl6_23 <=> (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true)),
  introduced(definition,[new_symbols(definition,[spl6_23])],[avatar_definition])).
thf(f440,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | ~spl6_23),
  inference(avatar_component_clause,[],[f438])).
thf(f446,plain,(
  spl6_23 | ~spl6_3 | ~spl6_7 | spl6_15),
  inference(avatar_split_clause,[],[f436,f319,f50,f35,f438])).
thf(f502,plain,(
  ($true != $true) | (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $true) | ~spl6_17),
  inference(equality_factoring,[],[f329])).
thf(f510,plain,(
  (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $true) | ~spl6_17),
  inference(trivial_inequality_removal,[],[f502])).
thf(f525,plain,(
  ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | ($true != $true) | (~spl6_7 | ~spl6_17)),
  inference(constrained_superposition,[],[f51,f510])).
thf(f526,plain,(
  ($true = (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_7 | ~spl6_17)),
  inference(trivial_inequality_removal,[],[f525])).
thf(f527,plain,(
  (((~ (sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0))))))) = $true) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_7 | ~spl6_17)),
  inference(beta-eta_normalization,[],[f526])).
thf(f528,plain,(
  (((sK4 @ (sK5 @ (^[Y0 : $i]: (~ (sK4 @ Y0)))))) = $false) | (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_7 | ~spl6_17)),
  inference(not_proxy_clausification,[],[f527])).
thf(f533,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | ($true = $false) | (~spl6_7 | ~spl6_17)),
  inference(forward_demodulation,[],[f528,f510])).
thf(f534,plain,(
  (((sP0 @ sK4 @ (^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3)) = $true) | (~spl6_7 | ~spl6_17)),
  inference(trivial_inequality_removal,[],[f533])).
thf(f537,plain,(
  spl6_23 | ~spl6_7 | ~spl6_17),
  inference(avatar_split_clause,[],[f534,f328,f50,f438])).
thf(f540,plain,(
  ($true != $true) | ($true != (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3))) | ~spl6_23),
  inference(constrained_superposition,[],[f15,f440])).
thf(f541,plain,(
  ($true != $true) | ($true != ((sK4 @ sK3))) | ~spl6_23),
  inference(constrained_superposition,[],[f14,f440])).
thf(f543,plain,(
  ($true != ((sK4 @ sK3))) | ~spl6_23),
  inference(trivial_inequality_removal,[],[f541])).
thf(f544,plain,(
  ($true != (((^[Y0 : $i]: (~ (sK4 @ Y0))) @ sK3))) | ~spl6_23),
  inference(trivial_inequality_removal,[],[f540])).
thf(f545,plain,(
  ($true != ((~ (sK4 @ sK3)))) | ~spl6_23),
  inference(beta-eta_normalization,[],[f544])).
thf(f546,plain,(
  ($true = ((sK4 @ sK3))) | ~spl6_23),
  inference(not_proxy_clausification,[],[f545])).
thf(f547,plain,(
  $false | (~spl6_15 | ~spl6_23)),
  inference(forward_subsumption_resolution,[],[f543,f320])).
thf(f548,plain,(
  ~spl6_15 | ~spl6_23),
  inference(avatar_contradiction_clause,[],[f547])).
thf(f551,plain,(
  spl6_15 | ~spl6_23),
  inference(avatar_split_clause,[],[f546,f438,f319])).
cnf(s2, plain, spl6_3 | spl6_4, inference(sat_conversion,[],[f40])).
cnf(s7, plain, spl6_4 | spl6_7, inference(sat_conversion,[],[f57])).
cnf(s14, plain, ~spl6_4, inference(sat_conversion,[],[f92])).
cnf(s21, plain, ~spl6_3 | ~spl6_15 | spl6_17, inference(sat_conversion,[],[f330])).
cnf(s28, plain, ~spl6_3 | ~spl6_7 | spl6_15 | spl6_23, inference(sat_conversion,[],[f446])).
cnf(s29, plain, ~spl6_7 | ~spl6_17 | spl6_23, inference(sat_conversion,[],[f537])).
cnf(s31, plain, ~spl6_15 | ~spl6_23, inference(sat_conversion,[],[f548])).
cnf(s32, plain, spl6_15 | ~spl6_23, inference(sat_conversion,[],[f551])).
cnf(s36, plain, spl6_7, inference(rat,[],[s7,s14])).
cnf(s38, plain, spl6_3, inference(rat,[],[s2,s14])).
cnf(s40, plain, spl6_15, inference(rat,[],[s28,s32,s36,s38])).
cnf(s41, plain, ~spl6_23, inference(rat,[],[s31,s40])).
cnf(s47, plain, spl6_17, inference(rat,[],[s21,s38,s40])).
cnf(s50, plain, $false, inference(rat,[],[s29,s36,s41,s47])).
thf(f552,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s50])).
% SZS output end Proof for theBenchmark