%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, cONE: (($i > $o) > $o)).
thf(func_def_1, type, cSUCC: ((($i > $o) > $o) > ($i > $o) > $o)).
thf(func_def_2, type, cZERO: (($i > $o) > $o)).
thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_5, type, vAND: ($o > $o > $o)).
thf(func_def_6, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_7, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_10, type, vNOT: ($o > $o)).
thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_12, type, sK0: (($i > $i) > ($i > $i) > $i)).
thf(func_def_15, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_16, type, sK1: ($i > $o)).
thf(func_def_17, type, sK2: ($i > $i)).
thf(func_def_21, type, sK6: ($i > $i)).
thf(f1,axiom,(
  ((^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))) = cZERO)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
thf(f2,axiom,(
  ((^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2))))))) = cSUCC)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
thf(f3,axiom,(
  (cONE = ((cSUCC @ cZERO)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cONE_def)).
thf(f4,conjecture,(
  ! [X4 : ($i > $i),X3 : ($i > $i)] : (! [X2 : $i] : (((X3 @ X2)) = ((X4 @ X2))) => (X3 = X4)) => (cONE = (^[X0 : ($i > $o)] : (? [X1 : $i] : (X0 = (((^[X2 : $i, X1 : $i] : ((X2 = X1))) @ X1))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_EXT_pme)).
thf(f5,negated_conjecture,(
  ~(! [X4 : ($i > $i),X3 : ($i > $i)] : (! [X2 : $i] : (((X3 @ X2)) = ((X4 @ X2))) => (X3 = X4)) => (cONE = (^[X0 : ($i > $o)] : (? [X1 : $i] : (X0 = (((^[X2 : $i, X1 : $i] : ((X2 = X1))) @ X1)))))))),
  inference(negated_conjecture,[status(cth)],[f4])).
thf(f6,plain,(
  ((^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2))))))) = cSUCC)),
  inference(rectify,[],[f2])).
thf(f7,plain,(
  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  ((^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))) = cZERO)),
  inference(rectify,[],[f1])).
thf(f9,plain,(
  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
  inference(fool_elimination,[],[f8])).
thf(f10,plain,(
  ~(! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => (cONE = (^[X3 : ($i > $o)] : (? [X4 : $i] : (X3 = (((^[X5 : $i, X6 : $i] : ((X5 = X6))) @ X4)))))))),
  inference(rectify,[],[f5])).
thf(f11,plain,(
  ~(! [X1 : ($i > $i),X0 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) => (cONE = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1)))))))),
  inference(fool_elimination,[],[f10])).
thf(f12,plain,(
  (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1)))))) & ! [X1 : ($i > $i),X0 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2))))),
  inference(ennf_transformation,[],[f11])).
thf(f13,plain,(
  (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1)))))) & ! [X0 : ($i > $i),X1 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2))))),
  inference(rectify,[],[f12])).
thf(f14,plain,(
  (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1)))))) & ! [X0 : ($i > $i),X1 : ($i > $i)] : ((X0 = X1) | (((X0 @ (sK0 @ X1 @ X0))) != ((X1 @ (sK0 @ X1 @ X0)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK0 @ X1 @ X0))],[f13])).
thf(f15,plain,(
  (cONE = ((cSUCC @ cZERO)))),
  inference(cnf_transformation,[],[f3])).
thf(f17,plain,(
  (cONE != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))))),
  inference(cnf_transformation,[],[f14])).
thf(f18,plain,(
  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
  inference(cnf_transformation,[],[f9])).
thf(f19,plain,(
  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f7])).
thf(f22,plain,(
  (cONE = (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
  inference(definition_unfolding,[],[f15,f19,f18])).
thf(f23,plain,(
  ((((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))) & (Y1 @ Y2))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2 = Y3)))) @ Y1))))))),
  inference(definition_unfolding,[],[f17,f22])).
thf(f24,plain,(
  ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) != (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))))),
  inference(beta-eta_normalization,[],[f23])).
thf(f26,plain,(
  ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) @ sK1)) != (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1)))),
  inference(negative_extensionality,[],[f24])).
thf(f27,plain,(
  ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1))) | ($true = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) @ sK1)))),
  inference(xor_proxy_clausification,[],[f26])).
thf(f28,plain,(
  ($false = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))) & (Y0 @ Y1))))) @ sK1))) | ($false = (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (Y0 = (= @ Y1))))) @ sK1)))),
  inference(xor_proxy_clausification,[],[f26])).
thf(f29,plain,(
  ($false = ((?? @ $i @ (^[Y0 : $i]: (sK1 = (= @ Y0)))))) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))))))),
  inference(beta-eta_normalization,[],[f28])).
thf(f30,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: (sK1 = (= @ Y0))) @ X1)) = $false) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))))))) )),
  inference(pi_proxy_clausification,[],[f29])).
thf(f31,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: (sK1 = (= @ Y0))) @ X1)) = $false) | ((((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))) @ X2)) = $false)) )),
  inference(pi_proxy_clausification,[],[f30])).
thf(f32,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((~ (?? @ $i @ (^[Y0 : $i]: ((~ (X2 = Y0)) & (sK1 @ Y0))))) & (sK1 @ X2)))) | ($false = ((sK1 = (= @ X1))))) )),
  inference(beta-eta_normalization,[],[f31])).
thf(f33,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (X2 = Y0)) & (sK1 @ Y0))))))) | ($false = ((sK1 = (= @ X1)))) | ($false = ((sK1 @ X2)))) )),
  inference(and_proxy_clausification,[],[f32])).
thf(f34,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 = (= @ X1)))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (X2 = Y0)) & (sK1 @ Y0)))))) | ($false = ((sK1 @ X2)))) )),
  inference(not_proxy_clausification,[],[f33])).
thf(f35,plain,(
  ( ! [X2 : $i,X1 : $i] : ((sK1 != ((= @ X1))) | ($false = ((sK1 @ X2))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (X2 = Y0)) & (sK1 @ Y0))))))) )),
  inference(equality_proxy_clausification,[],[f34])).
thf(f36,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ X2))) | ($true = (((^[Y0 : $i]: ((~ (X2 = Y0)) & (sK1 @ Y0))) @ (sK2 @ X2)))) | (sK1 != ((= @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f35])).
thf(f37,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ X2))) | ($true = (((~ (X2 = (sK2 @ X2))) & (sK1 @ (sK2 @ X2))))) | (sK1 != ((= @ X1)))) )),
  inference(beta-eta_normalization,[],[f36])).
thf(f38,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK1 @ (sK2 @ X2)))) | (sK1 != ((= @ X1))) | ($false = ((sK1 @ X2)))) )),
  inference(and_proxy_clausification,[],[f37])).
thf(f39,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ X2))) | ($true = ((~ (X2 = (sK2 @ X2))))) | (sK1 != ((= @ X1)))) )),
  inference(and_proxy_clausification,[],[f37])).
thf(f40,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ X2))) | (sK1 != ((= @ X1))) | ($false = ((X2 = (sK2 @ X2))))) )),
  inference(not_proxy_clausification,[],[f39])).
thf(f41,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ X2))) | (((sK2 @ X2)) != X2) | (sK1 != ((= @ X1)))) )),
  inference(equality_proxy_clausification,[],[f40])).
thf(f42,plain,(
  ($true = ((?? @ $i @ (^[Y0 : $i]: (sK1 = (= @ Y0)))))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))))))),
  inference(beta-eta_normalization,[],[f27])).
thf(f43,plain,(
  ($true = (((^[Y0 : $i]: (sK1 = (= @ Y0))) @ sK3))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))))))),
  inference(sigma_proxy_clausification,[],[f42])).
thf(f44,plain,(
  ($true = (((^[Y0 : $i]: (sK1 = (= @ Y0))) @ sK3))) | ($true = (((^[Y0 : $i]: ((~ (?? @ $i @ (^[Y1 : $i]: ((~ (Y0 = Y1)) & (sK1 @ Y1))))) & (sK1 @ Y0))) @ sK4)))),
  inference(sigma_proxy_clausification,[],[f43])).
thf(f45,plain,(
  ($true = (((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))))) & (sK1 @ sK4)))) | ($true = ((sK1 = (= @ sK3))))),
  inference(beta-eta_normalization,[],[f44])).
thf(f46,plain,(
  ($true = ((sK1 = (= @ sK3)))) | (((sK1 @ sK4)) = $true)),
  inference(and_proxy_clausification,[],[f45])).
thf(f47,plain,(
  ($true = ((~ (?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))))))) | ($true = ((sK1 = (= @ sK3))))),
  inference(and_proxy_clausification,[],[f45])).
thf(f48,plain,(
  ($true = ((sK1 = (= @ sK3)))) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))))))),
  inference(not_proxy_clausification,[],[f47])).
thf(f49,plain,(
  ($false = ((?? @ $i @ (^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0)))))) | (((= @ sK3)) = sK1)),
  inference(equality_proxy_clausification,[],[f48])).
thf(f50,plain,(
  ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (sK4 = Y0)) & (sK1 @ Y0))) @ X1))) | (((= @ sK3)) = sK1)) )),
  inference(pi_proxy_clausification,[],[f49])).
thf(f51,plain,(
  ( ! [X1 : $i] : ((((= @ sK3)) = sK1) | ($false = (((~ (sK4 = X1)) & (sK1 @ X1))))) )),
  inference(beta-eta_normalization,[],[f50])).
thf(f52,plain,(
  ( ! [X1 : $i] : (($false = ((~ (sK4 = X1)))) | ($false = ((sK1 @ X1))) | (((= @ sK3)) = sK1)) )),
  inference(and_proxy_clausification,[],[f51])).
thf(f53,plain,(
  ( ! [X1 : $i] : (($true = ((sK4 = X1))) | ($false = ((sK1 @ X1))) | (((= @ sK3)) = sK1)) )),
  inference(not_proxy_clausification,[],[f52])).
thf(f54,plain,(
  ( ! [X1 : $i] : ((((= @ sK3)) = sK1) | (sK4 = X1) | ($false = ((sK1 @ X1)))) )),
  inference(equality_proxy_clausification,[],[f53])).
thf(f55,plain,(
  (((sK1 @ sK4)) = $true) | (((= @ sK3)) = sK1)),
  inference(equality_proxy_clausification,[],[f46])).
thf(f57,definition,(
  spl5_1 <=> ! [X2 : $i] : (($false = ((sK1 @ X2))) | (((sK2 @ X2)) != X2))),
  introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
thf(f58,plain,(
  ( ! [X2 : $i] : ((((sK2 @ X2)) != X2) | ($false = ((sK1 @ X2)))) ) | ~spl5_1),
  inference(avatar_component_clause,[],[f57])).
thf(f60,definition,(
  spl5_2 <=> ! [X1 : $i] : (sK1 != ((= @ X1)))),
  introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
thf(f61,plain,(
  ( ! [X1 : $i] : ((sK1 != ((= @ X1)))) ) | ~spl5_2),
  inference(avatar_component_clause,[],[f60])).
thf(f62,plain,(
  spl5_1 | spl5_2),
  inference(avatar_split_clause,[],[f41,f60,f57])).
thf(f64,definition,(
  spl5_3 <=> ! [X2 : $i] : (($true = ((sK1 @ (sK2 @ X2)))) | ($false = ((sK1 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
thf(f65,plain,(
  ( ! [X2 : $i] : (($true = ((sK1 @ (sK2 @ X2)))) | ($false = ((sK1 @ X2)))) ) | ~spl5_3),
  inference(avatar_component_clause,[],[f64])).
thf(f66,plain,(
  spl5_2 | spl5_3),
  inference(avatar_split_clause,[],[f38,f64,f60])).
thf(f68,definition,(
  spl5_4 <=> ! [X1 : $i] : ((sK4 = X1) | ($false = ((sK1 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
thf(f69,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ X1))) | (sK4 = X1)) ) | ~spl5_4),
  inference(avatar_component_clause,[],[f68])).
thf(f71,definition,(
  spl5_5 <=> (((= @ sK3)) = sK1)),
  introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
thf(f73,plain,(
  (((= @ sK3)) = sK1) | ~spl5_5),
  inference(avatar_component_clause,[],[f71])).
thf(f74,plain,(
  spl5_4 | spl5_5),
  inference(avatar_split_clause,[],[f54,f71,f68])).
thf(f76,definition,(
  spl5_6 <=> (((sK1 @ sK4)) = $true)),
  introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
thf(f78,plain,(
  (((sK1 @ sK4)) = $true) | ~spl5_6),
  inference(avatar_component_clause,[],[f76])).
thf(f79,plain,(
  spl5_6 | spl5_5),
  inference(avatar_split_clause,[],[f55,f71,f76])).
thf(f80,plain,(
  ( ! [X1 : $i] : ((((sK1 @ (sK6 @ X1))) != ((X1 = (sK6 @ X1))))) ) | ~spl5_2),
  inference(negative_extensionality,[],[f61])).
thf(f81,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ (sK6 @ X1)))) | ($true = ((X1 = (sK6 @ X1))))) ) | ~spl5_2),
  inference(xor_proxy_clausification,[],[f80])).
thf(f82,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ (sK6 @ X1)))) | ($false = ((X1 = (sK6 @ X1))))) ) | ~spl5_2),
  inference(xor_proxy_clausification,[],[f80])).
thf(f83,plain,(
  ( ! [X1 : $i] : ((((sK6 @ X1)) != X1) | ($false = ((sK1 @ (sK6 @ X1))))) ) | ~spl5_2),
  inference(equality_proxy_clausification,[],[f82])).
thf(f84,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ (sK6 @ X1)))) | (((sK6 @ X1)) = X1)) ) | ~spl5_2),
  inference(equality_proxy_clausification,[],[f81])).
thf(f85,plain,(
  ( ! [X1 : $i] : ((((sK3 = X1)) = ((sK1 @ X1)))) ) | ~spl5_5),
  inference(argument_congruence,[],[f73])).
thf(f86,plain,(
  (sK1 != sK1) | (~spl5_2 | ~spl5_5)),
  inference(constrained_superposition,[],[f61,f73])).
thf(f87,plain,(
  $false | (~spl5_2 | ~spl5_5)),
  inference(trivial_inequality_removal,[],[f86])).
thf(f88,plain,(
  ~spl5_2 | ~spl5_5),
  inference(avatar_contradiction_clause,[],[f87])).
thf(f89,plain,(
  ( ! [X1 : $i] : ((((sK3 = X1)) = $true) | ($false = ((sK1 @ X1)))) ) | ~spl5_5),
  inference(iff_proxy_clausification,[],[f85])).
thf(f90,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ X1))) | (((sK3 = X1)) = $false)) ) | ~spl5_5),
  inference(iff_proxy_clausification,[],[f85])).
thf(f91,plain,(
  ( ! [X1 : $i] : ((sK3 != X1) | ($true = ((sK1 @ X1)))) ) | ~spl5_5),
  inference(equality_proxy_clausification,[],[f90])).
thf(f92,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ X1))) | (sK3 = X1)) ) | ~spl5_5),
  inference(equality_proxy_clausification,[],[f89])).
thf(f95,plain,(
  ( ! [X0 : $i] : ((((sK6 @ X0)) = X0) | (((sK6 @ X0)) = sK4) | ($false = $true)) ) | (~spl5_2 | ~spl5_4)),
  inference(constrained_superposition,[],[f69,f84])).
thf(f96,plain,(
  ( ! [X0 : $i] : ((((sK6 @ X0)) = sK4) | (((sK6 @ X0)) = X0)) ) | (~spl5_2 | ~spl5_4)),
  inference(trivial_inequality_removal,[],[f95])).
thf(f101,plain,(
  ( ! [X0 : $i] : ((sK4 != X0) | (((sK6 @ X0)) = X0)) ) | (~spl5_2 | ~spl5_4)),
  inference(equality_factoring,[],[f96])).
thf(f104,plain,(
  (((sK6 @ sK4)) = sK4) | (sK4 != sK4) | (~spl5_2 | ~spl5_4)),
  inference(imitation,[],[f101])).
thf(f106,plain,(
  (((sK6 @ sK4)) = sK4) | (~spl5_2 | ~spl5_4)),
  inference(trivial_inequality_removal,[],[f104])).
thf(f107,plain,(
  (((sK1 @ sK4)) = $false) | (sK4 != sK4) | (~spl5_2 | ~spl5_4)),
  inference(constrained_superposition,[],[f83,f106])).
thf(f108,plain,(
  (((sK1 @ sK4)) = $false) | (~spl5_2 | ~spl5_4)),
  inference(trivial_inequality_removal,[],[f107])).
thf(f109,plain,(
  ($false = $true) | (~spl5_2 | ~spl5_4 | ~spl5_6)),
  inference(forward_demodulation,[],[f108,f78])).
thf(f110,plain,(
  $false | (~spl5_2 | ~spl5_4 | ~spl5_6)),
  inference(trivial_inequality_removal,[],[f109])).
thf(f111,plain,(
  ~spl5_2 | ~spl5_4 | ~spl5_6),
  inference(avatar_contradiction_clause,[],[f110])).
thf(f139,plain,(
  ( ! [X0 : $i] : (($false = $true) | (sK4 = ((sK2 @ X0))) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_4)),
  inference(constrained_superposition,[],[f69,f65])).
thf(f140,plain,(
  ( ! [X0 : $i] : ((sK4 = ((sK2 @ X0))) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_4)),
  inference(trivial_inequality_removal,[],[f139])).
thf(f143,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | ($false = ((sK1 @ X0))) | (sK4 != X0)) ) | (~spl5_1 | ~spl5_3 | ~spl5_4)),
  inference(constrained_superposition,[],[f58,f140])).
thf(f145,plain,(
  ( ! [X0 : $i] : ((sK4 != X0) | ($false = ((sK1 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_4)),
  inference(duplicate_literal_removal,[],[f143])).
thf(f146,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_4)),
  inference(forward_subsumption_resolution,[],[f145,f69])).
thf(f148,plain,(
  ($false = $true) | (~spl5_1 | ~spl5_3 | ~spl5_4 | ~spl5_6)),
  inference(constrained_superposition,[],[f146,f78])).
thf(f157,plain,(
  $false | (~spl5_1 | ~spl5_3 | ~spl5_4 | ~spl5_6)),
  inference(trivial_inequality_removal,[],[f148])).
thf(f158,plain,(
  ~spl5_1 | ~spl5_3 | ~spl5_4 | ~spl5_6),
  inference(avatar_contradiction_clause,[],[f157])).
thf(f172,plain,(
  ($true = ((sK1 @ sK3))) | (sK3 != sK3) | ~spl5_5),
  inference(imitation,[],[f91])).
thf(f174,plain,(
  ($true = ((sK1 @ sK3))) | ~spl5_5),
  inference(trivial_inequality_removal,[],[f172])).
thf(f175,plain,(
  ( ! [X0 : $i] : ((sK3 = ((sK2 @ X0))) | ($false = $true) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_5)),
  inference(constrained_superposition,[],[f92,f65])).
thf(f179,plain,(
  ( ! [X0 : $i] : ((sK3 = ((sK2 @ X0))) | ($false = ((sK1 @ X0)))) ) | (~spl5_3 | ~spl5_5)),
  inference(trivial_inequality_removal,[],[f175])).
thf(f187,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | ($false = ((sK1 @ X0))) | (sK3 != X0)) ) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
  inference(constrained_superposition,[],[f58,f179])).
thf(f188,plain,(
  ( ! [X0 : $i] : ((sK3 != X0) | ($false = ((sK1 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
  inference(duplicate_literal_removal,[],[f187])).
thf(f190,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
  inference(forward_subsumption_resolution,[],[f188,f92])).
thf(f194,plain,(
  ($false = $true) | (~spl5_1 | ~spl5_3 | ~spl5_5)),
  inference(constrained_superposition,[],[f174,f190])).
thf(f201,plain,(
  $false | (~spl5_1 | ~spl5_3 | ~spl5_5)),
  inference(trivial_inequality_removal,[],[f194])).
thf(f202,plain,(
  ~spl5_1 | ~spl5_3 | ~spl5_5),
  inference(avatar_contradiction_clause,[],[f201])).
cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f62])).
cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f66])).
cnf(s3, plain, spl5_4 | spl5_5, inference(sat_conversion,[],[f74])).
cnf(s4, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f79])).
cnf(s5, plain, ~spl5_2 | ~spl5_5, inference(sat_conversion,[],[f88])).
cnf(s6, plain, ~spl5_2 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f111])).
cnf(s11, plain, ~spl5_1 | ~spl5_3 | ~spl5_4 | ~spl5_6, inference(sat_conversion,[],[f158])).
cnf(s16, plain, ~spl5_1 | ~spl5_3 | ~spl5_5, inference(sat_conversion,[],[f202])).
cnf(s17, plain, ~spl5_2, inference(rat,[],[s6,s3,s4,s5])).
cnf(s18, plain, spl5_3, inference(rat,[],[s2,s17])).
cnf(s19, plain, spl5_1, inference(rat,[],[s1,s17])).
cnf(s20, plain, ~spl5_5, inference(rat,[],[s16,s18,s19])).
cnf(s21, plain, spl5_6, inference(rat,[],[s4,s20])).
cnf(s22, plain, spl5_4, inference(rat,[],[s3,s20])).
cnf(s23, plain, $false, inference(rat,[],[s11,s18,s19,s21,s22])).
thf(f203,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s23])).
% SZS output end Proof for theBenchmark