%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, sP0: ((a > a > $o) > (a > a > $o) > $o)).
thf(func_def_4, type, sP1: ((a > a > $o) > a > a > $o)).
thf(func_def_5, type, sP2: ((a > a > $o) > a > a > $o)).
thf(func_def_6, type, sK3: ((a > a > $o) > a > a > a > a > $o)).
thf(func_def_7, type, sK4: ((a > a > $o) > a)).
thf(func_def_8, type, sK5: ((a > a > $o) > a)).
thf(func_def_9, type, sK6: ((a > a > $o) > (a > a > $o) > a)).
thf(func_def_10, type, sK7: ((a > a > $o) > (a > a > $o) > a)).
thf(func_def_11, type, sK8: a).
thf(func_def_12, type, sK9: (a > a > $o)).
thf(func_def_13, type, sK10: a).
thf(func_def_14, type, sF11: $o).
thf(func_def_15, type, sF12: $o).
thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : ((X3 @ X4 @ X5) => (X3 @ X5 @ X4)) & ! [X5 : a,X4 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM522_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((! [X5 : a,X4 : a] : ((X3 @ X4 @ X5) => (X3 @ X5 @ X4)) & ! [X5 : a,X4 : a] : ((X0 @ X4 @ X5) => (X3 @ X4 @ X5))) => (X3 @ X1 @ X2)) <=> ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((! [X4 : a,X5 : a] : ((X3 @ X5 @ X4) => (X3 @ X4 @ X5)) & ! [X6 : a,X7 : a] : ((X0 @ X7 @ X6) => (X3 @ X7 @ X6))) => (X3 @ X1 @ X2)) <=> ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((! [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) = $true) => (((X3 @ X7 @ X6)) = $true)) & ! [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) => (((X3 @ X4 @ X5)) = $true))) => (((X3 @ X1 @ X2)) = $true)) <=> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X0 : (a > a > $o),X1 : a,X2 : a] : (! [X3 : (a > a > $o)] : ((((X3 @ X1 @ X2)) = $true) | (? [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) = $true) & (((X3 @ X7 @ X6)) != $true)) | ? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) & (((X3 @ X4 @ X5)) != $true)))) <~> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X1 : a,X0 : (a > a > $o),X2 : a] : (((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)) <~> ! [X3 : (a > a > $o)] : ((((X3 @ X1 @ X2)) = $true) | ? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) & (((X3 @ X4 @ X5)) != $true)) | ? [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) = $true) & (((X3 @ X7 @ X6)) != $true))))),
  inference(flattening,[],[f5])).
thf(f7,definition,(
  ! [X0 : (a > a > $o),X3 : (a > a > $o)] : ((((sP0 @ X3 @ X0)) = $true) <=> ? [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) = $true) & (((X3 @ X7 @ X6)) != $true)))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f8,definition,(
  ! [X2 : a,X1 : a,X0 : (a > a > $o)] : ((((sP1 @ X0 @ X1 @ X2)) = $true) <=> ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f9,definition,(
  ! [X2 : a,X1 : a,X0 : (a > a > $o)] : ((((sP2 @ X0 @ X1 @ X2)) = $true) <=> ! [X3 : (a > a > $o)] : ((((X3 @ X1 @ X2)) = $true) | ? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) & (((X3 @ X4 @ X5)) != $true)) | (((sP0 @ X3 @ X0)) = $true)))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f10,plain,(
  ? [X1 : a,X0 : (a > a > $o),X2 : a] : ((((sP1 @ X0 @ X1 @ X2)) = $true) <~> (((sP2 @ X0 @ X1 @ X2)) = $true))),
  inference(definition_folding,[],[f6,f9,f8,f7])).
thf(f11,plain,(
  ! [X2 : a,X1 : a,X0 : (a > a > $o)] : (((((sP2 @ X0 @ X1 @ X2)) = $true) | ? [X3 : (a > a > $o)] : ((((X3 @ X1 @ X2)) != $true) & ! [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) | (((X3 @ X4 @ X5)) = $true)) & (((sP0 @ X3 @ X0)) != $true))) & (! [X3 : (a > a > $o)] : ((((X3 @ X1 @ X2)) = $true) | ? [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) = $true) & (((X3 @ X4 @ X5)) != $true)) | (((sP0 @ X3 @ X0)) = $true)) | (((sP2 @ X0 @ X1 @ X2)) != $true)))),
  inference(nnf_transformation,[],[f9])).
thf(f12,plain,(
  ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (((((sP2 @ X2 @ X1 @ X0)) = $true) | ? [X3 : (a > a > $o)] : ((((X3 @ X1 @ X0)) != $true) & ! [X4 : a,X5 : a] : ((((X3 @ X5 @ X4)) != $true) | (((X3 @ X4 @ X5)) = $true)) & (((sP0 @ X3 @ X2)) != $true))) & (! [X6 : (a > a > $o)] : ((((X6 @ X1 @ X0)) = $true) | ? [X7 : a,X8 : a] : ((((X6 @ X8 @ X7)) = $true) & (((X6 @ X7 @ X8)) != $true)) | (((sP0 @ X6 @ X2)) = $true)) | (((sP2 @ X2 @ X1 @ X0)) != $true)))),
  inference(rectify,[],[f11])).
thf(f13,plain,(
  ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (((((sP2 @ X2 @ X1 @ X0)) = $true) | ((((sK3 @ X2 @ X1 @ X0 @ X1 @ X0)) != $true) & ! [X4 : a,X5 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X5 @ X4)) != $true) | (((sK3 @ X2 @ X1 @ X0 @ X4 @ X5)) = $true)) & (((sP0 @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true))) & (! [X6 : (a > a > $o)] : ((((X6 @ X1 @ X0)) = $true) | ((((X6 @ (sK5 @ X6) @ (sK4 @ X6))) = $true) & (((X6 @ (sK4 @ X6) @ (sK5 @ X6))) != $true)) | (((sP0 @ X6 @ X2)) = $true)) | (((sP2 @ X2 @ X1 @ X0)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X8,$thf(sK5 @ X6)),skolemize(X8,$thf(sK5 @ X6)),skolemize(X8,$thf(sK5 @ X6))],[f12])).
thf(f14,plain,(
  ! [X2 : a,X1 : a,X0 : (a > a > $o)] : (((((sP1 @ X0 @ X1 @ X2)) = $true) | ((((X0 @ X1 @ X2)) != $true) & (((X0 @ X2 @ X1)) != $true))) & (((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true)) | (((sP1 @ X0 @ X1 @ X2)) != $true)))),
  inference(nnf_transformation,[],[f8])).
thf(f15,plain,(
  ! [X2 : a,X1 : a,X0 : (a > a > $o)] : (((((sP1 @ X0 @ X1 @ X2)) = $true) | ((((X0 @ X1 @ X2)) != $true) & (((X0 @ X2 @ X1)) != $true))) & ((((X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) = $true) | (((sP1 @ X0 @ X1 @ X2)) != $true)))),
  inference(flattening,[],[f14])).
thf(f16,plain,(
  ! [X0 : a,X1 : a,X2 : (a > a > $o)] : (((((sP1 @ X2 @ X1 @ X0)) = $true) | ((((X2 @ X1 @ X0)) != $true) & (((X2 @ X0 @ X1)) != $true))) & ((((X2 @ X1 @ X0)) = $true) | (((X2 @ X0 @ X1)) = $true) | (((sP1 @ X2 @ X1 @ X0)) != $true)))),
  inference(rectify,[],[f15])).
thf(f17,plain,(
  ! [X0 : (a > a > $o),X3 : (a > a > $o)] : (((((sP0 @ X3 @ X0)) = $true) | ! [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) != $true) | (((X3 @ X7 @ X6)) = $true))) & (? [X6 : a,X7 : a] : ((((X0 @ X7 @ X6)) = $true) & (((X3 @ X7 @ X6)) != $true)) | (((sP0 @ X3 @ X0)) != $true)))),
  inference(nnf_transformation,[],[f7])).
thf(f18,plain,(
  ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (((((sP0 @ X1 @ X0)) = $true) | ! [X2 : a,X3 : a] : ((((X0 @ X3 @ X2)) != $true) | (((X1 @ X3 @ X2)) = $true))) & (? [X4 : a,X5 : a] : ((((X0 @ X5 @ X4)) = $true) & (((X1 @ X5 @ X4)) != $true)) | (((sP0 @ X1 @ X0)) != $true)))),
  inference(rectify,[],[f17])).
thf(f19,plain,(
  ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (((((sP0 @ X1 @ X0)) = $true) | ! [X2 : a,X3 : a] : ((((X0 @ X3 @ X2)) != $true) | (((X1 @ X3 @ X2)) = $true))) & (((((X0 @ (sK7 @ X1 @ X0) @ (sK6 @ X1 @ X0))) = $true) & (((X1 @ (sK7 @ X1 @ X0) @ (sK6 @ X1 @ X0))) != $true)) | (((sP0 @ X1 @ X0)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X8,$thf(sK5 @ X6)),skolemize(X8,$thf(sK5 @ X6))],[f18])).
thf(f20,plain,(
  ? [X1 : a,X0 : (a > a > $o),X2 : a] : (((((sP2 @ X0 @ X1 @ X2)) != $true) | (((sP1 @ X0 @ X1 @ X2)) != $true)) & ((((sP2 @ X0 @ X1 @ X2)) = $true) | (((sP1 @ X0 @ X1 @ X2)) = $true)))),
  inference(nnf_transformation,[],[f10])).
thf(f21,plain,(
  ? [X0 : a,X1 : (a > a > $o),X2 : a] : (((((sP2 @ X1 @ X0 @ X2)) != $true) | (((sP1 @ X1 @ X0 @ X2)) != $true)) & ((((sP2 @ X1 @ X0 @ X2)) = $true) | (((sP1 @ X1 @ X0 @ X2)) = $true)))),
  inference(rectify,[],[f20])).
thf(f22,plain,(
  ((((sP2 @ sK9 @ sK8 @ sK10)) != $true) | (((sP1 @ sK9 @ sK8 @ sK10)) != $true)) & ((((sP2 @ sK9 @ sK8 @ sK10)) = $true) | (((sP1 @ sK9 @ sK8 @ sK10)) = $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,$thf(sK8)),skolemize(X1,$thf(sK9)),skolemize(X2,$thf(sK10))],[f21])).
thf(f23,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X6 : (a > a > $o)] : ((((X6 @ (sK4 @ X6) @ (sK5 @ X6))) != $true) | (((sP2 @ X2 @ X1 @ X0)) != $true) | (((X6 @ X1 @ X0)) = $true) | (((sP0 @ X6 @ X2)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f24,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X6 : (a > a > $o)] : ((((X6 @ (sK5 @ X6) @ (sK4 @ X6))) = $true) | (((X6 @ X1 @ X0)) = $true) | (((sP2 @ X2 @ X1 @ X0)) != $true) | (((sP0 @ X6 @ X2)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f25,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP0 @ (sK3 @ X2 @ X1 @ X0) @ X2)) != $true) | (((sP2 @ X2 @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f26,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a,X4 : a,X5 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X4 @ X5)) = $true) | (((sK3 @ X2 @ X1 @ X0 @ X5 @ X4)) != $true) | (((sP2 @ X2 @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f27,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sK3 @ X2 @ X1 @ X0 @ X1 @ X0)) != $true) | (((sP2 @ X2 @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f28,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP1 @ X2 @ X1 @ X0)) != $true) | (((X2 @ X0 @ X1)) = $true) | (((X2 @ X1 @ X0)) = $true)) )),
  inference(cnf_transformation,[],[f16])).
thf(f29,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP1 @ X2 @ X1 @ X0)) = $true) | (((X2 @ X0 @ X1)) != $true)) )),
  inference(cnf_transformation,[],[f16])).
thf(f30,plain,(
  ( ! [X2 : (a > a > $o),X0 : a,X1 : a] : ((((sP1 @ X2 @ X1 @ X0)) = $true) | (((X2 @ X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f16])).
thf(f31,plain,(
  ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X1 @ (sK7 @ X1 @ X0) @ (sK6 @ X1 @ X0))) != $true) | (((sP0 @ X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f19])).
thf(f32,plain,(
  ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X0 @ (sK7 @ X1 @ X0) @ (sK6 @ X1 @ X0))) = $true) | (((sP0 @ X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f19])).
thf(f33,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : ((((sP0 @ X1 @ X0)) = $true) | (((X0 @ X3 @ X2)) != $true) | (((X1 @ X3 @ X2)) = $true)) )),
  inference(cnf_transformation,[],[f19])).
thf(f34,plain,(
  (((sP2 @ sK9 @ sK8 @ sK10)) = $true) | (((sP1 @ sK9 @ sK8 @ sK10)) = $true)),
  inference(cnf_transformation,[],[f22])).
thf(f35,plain,(
  (((sP2 @ sK9 @ sK8 @ sK10)) != $true) | (((sP1 @ sK9 @ sK8 @ sK10)) != $true)),
  inference(cnf_transformation,[],[f22])).
thf(f37,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f38,definition,(
  (sF11 = ((sP2 @ sK9 @ sK8 @ sK10)))),
  introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
thf(f39,definition,(
  (sF12 = ((sP1 @ sK9 @ sK8 @ sK10)))),
  introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
thf(f40,plain,(
  (sF12 != $true) | (sF11 != $true)),
  inference(definition_folding,[],[f35,f39,f38])).
thf(f41,plain,(
  (sF12 = $true) | (sF11 = $true)),
  inference(definition_folding,[],[f34,f39,f38])).
thf(f42,plain,(
  (sF11 = $true) | ($false = ((sP2 @ sK9 @ sK8 @ sK10)))),
  inference(iff_proxy_clausification,[],[f38])).
thf(f43,plain,(
  (((sP2 @ sK9 @ sK8 @ sK10)) = $true) | (sF11 = $false)),
  inference(iff_proxy_clausification,[],[f38])).
thf(f44,plain,(
  ($false = ((sP1 @ sK9 @ sK8 @ sK10))) | (sF12 = $true)),
  inference(iff_proxy_clausification,[],[f39])).
thf(f45,plain,(
  ($false = sF12) | (((sP1 @ sK9 @ sK8 @ sK10)) = $true)),
  inference(iff_proxy_clausification,[],[f39])).
thf(f47,definition,(
  spl13_1 <=> (sF12 = $true)),
  introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition])).
thf(f48,plain,(
  (sF12 = $true) | ~spl13_1),
  inference(avatar_component_clause,[],[f47])).
thf(f51,definition,(
  spl13_2 <=> (sF11 = $true)),
  introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition])).
thf(f52,plain,(
  (sF11 = $true) | ~spl13_2),
  inference(avatar_component_clause,[],[f51])).
thf(f54,plain,(
  ~spl13_1 | ~spl13_2),
  inference(avatar_split_clause,[],[f40,f51,f47])).
thf(f56,definition,(
  spl13_3 <=> (sF11 = $false)),
  introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition])).
thf(f58,plain,(
  (sF11 = $false) | ~spl13_3),
  inference(avatar_component_clause,[],[f56])).
thf(f60,definition,(
  spl13_4 <=> (((sP2 @ sK9 @ sK8 @ sK10)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition])).
thf(f62,plain,(
  (((sP2 @ sK9 @ sK8 @ sK10)) = $true) | ~spl13_4),
  inference(avatar_component_clause,[],[f60])).
thf(f63,plain,(
  spl13_3 | spl13_4),
  inference(avatar_split_clause,[],[f43,f60,f56])).
thf(f65,definition,(
  spl13_5 <=> ($false = ((sP2 @ sK9 @ sK8 @ sK10)))),
  introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition])).
thf(f67,plain,(
  ($false = ((sP2 @ sK9 @ sK8 @ sK10))) | ~spl13_5),
  inference(avatar_component_clause,[],[f65])).
thf(f68,plain,(
  spl13_2 | spl13_5),
  inference(avatar_split_clause,[],[f42,f65,f51])).
thf(f69,plain,(
  spl13_2 | spl13_1),
  inference(avatar_split_clause,[],[f41,f47,f51])).
thf(f71,definition,(
  spl13_6 <=> ($false = sF12)),
  introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition])).
thf(f73,plain,(
  ($false = sF12) | ~spl13_6),
  inference(avatar_component_clause,[],[f71])).
thf(f75,definition,(
  spl13_7 <=> (((sP1 @ sK9 @ sK8 @ sK10)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition])).
thf(f77,plain,(
  (((sP1 @ sK9 @ sK8 @ sK10)) = $true) | ~spl13_7),
  inference(avatar_component_clause,[],[f75])).
thf(f78,plain,(
  spl13_6 | spl13_7),
  inference(avatar_split_clause,[],[f45,f75,f71])).
thf(f80,definition,(
  spl13_8 <=> ($false = ((sP1 @ sK9 @ sK8 @ sK10)))),
  introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition])).
thf(f82,plain,(
  ($false = ((sP1 @ sK9 @ sK8 @ sK10))) | ~spl13_8),
  inference(avatar_component_clause,[],[f80])).
thf(f83,plain,(
  spl13_8 | spl13_1),
  inference(avatar_split_clause,[],[f44,f47,f80])).
thf(f84,plain,(
  ($false = $true) | (~spl13_2 | ~spl13_3)),
  inference(forward_demodulation,[],[f58,f52])).
thf(f85,plain,(
  $false | (~spl13_2 | ~spl13_3)),
  inference(trivial_inequality_removal,[],[f84])).
thf(f86,plain,(
  ~spl13_2 | ~spl13_3),
  inference(avatar_contradiction_clause,[],[f85])).
thf(f88,plain,(
  ($false = $true) | (~spl13_1 | ~spl13_6)),
  inference(forward_demodulation,[],[f73,f48])).
thf(f89,plain,(
  $false | (~spl13_1 | ~spl13_6)),
  inference(trivial_inequality_removal,[],[f88])).
thf(f90,plain,(
  ~spl13_1 | ~spl13_6),
  inference(avatar_contradiction_clause,[],[f89])).
thf(f122,plain,(
  (((sK9 @ sK10 @ sK8)) = $true) | (((sK9 @ sK8 @ sK10)) = $true) | ($true != $true) | ~spl13_7),
  inference(constrained_superposition,[],[f28,f77])).
thf(f125,plain,(
  (((sK9 @ sK8 @ sK10)) = $true) | (((sK9 @ sK10 @ sK8)) = $true) | ~spl13_7),
  inference(trivial_inequality_removal,[],[f122])).
thf(f127,definition,(
  spl13_9 <=> (((sK9 @ sK10 @ sK8)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition])).
thf(f129,plain,(
  (((sK9 @ sK10 @ sK8)) = $true) | ~spl13_9),
  inference(avatar_component_clause,[],[f127])).
thf(f131,definition,(
  spl13_10 <=> (((sK9 @ sK8 @ sK10)) = $true)),
  introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition])).
thf(f134,plain,(
  spl13_9 | spl13_10 | ~spl13_7),
  inference(avatar_split_clause,[],[f125,f75,f131,f127])).
thf(f147,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sK3 @ X0 @ X1 @ X2 @ X1 @ X2)) = $false)) )),
  inference(constrained_superposition,[],[f27,f37])).
thf(f148,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X1 @ X2)) = $false) | (((sP2 @ X0 @ X1 @ X2)) = $true)) )),
  inference(trivial_inequality_removal,[],[f147])).
thf(f155,plain,(
  ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != $true) | (((X0 @ (sK7 @ (sP1 @ X0) @ X1) @ (sK6 @ (sP1 @ X0) @ X1))) != $true) | ($true != ((sP0 @ (sP1 @ X0) @ X1)))) )),
  inference(constrained_superposition,[],[f31,f30])).
thf(f162,plain,(
  ( ! [X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X0 @ (sK7 @ (sP1 @ X0) @ X1) @ (sK6 @ (sP1 @ X0) @ X1))) != $true) | ($true != ((sP0 @ (sP1 @ X0) @ X1)))) )),
  inference(trivial_inequality_removal,[],[f155])).
thf(f215,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : (($true != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sK3 @ X0 @ X1 @ X2 @ X3 @ X4)) = $true) | (((X0 @ X3 @ X4)) != $true)) )),
  inference(constrained_superposition,[],[f25,f33])).
thf(f217,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : a,X4 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X3 @ X4)) = $true) | (((X0 @ X3 @ X4)) != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true)) )),
  inference(trivial_inequality_removal,[],[f215])).
thf(f227,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((X0 @ X1 @ X2)) != $true) | ($false = $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X0 @ X1 @ X2)) = $true)) )),
  inference(constrained_superposition,[],[f217,f148])).
thf(f234,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($false = $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((X0 @ X1 @ X2)) != $true)) )),
  inference(duplicate_literal_removal,[],[f227])).
thf(f235,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP2 @ X0 @ X1 @ X2)) = $true) | (((X0 @ X1 @ X2)) != $true)) )),
  inference(trivial_inequality_removal,[],[f234])).
thf(f242,plain,(
  ($false = $true) | (((sK9 @ sK8 @ sK10)) != $true) | ~spl13_5),
  inference(constrained_superposition,[],[f235,f67])).
thf(f250,plain,(
  (((sK9 @ sK8 @ sK10)) != $true) | ~spl13_5),
  inference(trivial_inequality_removal,[],[f242])).
thf(f252,plain,(
  ~spl13_10 | ~spl13_5),
  inference(avatar_split_clause,[],[f250,f65,f131])).
thf(f256,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != $true) | (((X0 @ (sK4 @ (sP1 @ X0)) @ (sK5 @ (sP1 @ X0)))) != $true) | ($true != ((sP2 @ X1 @ X2 @ X3))) | ($true = ((sP0 @ (sP1 @ X0) @ X1))) | (((sP1 @ X0 @ X2 @ X3)) = $true)) )),
  inference(constrained_superposition,[],[f23,f30])).
thf(f257,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : (($true != $true) | (((X0 @ (sK5 @ (sP1 @ X0)) @ (sK4 @ (sP1 @ X0)))) != $true) | (((sP1 @ X0 @ X2 @ X3)) = $true) | ($true != ((sP2 @ X1 @ X2 @ X3))) | ($true = ((sP0 @ (sP1 @ X0) @ X1)))) )),
  inference(constrained_superposition,[],[f23,f29])).
thf(f263,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X0 @ (sK4 @ (sP1 @ X0)) @ (sK5 @ (sP1 @ X0)))) != $true) | ($true != ((sP2 @ X1 @ X2 @ X3))) | ($true = ((sP0 @ (sP1 @ X0) @ X1))) | (((sP1 @ X0 @ X2 @ X3)) = $true)) )),
  inference(trivial_inequality_removal,[],[f256])).
thf(f264,plain,(
  ( ! [X2 : a,X3 : a,X0 : (a > a > $o),X1 : (a > a > $o)] : ((((X0 @ (sK5 @ (sP1 @ X0)) @ (sK4 @ (sP1 @ X0)))) != $true) | ($true = ((sP0 @ (sP1 @ X0) @ X1))) | (((sP1 @ X0 @ X2 @ X3)) = $true) | ($true != ((sP2 @ X1 @ X2 @ X3)))) )),
  inference(trivial_inequality_removal,[],[f257])).
thf(f273,plain,(
  ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP2 @ X3 @ X1 @ X2)) != $true) | (((X0 @ (sK4 @ (sP1 @ X0)) @ (sK5 @ (sP1 @ X0)))) = $true) | (((sP1 @ X0 @ X1 @ X2)) = $true) | (((X0 @ (sK5 @ (sP1 @ X0)) @ (sK4 @ (sP1 @ X0)))) = $true) | (((sP0 @ (sP1 @ X0) @ X3)) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f28,f24])).
thf(f276,plain,(
  ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP0 @ (sP1 @ X0) @ X3)) = $true) | (((sP1 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X3 @ X1 @ X2)) != $true) | (((X0 @ (sK5 @ (sP1 @ X0)) @ (sK4 @ (sP1 @ X0)))) = $true) | (((X0 @ (sK4 @ (sP1 @ X0)) @ (sK5 @ (sP1 @ X0)))) = $true)) )),
  inference(trivial_inequality_removal,[],[f273])).
thf(f304,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f27,f26])).
thf(f313,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : (($true != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true)) )),
  inference(duplicate_literal_removal,[],[f304])).
thf(f314,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sK3 @ X0 @ X1 @ X2 @ X2 @ X1)) != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true)) )),
  inference(trivial_inequality_removal,[],[f313])).
thf(f326,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((X0 @ X2 @ X1)) != $true) | ($true != $true) | (((sP2 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X0 @ X1 @ X2)) = $true)) )),
  inference(constrained_superposition,[],[f314,f217])).
thf(f331,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP2 @ X0 @ X1 @ X2)) = $true) | ($true != $true) | (((X0 @ X2 @ X1)) != $true)) )),
  inference(duplicate_literal_removal,[],[f326])).
thf(f332,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP2 @ X0 @ X1 @ X2)) = $true) | (((X0 @ X2 @ X1)) != $true)) )),
  inference(trivial_inequality_removal,[],[f331])).
thf(f337,plain,(
  (((sK9 @ sK10 @ sK8)) != $true) | ($false = $true) | ~spl13_5),
  inference(constrained_superposition,[],[f67,f332])).
thf(f346,plain,(
  (((sK9 @ sK10 @ sK8)) != $true) | ~spl13_5),
  inference(trivial_inequality_removal,[],[f337])).
thf(f352,plain,(
  $false | (~spl13_5 | ~spl13_9)),
  inference(forward_subsumption_resolution,[],[f346,f129])).
thf(f353,plain,(
  ~spl13_5 | ~spl13_9),
  inference(avatar_contradiction_clause,[],[f352])).
thf(f501,plain,(
  ( ! [X0 : (a > a > $o)] : (($true != $true) | (((sP0 @ (sP1 @ X0) @ X0)) != $true) | (((sP0 @ (sP1 @ X0) @ X0)) != $true)) )),
  inference(constrained_superposition,[],[f162,f32])).
thf(f508,plain,(
  ( ! [X0 : (a > a > $o)] : (($true != $true) | (((sP0 @ (sP1 @ X0) @ X0)) != $true)) )),
  inference(duplicate_literal_removal,[],[f501])).
thf(f509,plain,(
  ( ! [X0 : (a > a > $o)] : ((((sP0 @ (sP1 @ X0) @ X0)) != $true)) )),
  inference(trivial_inequality_removal,[],[f508])).
thf(f934,plain,(
  ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP2 @ X3 @ X1 @ X2)) != $true) | (((sP1 @ X0 @ X1 @ X2)) = $true) | (((sP0 @ (sP1 @ X0) @ X3)) = $true) | (((X0 @ (sK4 @ (sP1 @ X0)) @ (sK5 @ (sP1 @ X0)))) = $true)) )),
  inference(forward_subsumption_resolution,[],[f276,f264])).
thf(f935,plain,(
  ( ! [X2 : a,X3 : (a > a > $o),X0 : (a > a > $o),X1 : a] : ((((sP0 @ (sP1 @ X0) @ X3)) = $true) | (((sP1 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X3 @ X1 @ X2)) != $true)) )),
  inference(forward_subsumption_resolution,[],[f934,f263])).
thf(f1048,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP2 @ X0 @ X1 @ X2)) != $true) | (((sP1 @ X0 @ X1 @ X2)) = $true) | ($true != $true)) )),
  inference(constrained_superposition,[],[f509,f935])).
thf(f1057,plain,(
  ( ! [X2 : a,X0 : (a > a > $o),X1 : a] : ((((sP1 @ X0 @ X1 @ X2)) = $true) | (((sP2 @ X0 @ X1 @ X2)) != $true)) )),
  inference(trivial_inequality_removal,[],[f1048])).
thf(f1061,plain,(
  ($false = $true) | (((sP2 @ sK9 @ sK8 @ sK10)) != $true) | ~spl13_8),
  inference(constrained_superposition,[],[f1057,f82])).
thf(f1099,plain,(
  (((sP2 @ sK9 @ sK8 @ sK10)) != $true) | ~spl13_8),
  inference(trivial_inequality_removal,[],[f1061])).
thf(f1106,plain,(
  $false | (~spl13_4 | ~spl13_8)),
  inference(forward_subsumption_resolution,[],[f1099,f62])).
thf(f1107,plain,(
  ~spl13_4 | ~spl13_8),
  inference(avatar_contradiction_clause,[],[f1106])).
cnf(s1, plain, ~spl13_1 | ~spl13_2, inference(sat_conversion,[],[f54])).
cnf(s2, plain, spl13_3 | spl13_4, inference(sat_conversion,[],[f63])).
cnf(s3, plain, spl13_2 | spl13_5, inference(sat_conversion,[],[f68])).
cnf(s4, plain, spl13_1 | spl13_2, inference(sat_conversion,[],[f69])).
cnf(s5, plain, spl13_6 | spl13_7, inference(sat_conversion,[],[f78])).
cnf(s6, plain, spl13_1 | spl13_8, inference(sat_conversion,[],[f83])).
cnf(s7, plain, ~spl13_2 | ~spl13_3, inference(sat_conversion,[],[f86])).
cnf(s8, plain, ~spl13_1 | ~spl13_6, inference(sat_conversion,[],[f90])).
cnf(s12, plain, ~spl13_7 | spl13_9 | spl13_10, inference(sat_conversion,[],[f134])).
cnf(s13, plain, ~spl13_5 | ~spl13_10, inference(sat_conversion,[],[f252])).
cnf(s16, plain, ~spl13_5 | ~spl13_9, inference(sat_conversion,[],[f353])).
cnf(s27, plain, ~spl13_4 | ~spl13_8, inference(sat_conversion,[],[f1107])).
cnf(s29, plain, spl13_1, inference(rat,[],[s2,s7,s27,s4,s6])).
cnf(s30, plain, ~spl13_6, inference(rat,[],[s8,s29])).
cnf(s31, plain, ~spl13_2, inference(rat,[],[s1,s29])).
cnf(s32, plain, spl13_7, inference(rat,[],[s5,s30])).
cnf(s34, plain, spl13_5, inference(rat,[],[s3,s31])).
cnf(s36, plain, ~spl13_9, inference(rat,[],[s16,s34])).
cnf(s37, plain, ~spl13_10, inference(rat,[],[s13,s34])).
cnf(s39, plain, $false, inference(rat,[],[s12,s32,s37,s36])).
thf(f1108,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s39])).
% SZS output end Proof for theBenchmark