%----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_0, type, cR: (a > a > $o)).
thf(func_def_4, type, sK0: ((a > $o) > a)).
thf(func_def_5, type, sK1: (a > (a > $o) > a)).
thf(func_def_6, type, sK2: a).
thf(func_def_7, type, vNOT: ($o > $o)).
thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X1 : (a > $o)] : (? [X2 : a] : (X1 @ X2) => ? [X2 : a] : (! [X3 : a] : (((X1 @ X3) & ! [X0 : a] : ((X1 @ X0) => (cR @ X3 @ X0))) => (X3 = X2)) & (X1 @ X2) & ! [X0 : a] : ((X1 @ X0) => (cR @ X2 @ X0)))) => ! [X0 : a] : (cR @ X0 @ X0)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM542_pme)).
thf(f2,negated_conjecture,(
  ~(! [X1 : (a > $o)] : (? [X2 : a] : (X1 @ X2) => ? [X2 : a] : (! [X3 : a] : (((X1 @ X3) & ! [X0 : a] : ((X1 @ X0) => (cR @ X3 @ X0))) => (X3 = X2)) & (X1 @ X2) & ! [X0 : a] : ((X1 @ X0) => (cR @ X2 @ X0)))) => ! [X0 : a] : (cR @ X0 @ X0))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(! [X0 : (a > $o)] : (? [X1 : a] : (X0 @ X1) => ? [X2 : a] : (! [X3 : a] : (((X0 @ X3) & ! [X4 : a] : ((X0 @ X4) => (cR @ X3 @ X4))) => (X3 = X2)) & (X0 @ X2) & ! [X5 : a] : ((X0 @ X5) => (cR @ X2 @ X5)))) => ! [X6 : a] : (cR @ X6 @ X6))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(! [X0 : (a > $o)] : (? [X1 : a] : (((X0 @ X1)) = $true) => ? [X2 : a] : (! [X3 : a] : ((! [X4 : a] : ((((X0 @ X4)) = $true) => (((cR @ X3 @ X4)) = $true)) & (((X0 @ X3)) = $true)) => (X2 = X3)) & ! [X5 : a] : ((((X0 @ X5)) = $true) => (((cR @ X2 @ X5)) = $true)) & (((X0 @ X2)) = $true))) => ! [X6 : a] : (((cR @ X6 @ X6)) = $true))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X6 : a] : (((cR @ X6 @ X6)) != $true) & ! [X0 : (a > $o)] : (? [X2 : a] : (! [X3 : a] : ((X2 = X3) | (? [X4 : a] : ((((X0 @ X4)) = $true) & (((cR @ X3 @ X4)) != $true)) | (((X0 @ X3)) != $true))) & ! [X5 : a] : ((((cR @ X2 @ X5)) = $true) | (((X0 @ X5)) != $true)) & (((X0 @ X2)) = $true)) | ! [X1 : a] : (((X0 @ X1)) != $true))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ! [X0 : (a > $o)] : (? [X2 : a] : (! [X3 : a] : ((X2 = X3) | ? [X4 : a] : ((((X0 @ X4)) = $true) & (((cR @ X3 @ X4)) != $true)) | (((X0 @ X3)) != $true)) & (((X0 @ X2)) = $true) & ! [X5 : a] : ((((cR @ X2 @ X5)) = $true) | (((X0 @ X5)) != $true))) | ! [X1 : a] : (((X0 @ X1)) != $true)) & ? [X6 : a] : (((cR @ X6 @ X6)) != $true)),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ! [X0 : (a > $o)] : (? [X1 : a] : (! [X2 : a] : ((X1 = X2) | ? [X3 : a] : ((((X0 @ X3)) = $true) & (((cR @ X2 @ X3)) != $true)) | (((X0 @ X2)) != $true)) & (((X0 @ X1)) = $true) & ! [X4 : a] : ((((cR @ X1 @ X4)) = $true) | (((X0 @ X4)) != $true))) | ! [X5 : a] : (((X0 @ X5)) != $true)) & ? [X6 : a] : (((cR @ X6 @ X6)) != $true)),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X0 : (a > $o)] : ((! [X2 : a] : ((((sK0 @ X0)) = X2) | ((((X0 @ (sK1 @ X2 @ X0))) = $true) & (((cR @ X2 @ (sK1 @ X2 @ X0))) != $true)) | (((X0 @ X2)) != $true)) & (((X0 @ (sK0 @ X0))) = $true) & ! [X4 : a] : ((((cR @ (sK0 @ X0) @ X4)) = $true) | (((X0 @ X4)) != $true))) | ! [X5 : a] : (((X0 @ X5)) != $true)) & (((cR @ sK2 @ sK2)) != $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK2]),skolemize(X3,$thf(sK1 @ X2 @ X0)),skolemize(X3,$thf(sK1 @ X2 @ X0)),skolemize(X6,$thf(sK2))],[f7])).
thf(f9,plain,(
  (((cR @ sK2 @ sK2)) != $true)),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ( ! [X0 : (a > $o),X4 : a,X5 : a] : ((((X0 @ X5)) != $true) | (((X0 @ X4)) != $true) | (((cR @ (sK0 @ X0) @ X4)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ( ! [X0 : (a > $o),X5 : a] : ((((X0 @ X5)) != $true) | (((X0 @ (sK0 @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X0 : a] : ((((sK0 @ (= @ X0))) = X0)) )),
  inference(leibniz_equality_elimination,[],[f11])).
thf(f19,plain,(
  ( ! [X6 : (a > $o),X5 : a] : (($true != (((^[Y0 : a]: (~ (X6 @ Y0))) @ X5))) | ((((^[Y0 : a]: (~ (X6 @ Y0))) @ (sK0 @ (^[Y0 : a]: (~ (X6 @ Y0)))))) = $true)) )),
  inference(primitive_instantiation,[],[f11])).
thf(f24,plain,(
  ( ! [X6 : (a > $o),X5 : a] : ((((~ (X6 @ X5))) != $true) | (((~ (X6 @ (sK0 @ (^[Y0 : a]: (~ (X6 @ Y0))))))) = $true)) )),
  inference(beta-eta_normalization,[],[f19])).
thf(f25,plain,(
  ( ! [X6 : (a > $o),X5 : a] : ((((~ (X6 @ (sK0 @ (^[Y0 : a]: (~ (X6 @ Y0))))))) = $true) | (((X6 @ X5)) = $true)) )),
  inference(not_proxy_clausification,[],[f24])).
thf(f26,plain,(
  ( ! [X6 : (a > $o),X5 : a] : (($false = ((X6 @ (sK0 @ (^[Y0 : a]: (~ (X6 @ Y0))))))) | (((X6 @ X5)) = $true)) )),
  inference(not_proxy_clausification,[],[f25])).
thf(f33,plain,(
  ( ! [X7 : (a > $o),X5 : a] : (((((^[Y0 : a]: (~ (X7 @ Y0))) @ X5)) = $true) | ((((^[Y0 : a]: (~ (X7 @ Y0))) @ (sK0 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (~ (X7 @ Y1))) @ Y0)))))) = $false)) )),
  inference(primitive_instantiation,[],[f26])).
thf(f38,plain,(
  ( ! [X7 : (a > $o),X5 : a] : ((((~ (X7 @ X5))) = $true) | ($false = ((~ (X7 @ (sK0 @ (^[Y0 : a]: (~ (~ (X7 @ Y0)))))))))) )),
  inference(beta-eta_normalization,[],[f33])).
thf(f39,plain,(
  ( ! [X7 : (a > $o),X5 : a] : ((((X7 @ X5)) = $false) | ($false = ((~ (X7 @ (sK0 @ (^[Y0 : a]: (~ (~ (X7 @ Y0)))))))))) )),
  inference(not_proxy_clausification,[],[f38])).
thf(f40,plain,(
  ( ! [X7 : (a > $o),X5 : a] : ((((X7 @ X5)) = $false) | (((X7 @ (sK0 @ (^[Y0 : a]: (~ (~ (X7 @ Y0))))))) = $true)) )),
  inference(not_proxy_clausification,[],[f39])).
thf(f41,plain,(
  ( ! [X7 : (a > $o),X5 : a] : ((((X7 @ (sK0 @ (^[Y0 : a]: (X7 @ Y0))))) = $true) | (((X7 @ X5)) = $false)) )),
  inference(boolean_simplification,[],[f40])).
thf(f42,plain,(
  ( ! [X7 : (a > $o),X5 : a] : ((((X7 @ (sK0 @ X7))) = $true) | (((X7 @ X5)) = $false)) )),
  inference(beta-eta_normalization,[],[f41])).
thf(f92,plain,(
  ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | ($true != $true) | ($false = ((X0 @ X2))) | (((cR @ (sK0 @ X0) @ X1)) = $true)) )),
  inference(constrained_superposition,[],[f10,f42])).
thf(f101,plain,(
  ( ! [X2 : a,X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | ($false = ((X0 @ X2))) | (((cR @ (sK0 @ X0) @ X1)) = $true)) )),
  inference(trivial_inequality_removal,[],[f92])).
thf(f130,plain,(
  ( ! [X2 : a,X0 : (a > $o),X1 : a] : (($true != $true) | ($false = ((X0 @ X2))) | (((cR @ (sK0 @ X0) @ (sK0 @ X0))) = $true) | ($false = ((X0 @ X1)))) )),
  inference(constrained_superposition,[],[f101,f42])).
thf(f141,plain,(
  ( ! [X2 : a,X0 : (a > $o),X1 : a] : (($false = ((X0 @ X1))) | (((cR @ (sK0 @ X0) @ (sK0 @ X0))) = $true) | ($false = ((X0 @ X2)))) )),
  inference(trivial_inequality_removal,[],[f130])).
thf(f168,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : ((((cR @ X0 @ X0)) = $true) | ($false = ((X0 = X2))) | (((X0 = X1)) = $false)) )),
  inference(constrained_superposition,[],[f141,f16])).
thf(f193,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : ((X0 != X2) | (((cR @ X0 @ X0)) = $true) | (((X0 = X1)) = $false)) )),
  inference(equality_proxy_clausification,[],[f168])).
thf(f194,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : ((((cR @ X0 @ X0)) = $true) | (X0 != X1) | (X0 != X2)) )),
  inference(equality_proxy_clausification,[],[f193])).
thf(f228,plain,(
  ( ! [X0 : a,X1 : a] : ((sK2 != X1) | (sK2 != X0) | ($true != $true)) )),
  inference(constrained_superposition,[],[f9,f194])).
thf(f232,plain,(
  ( ! [X0 : a,X1 : a] : ((sK2 != X0) | (sK2 != X1)) )),
  inference(trivial_inequality_removal,[],[f228])).
thf(f237,definition,(
  spl3_1 <=> ! [X1 : a] : (sK2 != X1)),
  introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
thf(f238,plain,(
  ( ! [X1 : a] : ((sK2 != X1)) ) | ~spl3_1),
  inference(avatar_component_clause,[],[f237])).
thf(f239,plain,(
  spl3_1 | spl3_1),
  inference(avatar_split_clause,[],[f232,f237,f237])).
thf(f240,plain,(
  (sK2 != sK2) | ~spl3_1),
  inference(imitation,[],[f238])).
thf(f243,plain,(
  $false | ~spl3_1),
  inference(trivial_inequality_removal,[],[f240])).
thf(f244,plain,(
  ~spl3_1),
  inference(avatar_contradiction_clause,[],[f243])).
cnf(s1, plain, spl3_1 | spl3_1, inference(sat_conversion,[],[f239])).
cnf(s2, plain, spl3_1, inference(rat,[],[s1])).
cnf(s4, plain, ~spl3_1, inference(sat_conversion,[],[f244])).
cnf(s5, plain, $false, inference(rat,[],[s2,s4])).
thf(f245,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s5])).
% SZS output end Proof for theBenchmark