%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, x_a: $tType).
thf(type_def_6, type, com: $tType).
thf(type_def_7, type, state: $tType).
thf(type_def_8, type, hoare_669141180iple_a: $tType).
thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, skip: com).
thf(func_def_1, type, semi: (com > com > com)).
thf(func_def_2, type, ex: ((hoare_669141180iple_a > $o) > $o)).
thf(func_def_3, type, finite957651855iple_a: ((hoare_669141180iple_a > $o) > $o)).
thf(func_def_4, type, finite840267660iple_a: ((hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a) > (hoare_669141180iple_a > $o) > hoare_669141180iple_a > $o)).
thf(func_def_5, type, finite684844060iple_a: ((hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a) > (hoare_669141180iple_a > $o) > hoare_669141180iple_a)).
thf(func_def_6, type, finite590756294iple_a: ((hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a) > hoare_669141180iple_a > (hoare_669141180iple_a > $o) > hoare_669141180iple_a > $o)).
thf(func_def_7, type, finite972428089iple_a: ((hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a) > ((hoare_669141180iple_a > $o) > hoare_669141180iple_a) > $o)).
thf(func_def_8, type, finite252461622iple_a: ((hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a) > ((hoare_669141180iple_a > $o) > hoare_669141180iple_a) > $o)).
thf(func_def_9, type, the_Ho49089901iple_a: ((hoare_669141180iple_a > $o) > hoare_669141180iple_a)).
thf(func_def_10, type, hoare_2128652938rivs_a: ((hoare_669141180iple_a > $o) > (hoare_669141180iple_a > $o) > $o)).
thf(func_def_11, type, hoare_1295064928iple_a: ((x_a > state > $o) > com > (x_a > state > $o) > hoare_669141180iple_a)).
thf(func_def_12, type, bot_bo280939947le_a_o: (hoare_669141180iple_a > $o)).
thf(func_def_13, type, bot_bot_o: $o).
thf(func_def_14, type, collec1717965009iple_a: ((hoare_669141180iple_a > $o) > hoare_669141180iple_a > $o)).
thf(func_def_15, type, insert175534902iple_a: (hoare_669141180iple_a > (hoare_669141180iple_a > $o) > hoare_669141180iple_a > $o)).
thf(func_def_16, type, the_el738790235iple_a: ((hoare_669141180iple_a > $o) > hoare_669141180iple_a)).
thf(func_def_17, type, fequal182287803iple_a: (hoare_669141180iple_a > hoare_669141180iple_a > $o)).
thf(func_def_18, type, member1016246415iple_a: (hoare_669141180iple_a > (hoare_669141180iple_a > $o) > $o)).
thf(func_def_19, type, g: (hoare_669141180iple_a > $o)).
thf(func_def_20, type, p: (x_a > state > $o)).
thf(func_def_21, type, b: (state > $o)).
thf(func_def_22, type, c: com).
thf(func_def_24, type, vIMP: ($o > $o > $o)).
thf(func_def_25, type, vNOT: ($o > $o)).
thf(func_def_26, type, vAND: ($o > $o > $o)).
thf(func_def_27, type, vOR: ($o > $o > $o)).
thf(func_def_30, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_31, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_32, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_33, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_34, type, sK0: ((x_a > state > $o) > com > (hoare_669141180iple_a > $o) > (x_a > state > $o) > state)).
thf(func_def_35, type, sK1: ((x_a > state > $o) > com > (hoare_669141180iple_a > $o) > (x_a > state > $o) > x_a)).
thf(func_def_36, type, sK2: ((x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > com > (hoare_669141180iple_a > $o) > (x_a > state > $o) > state)).
thf(func_def_37, type, sK3: ((x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > state)).
thf(func_def_38, type, sK4: ((x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > x_a)).
thf(func_def_39, type, sK5: ((x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > (x_a > state > $o) > state)).
thf(func_def_40, type, sK6: ((x_a > state > $o) > (x_a > state > $o) > x_a)).
thf(func_def_41, type, sK7: ((x_a > state > $o) > (x_a > state > $o) > state)).
thf(func_def_42, type, sK8: ((x_a > state > $o) > (x_a > state > $o) > state)).
thf(func_def_43, type, sK9: ((x_a > state > $o) > (x_a > state > $o) > x_a)).
thf(func_def_44, type, sK10: (hoare_669141180iple_a > com)).
thf(func_def_45, type, sK11: (hoare_669141180iple_a > x_a > state > $o)).
thf(func_def_46, type, sK12: (hoare_669141180iple_a > x_a > state > $o)).
thf(func_def_47, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_48, type, db3: !>[X0: $tType]:(X0)).
thf(f14,conjecture,(
  (hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[X0 : x_a, X1 : state] : ($false)) @ c @ (^[X0 : x_a, X1 : state] : (((p @ X0 @ X1) & (~ (b @ X1)))))) @ bot_bo280939947le_a_o))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
thf(f15,negated_conjecture,(
  ~(hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[X0 : x_a, X1 : state] : ($false)) @ c @ (^[X0 : x_a, X1 : state] : (((p @ X0 @ X1) & (~ (b @ X1)))))) @ bot_bo280939947le_a_o))),
  inference(negated_conjecture,[status(cth)],[f14])).
thf(f31,axiom,(
  ! [X3 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X0 : (x_a > state > $o),X2 : com] : (! [X5 : state,X4 : x_a] : ((X3 @ X4 @ X5) => ? [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : (! [X8 : state] : (! [X9 : x_a] : ((X6 @ X9 @ X5) => (X7 @ X9 @ X8)) => (X0 @ X4 @ X8)) & (hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X2 @ X7) @ bot_bo280939947le_a_o)))) => (hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X3 @ X2 @ X0) @ bot_bo280939947le_a_o)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_conseq)).
thf(f71,axiom,(
  (bot_bo280939947le_a_o = ((collec1717965009iple_a @ (^[X0 : hoare_669141180iple_a] : ($false)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__def)).
thf(f130,plain,(
  (bot_bo280939947le_a_o = ((collec1717965009iple_a @ (^[X0 : hoare_669141180iple_a] : ($false)))))),
  inference(rectify,[],[f71])).
thf(f131,plain,(
  (bot_bo280939947le_a_o = ((collec1717965009iple_a @ (^[Y0 : hoare_669141180iple_a]: ($false)))))),
  inference(fool_elimination,[],[f130])).
thf(f132,plain,(
  ~(hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[X0 : x_a, X1 : state] : ($false)) @ c @ (^[X2 : x_a, X3 : state] : (((p @ X2 @ X3) & (~ (b @ X3)))))) @ bot_bo280939947le_a_o))),
  inference(rectify,[],[f15])).
thf(f133,plain,(
  ~ (((hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false)))) @ c @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1))))))) @ bot_bo280939947le_a_o))) = $true)),
  inference(fool_elimination,[],[f132])).
thf(f158,plain,(
  ! [X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X2 : (x_a > state > $o),X3 : com] : (! [X4 : state,X5 : x_a] : ((X0 @ X5 @ X4) => ? [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : (! [X8 : state] : (! [X9 : x_a] : ((X6 @ X9 @ X4) => (X7 @ X9 @ X8)) => (X2 @ X5 @ X8)) & (hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X3 @ X7) @ bot_bo280939947le_a_o)))) => (hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X3 @ X2) @ bot_bo280939947le_a_o)))),
  inference(rectify,[],[f31])).
thf(f159,plain,(
  ! [X3 : com,X2 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X0 : (x_a > state > $o)] : (! [X4 : state,X5 : x_a] : ((((X0 @ X5 @ X4)) = $true) => ? [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : ((((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X3 @ X7) @ bot_bo280939947le_a_o))) = $true) & ! [X8 : state] : (! [X9 : x_a] : ((((X6 @ X9 @ X4)) = $true) => (((X7 @ X9 @ X8)) = $true)) => (((X2 @ X5 @ X8)) = $true)))) => (((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X3 @ X2) @ bot_bo280939947le_a_o))) = $true))),
  inference(fool_elimination,[],[f158])).
thf(f260,plain,(
  (((hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false)))) @ c @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1))))))) @ bot_bo280939947le_a_o))) != $true)),
  inference(flattening,[],[f133])).
thf(f270,plain,(
  ! [X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X3 : com,X2 : (x_a > state > $o)] : ((((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X3 @ X2) @ bot_bo280939947le_a_o))) = $true) | ? [X4 : state,X5 : x_a] : (! [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : (? [X8 : state] : (! [X9 : x_a] : ((((X7 @ X9 @ X8)) = $true) | (((X6 @ X9 @ X4)) != $true)) & (((X2 @ X5 @ X8)) != $true)) | (((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X3 @ X7) @ bot_bo280939947le_a_o))) != $true)) & (((X0 @ X5 @ X4)) = $true)))),
  inference(ennf_transformation,[],[f159])).
thf(f295,plain,(
  ! [X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X2 : com,X3 : (x_a > state > $o)] : ((((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X2 @ X3) @ bot_bo280939947le_a_o))) = $true) | ? [X4 : state,X5 : x_a] : (! [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : (? [X8 : state] : (! [X9 : x_a] : ((((X7 @ X9 @ X8)) = $true) | (((X6 @ X9 @ X4)) != $true)) & (((X3 @ X5 @ X8)) != $true)) | (((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X2 @ X7) @ bot_bo280939947le_a_o))) != $true)) & (((X0 @ X5 @ X4)) = $true)))),
  inference(rectify,[],[f270])).
thf(f296,plain,(
  ! [X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o),X2 : com,X3 : (x_a > state > $o)] : ((((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X2 @ X3) @ bot_bo280939947le_a_o))) = $true) | (! [X6 : (x_a > state > $o),X7 : (x_a > state > $o)] : ((! [X9 : x_a] : ((((X7 @ X9 @ (sK2 @ X7 @ X6 @ X3 @ X2 @ X1 @ X0))) = $true) | (((X6 @ X9 @ (sK0 @ X3 @ X2 @ X1 @ X0))) != $true)) & (((X3 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X7 @ X6 @ X3 @ X2 @ X1 @ X0))) != $true)) | (((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X6 @ X2 @ X7) @ bot_bo280939947le_a_o))) != $true)) & (((X0 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK0 @ X3 @ X2 @ X1 @ X0))) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X8,$thf(sK2 @ X7 @ X6 @ X3 @ X2 @ X1 @ X0)),skolemize(X8,$thf(sK2 @ X7 @ X6 @ X3 @ X2 @ X1 @ X0)),skolemize(X8,$thf(sK2 @ X7 @ X6 @ X3 @ X2 @ X1 @ X0))],[f295])).
thf(f323,plain,(
  ( ! [X2 : com,X3 : (x_a > state > $o),X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o)] : ((((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X2 @ X3) @ bot_bo280939947le_a_o))) = $true) | (((X0 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK0 @ X3 @ X2 @ X1 @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f296])).
thf(f339,plain,(
  (bot_bo280939947le_a_o = ((collec1717965009iple_a @ (^[Y0 : hoare_669141180iple_a]: ($false)))))),
  inference(cnf_transformation,[],[f131])).
thf(f340,plain,(
  (((hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false)))) @ c @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1))))))) @ bot_bo280939947le_a_o))) != $true)),
  inference(cnf_transformation,[],[f260])).
thf(f360,plain,(
  ( ! [X2 : com,X3 : (x_a > state > $o),X0 : (x_a > state > $o),X1 : (hoare_669141180iple_a > $o)] : ((((X0 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK0 @ X3 @ X2 @ X1 @ X0))) = $true) | (((hoare_2128652938rivs_a @ X1 @ (insert175534902iple_a @ (hoare_1295064928iple_a @ X0 @ X2 @ X3) @ (collec1717965009iple_a @ (^[Y0 : hoare_669141180iple_a]: ($false)))))) = $true)) )),
  inference(definition_unfolding,[],[f323,f339])).
thf(f373,plain,(
  (((hoare_2128652938rivs_a @ g @ (insert175534902iple_a @ (hoare_1295064928iple_a @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false)))) @ c @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1))))))) @ (collec1717965009iple_a @ (^[Y0 : hoare_669141180iple_a]: ($false)))))) != $true)),
  inference(definition_unfolding,[],[f340,f339])).
thf(f394,plain,(
  ((((^[Y0 : x_a]: ((^[Y1 : state]: ($false)))) @ (sK1 @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1)))))) @ c @ g @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false))))) @ (sK0 @ (^[Y0 : x_a]: ((^[Y1 : state]: ((p @ Y0 @ Y1) & (~ (b @ Y1)))))) @ c @ g @ (^[Y0 : x_a]: ((^[Y1 : state]: ($false))))))) = $true)),
  inference(unit_resulting_resolution,[],[f360,f373])).
thf(f401,plain,(
  ($false = $true)),
  inference(beta-eta_normalization,[],[f394])).
thf(f402,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f401])).
% SZS output end Proof for theBenchmark