%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, num: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, believes_THFTYPE_IiooI: ($i > $o > $o)).
thf(func_def_1, type, considers_THFTYPE_IiooI: ($i > $o > $o)).
thf(func_def_2, type, holdsDuring_THFTYPE_IiooI: ($i > $o > $o)).
thf(func_def_3, type, husband_THFTYPE_IiioI: ($i > $i > $o)).
thf(func_def_5, type, wife_THFTYPE_IiioI: ($i > $i > $o)).
thf(func_def_6, type, inverse_THFTYPE_IIiioIIiioIoI: (($i > $i > $o) > ($i > $i > $o) > $o)).
thf(func_def_7, type, vNOT: ($o > $o)).
thf(func_def_11, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_14, type, sK0: ($i > $o > $i)).
thf(f1,axiom,(
  ! [X0 : $i] : (~ ? [X1 : $i] : (holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_003)).
thf(f2,axiom,(
  ! [X0 : $o,X1 : $i] : ((believes_THFTYPE_IiooI @ X1 @ X0) => ? [X2 : $i] : (holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_002)).
thf(f3,axiom,(
  ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_001)).
thf(f4,axiom,(
  (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax)).
thf(f5,conjecture,(
  ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
thf(f6,negated_conjecture,(
  ~ ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
  inference(negated_conjecture,[status(cth)],[f5])).
thf(f7,plain,(
  ~ ? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ~ ? [X0 : $i] : (((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) = $true)),
  inference(fool_elimination,[],[f7])).
thf(f9,plain,(
  (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
  inference(rectify,[],[f4])).
thf(f10,plain,(
  (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
  inference(fool_elimination,[],[f9])).
thf(f11,plain,(
  ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X1 @ X2 @ X3) <=> (X0 @ X3 @ X2)))),
  inference(rectify,[],[f3])).
thf(f12,plain,(
  ! [X1 : ($i > $i > $o),X0 : ($i > $i > $o)] : ((((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) = $true) => ! [X3 : $i,X2 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))))),
  inference(fool_elimination,[],[f11])).
thf(f13,plain,(
  ! [X0 : $o,X1 : $i] : ((believes_THFTYPE_IiooI @ X1 @ X0) => ? [X2 : $i] : (holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)))),
  inference(rectify,[],[f2])).
thf(f14,plain,(
  ! [X0 : $o,X1 : $i] : ((((believes_THFTYPE_IiooI @ X1 @ X0)) = $true) => ? [X2 : $i] : (((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true))),
  inference(fool_elimination,[],[f13])).
thf(f15,plain,(
  ! [X0 : $i] : (~ ? [X1 : $i] : (holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))),
  inference(rectify,[],[f1])).
thf(f16,plain,(
  ! [X0 : $i] : (((~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))))) = $true)),
  inference(fool_elimination,[],[f15])).
thf(f17,plain,(
  ! [X0 : $i] : (((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) != $true)),
  inference(ennf_transformation,[],[f8])).
thf(f18,plain,(
  ! [X0 : $o,X1 : $i] : (? [X2 : $i] : (((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true) | (((believes_THFTYPE_IiooI @ X1 @ X0)) != $true))),
  inference(ennf_transformation,[],[f14])).
thf(f19,plain,(
  ! [X1 : ($i > $i > $o),X0 : ($i > $i > $o)] : (! [X3 : $i,X2 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | (((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0)) != $true))),
  inference(ennf_transformation,[],[f12])).
thf(f20,plain,(
  ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (! [X2 : $i,X3 : $i] : (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2))) | ($true != ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1))))),
  inference(rectify,[],[f19])).
thf(f21,plain,(
  ! [X0 : $o,X1 : $i] : ((((holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true) | (((believes_THFTYPE_IiooI @ X1 @ X0)) != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK0 @ X1 @ X0))],[f18])).
thf(f22,plain,(
  ( ! [X0 : $i] : ((((~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))))) = $true)) )),
  inference(cnf_transformation,[],[f16])).
thf(f23,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true != ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1))) | (((X1 @ X2 @ X3)) = ((X0 @ X3 @ X2)))) )),
  inference(cnf_transformation,[],[f20])).
thf(f24,plain,(
  ( ! [X0 : $o,X1 : $i] : ((((holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X1 @ X0))) = $true) | (((believes_THFTYPE_IiooI @ X1 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f21])).
thf(f25,plain,(
  (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
  inference(cnf_transformation,[],[f10])).
thf(f26,plain,(
  ( ! [X0 : $i] : ((((~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) != $true)) )),
  inference(cnf_transformation,[],[f17])).
thf(f28,plain,(
  ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))) = $true)) )),
  inference(not_proxy_clausification,[],[f26])).
thf(f29,plain,(
  ( ! [X0 : $i] : ((((?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))))) = $false)) )),
  inference(not_proxy_clausification,[],[f22])).
thf(f30,plain,(
  ( ! [X0 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f29])).
thf(f31,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) = $false)) )),
  inference(beta-eta_normalization,[],[f30])).
thf(f32,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true != ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1))) | (((X1 @ X2 @ X3)) = $true) | (((X0 @ X3 @ X2)) = $false)) )),
  inference(iff_proxy_clausification,[],[f23])).
thf(f33,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true != ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1))) | (((X1 @ X2 @ X3)) = $false) | (((X0 @ X3 @ X2)) = $true)) )),
  inference(iff_proxy_clausification,[],[f23])).
thf(f35,definition,(
  spl1_1 <=> (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true)),
  introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
thf(f37,plain,(
  (((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)) = $true) | ~spl1_1),
  inference(avatar_component_clause,[],[f35])).
thf(f38,plain,(
  spl1_1),
  inference(avatar_split_clause,[],[f25,f35])).
thf(f39,plain,(
  ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $true) | (((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $false)) )),
  inference(fool_paramodulation,[],[f28])).
thf(f41,definition,(
  spl1_2 <=> (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $true)),
  introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
thf(f45,definition,(
  spl1_3 <=> ! [X0 : $i] : (((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
thf(f46,plain,(
  ( ! [X0 : $i] : ((((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $false)) ) | ~spl1_3),
  inference(avatar_component_clause,[],[f45])).
thf(f47,plain,(
  spl1_2 | spl1_3),
  inference(avatar_split_clause,[],[f39,f45,f41])).
thf(f48,plain,(
  (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $true) | ~spl1_3),
  inference(superposition,[],[f28,f46])).
thf(f50,definition,(
  spl1_4 <=> (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $true)),
  introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
thf(f52,plain,(
  (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $true) | ~spl1_4),
  inference(avatar_component_clause,[],[f50])).
thf(f53,plain,(
  spl1_4 | ~spl1_3),
  inference(avatar_split_clause,[],[f48,f45,f50])).
thf(f67,definition,(
  spl1_8 <=> ! [X0 : $i] : (((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition])).
thf(f68,plain,(
  ( ! [X0 : $i] : ((((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $false)) ) | ~spl1_8),
  inference(avatar_component_clause,[],[f67])).
thf(f71,plain,(
  ( ! [X0 : $i] : (($true != ((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) | ($false = $true)) )),
  inference(superposition,[],[f24,f31])).
thf(f73,plain,(
  ( ! [X0 : $i] : (($true != ((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))) )),
  inference(trivial_inequality_removal,[],[f71])).
thf(f75,plain,(
  ( ! [X0 : $i] : ((((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $false) | (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) != $true)) )),
  inference(fool_paramodulation,[],[f73])).
thf(f76,plain,(
  ~spl1_2 | spl1_8),
  inference(avatar_split_clause,[],[f75,f67,f41])).
thf(f86,plain,(
  (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) != $true) | ~spl1_8),
  inference(superposition,[],[f73,f68])).
thf(f88,plain,(
  $false | (~spl1_4 | ~spl1_8)),
  inference(forward_subsumption_resolution,[],[f86,f52])).
thf(f89,plain,(
  ~spl1_4 | ~spl1_8),
  inference(avatar_contradiction_clause,[],[f88])).
thf(f104,plain,(
  ( ! [X0 : $i,X1 : $i] : (($false = ((husband_THFTYPE_IiioI @ X1 @ X0))) | ($true != $true) | ($true = ((wife_THFTYPE_IiioI @ X0 @ X1)))) ) | ~spl1_1),
  inference(superposition,[],[f32,f37])).
thf(f105,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((wife_THFTYPE_IiioI @ X0 @ X1))) | ($false = ((husband_THFTYPE_IiioI @ X1 @ X0)))) ) | ~spl1_1),
  inference(trivial_inequality_removal,[],[f104])).
thf(f107,plain,(
  ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) != $true) | (((husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $false)) ) | ~spl1_1),
  inference(superposition,[],[f73,f105])).
thf(f109,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((husband_THFTYPE_IiioI @ X1 @ X0))) | ($false = ((wife_THFTYPE_IiioI @ X0 @ X1)))) ) | ~spl1_1),
  inference(superposition,[],[f33,f37])).
thf(f110,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((husband_THFTYPE_IiioI @ X1 @ X0))) | ($false = ((wife_THFTYPE_IiioI @ X0 @ X1)))) ) | ~spl1_1),
  inference(trivial_inequality_removal,[],[f109])).
thf(f113,plain,(
  ( ! [X0 : $i] : ((((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $true) | (((wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)) = $false)) ) | ~spl1_1),
  inference(superposition,[],[f28,f110])).
thf(f119,plain,(
  ~spl1_2 | spl1_3 | ~spl1_1),
  inference(avatar_split_clause,[],[f107,f35,f45,f41])).
thf(f120,plain,(
  spl1_2 | spl1_8 | ~spl1_1),
  inference(avatar_split_clause,[],[f113,f35,f67,f41])).
cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f38])).
cnf(s2, plain, spl1_2 | spl1_3, inference(sat_conversion,[],[f47])).
cnf(s3, plain, ~spl1_3 | spl1_4, inference(sat_conversion,[],[f53])).
cnf(s6, plain, ~spl1_2 | spl1_8, inference(sat_conversion,[],[f76])).
cnf(s8, plain, ~spl1_4 | ~spl1_8, inference(sat_conversion,[],[f89])).
cnf(s16, plain, ~spl1_1 | ~spl1_2 | spl1_3, inference(sat_conversion,[],[f119])).
cnf(s17, plain, ~spl1_1 | spl1_2 | spl1_8, inference(sat_conversion,[],[f120])).
cnf(s19, plain, spl1_2, inference(rat,[],[s3,s8,s2,s17,s1])).
cnf(s20, plain, spl1_3, inference(rat,[],[s16,s1,s19])).
cnf(s22, plain, spl1_8, inference(rat,[],[s6,s19])).
cnf(s23, plain, spl1_4, inference(rat,[],[s3,s20])).
cnf(s24, plain, $false, inference(rat,[],[s8,s22,s23])).
thf(f125,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s24])).
% SZS output end Proof for theBenchmark