%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, cQ: ($i > $o)).
thf(func_def_1, type, cP: ($i > $o)).
thf(func_def_5, type, sP0: $o).
thf(func_def_8, type, sK3: ($i > $i)).
thf(func_def_17, type, sK12: ($i > $i)).
thf(func_def_18, type, sK13: ($i > $i)).
thf(func_def_26, type, sK21: ($i > $i)).
thf(f1,conjecture,(
  ((? [X0 : $i] : (cQ @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1) <=> (cP @ X0))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2129)).
thf(f2,negated_conjecture,(
  ~(((? [X0 : $i] : (cQ @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1) <=> (cP @ X0))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~(((? [X0 : $i] : (cQ @ X0) <=> ! [X1 : $i] : (cP @ X1)) <=> ? [X2 : $i] : ! [X3 : $i] : ((cP @ X3) <=> (cP @ X2))) <=> ((? [X4 : $i] : (cP @ X4) <=> ! [X5 : $i] : (cQ @ X5)) <=> ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X7) <=> (cQ @ X6))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~(((? [X4 : $i] : ($true = ((cP @ X4))) <=> ! [X5 : $i] : (((cQ @ X5)) = $true)) <=> ? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6)))) <=> (? [X2 : $i] : ! [X3 : $i] : (((cP @ X2)) = ((cP @ X3))) <=> (! [X1 : $i] : (((cP @ X1)) = $true) <=> ? [X0 : $i] : (((cQ @ X0)) = $true))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  (? [X2 : $i] : ! [X3 : $i] : (((cP @ X2)) = ((cP @ X3))) <=> (! [X1 : $i] : (((cP @ X1)) = $true) <=> ? [X0 : $i] : (((cQ @ X0)) = $true))) <~> ((? [X4 : $i] : ($true = ((cP @ X4))) <=> ! [X5 : $i] : (((cQ @ X5)) = $true)) <=> ? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,definition,(
  ($true = sP0) <=> (? [X2 : $i] : ! [X3 : $i] : (((cP @ X2)) = ((cP @ X3))) <=> (! [X1 : $i] : (((cP @ X1)) = $true) <=> ? [X0 : $i] : (((cQ @ X0)) = $true)))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f7,plain,(
  ($true = sP0) <~> ((? [X4 : $i] : ($true = ((cP @ X4))) <=> ! [X5 : $i] : (((cQ @ X5)) = $true)) <=> ? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6))))),
  inference(definition_folding,[],[f5,f6])).
thf(f8,plain,(
  (($true = sP0) | ((((! [X0 : $i] : (((cQ @ X0)) != $true) | ? [X1 : $i] : (((cP @ X1)) != $true)) & (? [X0 : $i] : (((cQ @ X0)) = $true) | ! [X1 : $i] : (((cP @ X1)) = $true))) | ! [X2 : $i] : ? [X3 : $i] : (((cP @ X2)) != ((cP @ X3)))) & (((! [X1 : $i] : (((cP @ X1)) = $true) | ! [X0 : $i] : (((cQ @ X0)) != $true)) & (? [X0 : $i] : (((cQ @ X0)) = $true) | ? [X1 : $i] : (((cP @ X1)) != $true))) | ? [X2 : $i] : ! [X3 : $i] : (((cP @ X2)) = ((cP @ X3)))))) & (((? [X2 : $i] : ! [X3 : $i] : (((cP @ X2)) = ((cP @ X3))) | ((! [X0 : $i] : (((cQ @ X0)) != $true) | ? [X1 : $i] : (((cP @ X1)) != $true)) & (? [X0 : $i] : (((cQ @ X0)) = $true) | ! [X1 : $i] : (((cP @ X1)) = $true)))) & (((! [X1 : $i] : (((cP @ X1)) = $true) | ! [X0 : $i] : (((cQ @ X0)) != $true)) & (? [X0 : $i] : (((cQ @ X0)) = $true) | ? [X1 : $i] : (((cP @ X1)) != $true))) | ! [X2 : $i] : ? [X3 : $i] : (((cP @ X2)) != ((cP @ X3))))) | ($true != sP0))),
  inference(nnf_transformation,[],[f6])).
thf(f9,plain,(
  (($true = sP0) | ((((! [X0 : $i] : (((cQ @ X0)) != $true) | ? [X1 : $i] : (((cP @ X1)) != $true)) & (? [X2 : $i] : ($true = ((cQ @ X2))) | ! [X3 : $i] : ($true = ((cP @ X3))))) | ! [X4 : $i] : ? [X5 : $i] : (((cP @ X5)) != ((cP @ X4)))) & (((! [X6 : $i] : ($true = ((cP @ X6))) | ! [X7 : $i] : ($true != ((cQ @ X7)))) & (? [X8 : $i] : ($true = ((cQ @ X8))) | ? [X9 : $i] : ($true != ((cP @ X9))))) | ? [X10 : $i] : ! [X11 : $i] : (((cP @ X10)) = ((cP @ X11)))))) & (((? [X12 : $i] : ! [X13 : $i] : (((cP @ X13)) = ((cP @ X12))) | ((! [X14 : $i] : (((cQ @ X14)) != $true) | ? [X15 : $i] : ($true != ((cP @ X15)))) & (? [X16 : $i] : (((cQ @ X16)) = $true) | ! [X17 : $i] : ($true = ((cP @ X17)))))) & (((! [X18 : $i] : ($true = ((cP @ X18))) | ! [X19 : $i] : (((cQ @ X19)) != $true)) & (? [X20 : $i] : (((cQ @ X20)) = $true) | ? [X21 : $i] : ($true != ((cP @ X21))))) | ! [X22 : $i] : ? [X23 : $i] : (((cP @ X23)) != ((cP @ X22))))) | ($true != sP0))),
  inference(rectify,[],[f8])).
thf(f10,plain,(
  (($true = sP0) | ((((! [X0 : $i] : (((cQ @ X0)) != $true) | (((cP @ sK1)) != $true)) & (($true = ((cQ @ sK2))) | ! [X3 : $i] : ($true = ((cP @ X3))))) | ! [X4 : $i] : (((cP @ (sK3 @ X4))) != ((cP @ X4)))) & (((! [X6 : $i] : ($true = ((cP @ X6))) | ! [X7 : $i] : ($true != ((cQ @ X7)))) & (($true = ((cQ @ sK4))) | ($true != ((cP @ sK5))))) | ! [X11 : $i] : (((cP @ sK6)) = ((cP @ X11)))))) & (((! [X13 : $i] : (((cP @ sK7)) = ((cP @ X13))) | ((! [X14 : $i] : (((cQ @ X14)) != $true) | ($true != ((cP @ sK8)))) & ((((cQ @ sK9)) = $true) | ! [X17 : $i] : ($true = ((cP @ X17)))))) & (((! [X18 : $i] : ($true = ((cP @ X18))) | ! [X19 : $i] : (((cQ @ X19)) != $true)) & (($true = ((cQ @ sK10))) | (((cP @ sK11)) != $true))) | ! [X22 : $i] : (((cP @ (sK12 @ X22))) != ((cP @ X22))))) | ($true != sP0))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,vAPP,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,vAPP]),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X23,$thf(sK12 @ X22)),skolemize(X8,$thf(sK4)),skolemize(X9,$thf(sK5)),skolemize(X10,$thf(sK6)),skolemize(X12,$thf(sK7)),skolemize(X15,$thf(sK8)),skolemize(X16,$thf(sK9)),skolemize(X20,$thf(sK10)),skolemize(X21,$thf(sK11)),skolemize(X23,$thf(sK12 @ X22))],[f9])).
thf(f11,plain,(
  (((! [X6 : $i] : ? [X7 : $i] : (((cQ @ X7)) != ((cQ @ X6))) | ((? [X5 : $i] : (((cQ @ X5)) != $true) | ! [X4 : $i] : ($true != ((cP @ X4)))) & (! [X5 : $i] : (((cQ @ X5)) = $true) | ? [X4 : $i] : ($true = ((cP @ X4)))))) & (? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6))) | ((? [X4 : $i] : ($true = ((cP @ X4))) | ? [X5 : $i] : (((cQ @ X5)) != $true)) & (! [X5 : $i] : (((cQ @ X5)) = $true) | ! [X4 : $i] : ($true != ((cP @ X4))))))) | ($true != sP0)) & (((((? [X4 : $i] : ($true = ((cP @ X4))) | ? [X5 : $i] : (((cQ @ X5)) != $true)) & (! [X5 : $i] : (((cQ @ X5)) = $true) | ! [X4 : $i] : ($true != ((cP @ X4))))) | ! [X6 : $i] : ? [X7 : $i] : (((cQ @ X7)) != ((cQ @ X6)))) & (? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6))) | ((? [X5 : $i] : (((cQ @ X5)) != $true) | ! [X4 : $i] : ($true != ((cP @ X4)))) & (! [X5 : $i] : (((cQ @ X5)) = $true) | ? [X4 : $i] : ($true = ((cP @ X4))))))) | ($true = sP0))),
  inference(nnf_transformation,[],[f7])).
thf(f12,plain,(
  (((! [X0 : $i] : ? [X1 : $i] : (((cQ @ X0)) != ((cQ @ X1))) | ((? [X2 : $i] : ($true != ((cQ @ X2))) | ! [X3 : $i] : ($true != ((cP @ X3)))) & (! [X4 : $i] : ($true = ((cQ @ X4))) | ? [X5 : $i] : (((cP @ X5)) = $true)))) & (? [X6 : $i] : ! [X7 : $i] : (((cQ @ X7)) = ((cQ @ X6))) | ((? [X8 : $i] : ($true = ((cP @ X8))) | ? [X9 : $i] : (((cQ @ X9)) != $true)) & (! [X10 : $i] : ($true = ((cQ @ X10))) | ! [X11 : $i] : ($true != ((cP @ X11))))))) | ($true != sP0)) & (((((? [X12 : $i] : ($true = ((cP @ X12))) | ? [X13 : $i] : (((cQ @ X13)) != $true)) & (! [X14 : $i] : (((cQ @ X14)) = $true) | ! [X15 : $i] : ($true != ((cP @ X15))))) | ! [X16 : $i] : ? [X17 : $i] : (((cQ @ X16)) != ((cQ @ X17)))) & (? [X18 : $i] : ! [X19 : $i] : (((cQ @ X19)) = ((cQ @ X18))) | ((? [X20 : $i] : (((cQ @ X20)) != $true) | ! [X21 : $i] : ($true != ((cP @ X21)))) & (! [X22 : $i] : ($true = ((cQ @ X22))) | ? [X23 : $i] : (((cP @ X23)) = $true))))) | ($true = sP0))),
  inference(rectify,[],[f11])).
thf(f13,plain,(
  (((! [X0 : $i] : (((cQ @ X0)) != ((cQ @ (sK13 @ X0)))) | ((($true != ((cQ @ sK14))) | ! [X3 : $i] : ($true != ((cP @ X3)))) & (! [X4 : $i] : ($true = ((cQ @ X4))) | (((cP @ sK15)) = $true)))) & (! [X7 : $i] : (((cQ @ X7)) = ((cQ @ sK16))) | (((((cP @ sK17)) = $true) | ($true != ((cQ @ sK18)))) & (! [X10 : $i] : ($true = ((cQ @ X10))) | ! [X11 : $i] : ($true != ((cP @ X11))))))) | ($true != sP0)) & (((((($true = ((cP @ sK19))) | ($true != ((cQ @ sK20)))) & (! [X14 : $i] : (((cQ @ X14)) = $true) | ! [X15 : $i] : ($true != ((cP @ X15))))) | ! [X16 : $i] : (((cQ @ (sK21 @ X16))) != ((cQ @ X16)))) & (! [X19 : $i] : (((cQ @ X19)) = ((cQ @ sK22))) | ((($true != ((cQ @ sK23))) | ! [X21 : $i] : ($true != ((cP @ X21)))) & (! [X22 : $i] : ($true = ((cQ @ X22))) | ($true = ((cP @ sK24))))))) | ($true = sP0))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK14,sK15,sK16,sK17,sK18,sK19,sK20,vAPP,sK22,sK23,sK24]),skolemize(X23,$thf(sK12 @ X22)),skolemize(X2,$thf(sK14)),skolemize(X5,$thf(sK15)),skolemize(X6,$thf(sK16)),skolemize(X8,$thf(sK17)),skolemize(X9,$thf(sK18)),skolemize(X12,$thf(sK19)),skolemize(X13,$thf(sK20)),skolemize(X23,$thf(sK12 @ X22)),skolemize(X18,$thf(sK22)),skolemize(X20,$thf(sK23)),skolemize(X23,$thf(sK24))],[f12])).
thf(f14,plain,(
  ( ! [X22 : $i] : (($true != sP0) | (((cP @ sK11)) != $true) | ($true = ((cQ @ sK10))) | (((cP @ (sK12 @ X22))) != ((cP @ X22)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f15,plain,(
  ( ! [X18 : $i,X19 : $i,X22 : $i] : ((((cP @ (sK12 @ X22))) != ((cP @ X22))) | ($true = ((cP @ X18))) | ($true != sP0) | (((cQ @ X19)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f16,plain,(
  ( ! [X17 : $i,X13 : $i] : (($true != sP0) | ($true = ((cP @ X17))) | (((cP @ sK7)) = ((cP @ X13))) | (((cQ @ sK9)) = $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f19,plain,(
  ( ! [X11 : $i,X6 : $i,X7 : $i] : (($true != ((cQ @ X7))) | ($true = ((cP @ X6))) | ($true = sP0) | (((cP @ sK6)) = ((cP @ X11)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f20,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true = ((cP @ X3))) | ($true = sP0) | (((cP @ (sK3 @ X4))) != ((cP @ X4))) | ($true = ((cQ @ sK2)))) )),
  inference(cnf_transformation,[],[f10])).
thf(f21,plain,(
  ( ! [X0 : $i,X4 : $i] : ((((cQ @ X0)) != $true) | ($true = sP0) | (((cP @ (sK3 @ X4))) != ((cP @ X4))) | (((cP @ sK1)) != $true)) )),
  inference(cnf_transformation,[],[f10])).
thf(f22,plain,(
  ( ! [X19 : $i,X22 : $i] : ((((cQ @ X19)) = ((cQ @ sK22))) | ($true = ((cP @ sK24))) | ($true = sP0) | ($true = ((cQ @ X22)))) )),
  inference(cnf_transformation,[],[f13])).
thf(f24,plain,(
  ( ! [X16 : $i,X14 : $i,X15 : $i] : ((((cQ @ X14)) = $true) | (((cQ @ (sK21 @ X16))) != ((cQ @ X16))) | ($true != ((cP @ X15))) | ($true = sP0)) )),
  inference(cnf_transformation,[],[f13])).
thf(f25,plain,(
  ( ! [X16 : $i] : ((((cQ @ (sK21 @ X16))) != ((cQ @ X16))) | ($true != ((cQ @ sK20))) | ($true = ((cP @ sK19))) | ($true = sP0)) )),
  inference(cnf_transformation,[],[f13])).
thf(f26,plain,(
  ( ! [X10 : $i,X11 : $i,X7 : $i] : ((((cQ @ X7)) = ((cQ @ sK16))) | ($true = ((cQ @ X10))) | ($true != ((cP @ X11))) | ($true != sP0)) )),
  inference(cnf_transformation,[],[f13])).
thf(f28,plain,(
  ( ! [X0 : $i,X4 : $i] : ((((cQ @ X0)) != ((cQ @ (sK13 @ X0)))) | ($true = ((cQ @ X4))) | ($true != sP0) | (((cP @ sK15)) = $true)) )),
  inference(cnf_transformation,[],[f13])).
thf(f29,plain,(
  ( ! [X3 : $i,X0 : $i] : (($true != ((cP @ X3))) | ($true != sP0) | ($true != ((cQ @ sK14))) | (((cQ @ X0)) != ((cQ @ (sK13 @ X0))))) )),
  inference(cnf_transformation,[],[f13])).
thf(f32,plain,(
  ( ! [X10 : $i,X11 : $i,X7 : $i] : (($false = ((cQ @ sK16))) | ($true = ((cQ @ X7))) | ($true = ((cQ @ X10))) | ($true != sP0) | ($true != ((cP @ X11)))) )),
  inference(iff_proxy_clausification,[],[f26])).
thf(f33,plain,(
  ( ! [X10 : $i,X11 : $i,X7 : $i] : (($true != sP0) | ($false = ((cQ @ X7))) | ($true = ((cQ @ X10))) | ($true != ((cP @ X11))) | ($true = ((cQ @ sK16)))) )),
  inference(iff_proxy_clausification,[],[f26])).
thf(f34,plain,(
  ( ! [X16 : $i,X14 : $i,X15 : $i] : (($true = sP0) | (((cQ @ X14)) = $true) | ($true != ((cP @ X15))) | (((cQ @ X16)) = $true) | (((cQ @ (sK21 @ X16))) = $true)) )),
  inference(xor_proxy_clausification,[],[f24])).
thf(f37,plain,(
  ( ! [X22 : $i] : (($true = ((cQ @ sK10))) | (((cP @ (sK12 @ X22))) = $false) | ($false = ((cP @ X22))) | (((cP @ sK11)) != $true) | ($true != sP0)) )),
  inference(xor_proxy_clausification,[],[f14])).
thf(f38,plain,(
  ( ! [X19 : $i,X22 : $i] : ((((cQ @ X19)) = $true) | ($true = sP0) | ($true = ((cQ @ X22))) | ($true = ((cP @ sK24))) | ($false = ((cQ @ sK22)))) )),
  inference(iff_proxy_clausification,[],[f22])).
thf(f39,plain,(
  ( ! [X19 : $i,X22 : $i] : (($true = sP0) | ($true = ((cQ @ sK22))) | (((cQ @ X19)) = $false) | ($true = ((cQ @ X22))) | ($true = ((cP @ sK24)))) )),
  inference(iff_proxy_clausification,[],[f22])).
thf(f42,plain,(
  ( ! [X17 : $i,X13 : $i] : ((((cQ @ sK9)) = $true) | ($true != sP0) | ($true = ((cP @ X17))) | (((cP @ sK7)) = $true) | ($false = ((cP @ X13)))) )),
  inference(iff_proxy_clausification,[],[f16])).
thf(f43,plain,(
  ( ! [X17 : $i,X13 : $i] : (($true != sP0) | (((cQ @ sK9)) = $true) | (((cP @ sK7)) = $false) | (((cP @ X13)) = $true) | ($true = ((cP @ X17)))) )),
  inference(iff_proxy_clausification,[],[f16])).
thf(f45,plain,(
  ( ! [X16 : $i] : (($true = ((cP @ sK19))) | ($false = ((cQ @ X16))) | ($true != ((cQ @ sK20))) | ($false = ((cQ @ (sK21 @ X16)))) | ($true = sP0)) )),
  inference(xor_proxy_clausification,[],[f25])).
thf(f46,plain,(
  ( ! [X18 : $i,X19 : $i,X22 : $i] : (($true = ((cP @ X18))) | ($true = ((cP @ X22))) | ($true != sP0) | (((cP @ (sK12 @ X22))) = $true) | (((cQ @ X19)) != $true)) )),
  inference(xor_proxy_clausification,[],[f15])).
thf(f49,plain,(
  ( ! [X0 : $i,X4 : $i] : (($true = sP0) | (((cQ @ X0)) != $true) | (((cP @ sK1)) != $true) | ($false = ((cP @ X4))) | ($false = ((cP @ (sK3 @ X4))))) )),
  inference(xor_proxy_clausification,[],[f21])).
thf(f50,plain,(
  ( ! [X0 : $i,X4 : $i] : ((((cP @ sK15)) = $true) | (((cQ @ (sK13 @ X0))) = $true) | ($true = ((cQ @ X4))) | (((cQ @ X0)) = $true) | ($true != sP0)) )),
  inference(xor_proxy_clausification,[],[f28])).
thf(f56,plain,(
  ( ! [X11 : $i,X6 : $i,X7 : $i] : (($true = ((cP @ X6))) | ($true != ((cQ @ X7))) | (((cP @ sK6)) = $true) | ($false = ((cP @ X11))) | ($true = sP0)) )),
  inference(iff_proxy_clausification,[],[f19])).
thf(f57,plain,(
  ( ! [X11 : $i,X6 : $i,X7 : $i] : (($true = ((cP @ X6))) | ($true != ((cQ @ X7))) | (((cP @ sK6)) = $false) | ($true = sP0) | ($true = ((cP @ X11)))) )),
  inference(iff_proxy_clausification,[],[f19])).
thf(f58,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true = ((cP @ X4))) | ($true = ((cQ @ sK2))) | ($true = ((cP @ (sK3 @ X4)))) | ($true = ((cP @ X3))) | ($true = sP0)) )),
  inference(xor_proxy_clausification,[],[f20])).
thf(f63,plain,(
  ( ! [X3 : $i,X0 : $i] : (($true != ((cQ @ sK14))) | (((cQ @ X0)) = $false) | ($true != sP0) | (((cQ @ (sK13 @ X0))) = $false) | ($true != ((cP @ X3)))) )),
  inference(xor_proxy_clausification,[],[f29])).
thf(f65,definition,(
  spl25_1 <=> ! [X11 : $i] : ($true != ((cP @ X11)))),
  introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition])).
thf(f66,plain,(
  ( ! [X11 : $i] : (($true != ((cP @ X11)))) ) | ~spl25_1),
  inference(avatar_component_clause,[],[f65])).
thf(f68,definition,(
  spl25_2 <=> ($true = sP0)),
  introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition])).
thf(f72,definition,(
  spl25_3 <=> ! [X7 : $i] : ($false = ((cQ @ X7)))),
  introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition])).
thf(f73,plain,(
  ( ! [X7 : $i] : (($false = ((cQ @ X7)))) ) | ~spl25_3),
  inference(avatar_component_clause,[],[f72])).
thf(f75,definition,(
  spl25_4 <=> ! [X10 : $i] : ($true = ((cQ @ X10)))),
  introduced(definition,[new_symbols(definition,[spl25_4])],[avatar_definition])).
thf(f76,plain,(
  ( ! [X10 : $i] : (($true = ((cQ @ X10)))) ) | ~spl25_4),
  inference(avatar_component_clause,[],[f75])).
thf(f78,definition,(
  spl25_5 <=> ($true = ((cQ @ sK16)))),
  introduced(definition,[new_symbols(definition,[spl25_5])],[avatar_definition])).
thf(f80,plain,(
  ($true = ((cQ @ sK16))) | ~spl25_5),
  inference(avatar_component_clause,[],[f78])).
thf(f81,plain,(
  spl25_1 | ~spl25_2 | spl25_3 | spl25_4 | spl25_5),
  inference(avatar_split_clause,[],[f33,f78,f75,f72,f68,f65])).
thf(f83,definition,(
  spl25_6 <=> ($false = ((cQ @ sK16)))),
  introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition])).
thf(f85,plain,(
  ($false = ((cQ @ sK16))) | ~spl25_6),
  inference(avatar_component_clause,[],[f83])).
thf(f86,plain,(
  ~spl25_2 | spl25_4 | spl25_6 | spl25_1 | spl25_4),
  inference(avatar_split_clause,[],[f32,f75,f65,f83,f75,f68])).
thf(f88,definition,(
  spl25_7 <=> ! [X16 : $i] : (($false = ((cQ @ (sK21 @ X16)))) | ($false = ((cQ @ X16))))),
  introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition])).
thf(f89,plain,(
  ( ! [X16 : $i] : (($false = ((cQ @ (sK21 @ X16)))) | ($false = ((cQ @ X16)))) ) | ~spl25_7),
  inference(avatar_component_clause,[],[f88])).
thf(f92,definition,(
  spl25_8 <=> ! [X16 : $i] : ((((cQ @ X16)) = $true) | (((cQ @ (sK21 @ X16))) = $true))),
  introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition])).
thf(f93,plain,(
  ( ! [X16 : $i] : ((((cQ @ (sK21 @ X16))) = $true) | (((cQ @ X16)) = $true)) ) | ~spl25_8),
  inference(avatar_component_clause,[],[f92])).
thf(f94,plain,(
  spl25_8 | spl25_1 | spl25_4 | spl25_2),
  inference(avatar_split_clause,[],[f34,f68,f75,f65,f92])).
thf(f96,definition,(
  spl25_9 <=> ($true = ((cQ @ sK10)))),
  introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition])).
thf(f98,plain,(
  ($true = ((cQ @ sK10))) | ~spl25_9),
  inference(avatar_component_clause,[],[f96])).
thf(f100,definition,(
  spl25_10 <=> (((cP @ sK11)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition])).
thf(f102,plain,(
  (((cP @ sK11)) != $true) | spl25_10),
  inference(avatar_component_clause,[],[f100])).
thf(f104,definition,(
  spl25_11 <=> ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $false) | ($false = ((cP @ X22))))),
  introduced(definition,[new_symbols(definition,[spl25_11])],[avatar_definition])).
thf(f105,plain,(
  ( ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $false) | ($false = ((cP @ X22)))) ) | ~spl25_11),
  inference(avatar_component_clause,[],[f104])).
thf(f106,plain,(
  spl25_9 | ~spl25_2 | ~spl25_10 | spl25_11),
  inference(avatar_split_clause,[],[f37,f104,f100,f68,f96])).
thf(f108,definition,(
  spl25_12 <=> ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $true) | ($true = ((cP @ X22))))),
  introduced(definition,[new_symbols(definition,[spl25_12])],[avatar_definition])).
thf(f109,plain,(
  ( ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $true) | ($true = ((cP @ X22)))) ) | ~spl25_12),
  inference(avatar_component_clause,[],[f108])).
thf(f112,definition,(
  spl25_13 <=> ($true = ((cQ @ sK22)))),
  introduced(definition,[new_symbols(definition,[spl25_13])],[avatar_definition])).
thf(f114,plain,(
  ($true = ((cQ @ sK22))) | ~spl25_13),
  inference(avatar_component_clause,[],[f112])).
thf(f116,definition,(
  spl25_14 <=> ($true = ((cP @ sK24)))),
  introduced(definition,[new_symbols(definition,[spl25_14])],[avatar_definition])).
thf(f118,plain,(
  ($true = ((cP @ sK24))) | ~spl25_14),
  inference(avatar_component_clause,[],[f116])).
thf(f119,plain,(
  spl25_13 | spl25_14 | spl25_4 | spl25_3 | spl25_2),
  inference(avatar_split_clause,[],[f39,f68,f72,f75,f116,f112])).
thf(f121,definition,(
  spl25_15 <=> ($false = ((cQ @ sK22)))),
  introduced(definition,[new_symbols(definition,[spl25_15])],[avatar_definition])).
thf(f123,plain,(
  ($false = ((cQ @ sK22))) | ~spl25_15),
  inference(avatar_component_clause,[],[f121])).
thf(f124,plain,(
  spl25_15 | spl25_2 | spl25_14 | spl25_4 | spl25_4),
  inference(avatar_split_clause,[],[f38,f75,f75,f116,f68,f121])).
thf(f126,definition,(
  spl25_16 <=> (((cP @ sK7)) = $false)),
  introduced(definition,[new_symbols(definition,[spl25_16])],[avatar_definition])).
thf(f128,plain,(
  (((cP @ sK7)) = $false) | ~spl25_16),
  inference(avatar_component_clause,[],[f126])).
thf(f134,definition,(
  spl25_18 <=> ! [X13 : $i] : (((cP @ X13)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_18])],[avatar_definition])).
thf(f135,plain,(
  ( ! [X13 : $i] : ((((cP @ X13)) = $true)) ) | ~spl25_18),
  inference(avatar_component_clause,[],[f134])).
thf(f137,definition,(
  spl25_19 <=> ! [X14 : $i] : (((cQ @ X14)) != $true)),
  introduced(definition,[new_symbols(definition,[spl25_19])],[avatar_definition])).
thf(f138,plain,(
  ( ! [X14 : $i] : ((((cQ @ X14)) != $true)) ) | ~spl25_19),
  inference(avatar_component_clause,[],[f137])).
thf(f141,definition,(
  spl25_20 <=> ! [X13 : $i] : ($false = ((cP @ X13)))),
  introduced(definition,[new_symbols(definition,[spl25_20])],[avatar_definition])).
thf(f142,plain,(
  ( ! [X13 : $i] : (($false = ((cP @ X13)))) ) | ~spl25_20),
  inference(avatar_component_clause,[],[f141])).
thf(f144,definition,(
  spl25_21 <=> (((cP @ sK7)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_21])],[avatar_definition])).
thf(f146,plain,(
  (((cP @ sK7)) = $true) | ~spl25_21),
  inference(avatar_component_clause,[],[f144])).
thf(f149,definition,(
  spl25_22 <=> (((cQ @ sK9)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_22])],[avatar_definition])).
thf(f151,plain,(
  (((cQ @ sK9)) = $true) | ~spl25_22),
  inference(avatar_component_clause,[],[f149])).
thf(f152,plain,(
  spl25_18 | spl25_22 | spl25_16 | spl25_18 | ~spl25_2),
  inference(avatar_split_clause,[],[f43,f68,f134,f126,f149,f134])).
thf(f153,plain,(
  spl25_18 | spl25_22 | spl25_21 | ~spl25_2 | spl25_20),
  inference(avatar_split_clause,[],[f42,f141,f68,f144,f149,f134])).
thf(f155,definition,(
  spl25_23 <=> ($true = ((cP @ sK19)))),
  introduced(definition,[new_symbols(definition,[spl25_23])],[avatar_definition])).
thf(f157,plain,(
  ($true = ((cP @ sK19))) | ~spl25_23),
  inference(avatar_component_clause,[],[f155])).
thf(f159,definition,(
  spl25_24 <=> ($true = ((cQ @ sK20)))),
  introduced(definition,[new_symbols(definition,[spl25_24])],[avatar_definition])).
thf(f161,plain,(
  ($true != ((cQ @ sK20))) | spl25_24),
  inference(avatar_component_clause,[],[f159])).
thf(f162,plain,(
  spl25_2 | spl25_23 | ~spl25_24 | spl25_7),
  inference(avatar_split_clause,[],[f45,f88,f159,f155,f68])).
thf(f165,plain,(
  spl25_19 | spl25_12 | spl25_18 | ~spl25_2),
  inference(avatar_split_clause,[],[f46,f68,f134,f108,f137])).
thf(f167,definition,(
  spl25_25 <=> ! [X4 : $i] : (($false = ((cP @ X4))) | ($false = ((cP @ (sK3 @ X4)))))),
  introduced(definition,[new_symbols(definition,[spl25_25])],[avatar_definition])).
thf(f168,plain,(
  ( ! [X4 : $i] : (($false = ((cP @ (sK3 @ X4)))) | ($false = ((cP @ X4)))) ) | ~spl25_25),
  inference(avatar_component_clause,[],[f167])).
thf(f170,definition,(
  spl25_26 <=> (((cP @ sK1)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_26])],[avatar_definition])).
thf(f172,plain,(
  (((cP @ sK1)) != $true) | spl25_26),
  inference(avatar_component_clause,[],[f170])).
thf(f173,plain,(
  spl25_2 | spl25_19 | spl25_25 | ~spl25_26),
  inference(avatar_split_clause,[],[f49,f170,f167,f137,f68])).
thf(f175,definition,(
  spl25_27 <=> ! [X4 : $i] : (($true = ((cP @ X4))) | ($true = ((cP @ (sK3 @ X4)))))),
  introduced(definition,[new_symbols(definition,[spl25_27])],[avatar_definition])).
thf(f176,plain,(
  ( ! [X4 : $i] : (($true = ((cP @ (sK3 @ X4)))) | ($true = ((cP @ X4)))) ) | ~spl25_27),
  inference(avatar_component_clause,[],[f175])).
thf(f179,definition,(
  spl25_28 <=> (((cP @ sK15)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_28])],[avatar_definition])).
thf(f181,plain,(
  (((cP @ sK15)) = $true) | ~spl25_28),
  inference(avatar_component_clause,[],[f179])).
thf(f183,definition,(
  spl25_29 <=> ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $false) | (((cQ @ X0)) = $false))),
  introduced(definition,[new_symbols(definition,[spl25_29])],[avatar_definition])).
thf(f184,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $false) | (((cQ @ X0)) = $false)) ) | ~spl25_29),
  inference(avatar_component_clause,[],[f183])).
thf(f187,definition,(
  spl25_30 <=> ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $true) | (((cQ @ X0)) = $true))),
  introduced(definition,[new_symbols(definition,[spl25_30])],[avatar_definition])).
thf(f188,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $true) | (((cQ @ X0)) = $true)) ) | ~spl25_30),
  inference(avatar_component_clause,[],[f187])).
thf(f189,plain,(
  spl25_30 | ~spl25_2 | spl25_28 | spl25_4),
  inference(avatar_split_clause,[],[f50,f75,f179,f68,f187])).
thf(f207,definition,(
  spl25_34 <=> (((cP @ sK6)) = $false)),
  introduced(definition,[new_symbols(definition,[spl25_34])],[avatar_definition])).
thf(f209,plain,(
  (((cP @ sK6)) = $false) | ~spl25_34),
  inference(avatar_component_clause,[],[f207])).
thf(f210,plain,(
  spl25_18 | spl25_18 | spl25_2 | spl25_19 | spl25_34),
  inference(avatar_split_clause,[],[f57,f207,f137,f68,f134,f134])).
thf(f212,definition,(
  spl25_35 <=> (((cP @ sK6)) = $true)),
  introduced(definition,[new_symbols(definition,[spl25_35])],[avatar_definition])).
thf(f214,plain,(
  (((cP @ sK6)) = $true) | ~spl25_35),
  inference(avatar_component_clause,[],[f212])).
thf(f215,plain,(
  spl25_2 | spl25_19 | spl25_18 | spl25_35 | spl25_20),
  inference(avatar_split_clause,[],[f56,f141,f212,f134,f137,f68])).
thf(f217,definition,(
  spl25_36 <=> ($true = ((cQ @ sK2)))),
  introduced(definition,[new_symbols(definition,[spl25_36])],[avatar_definition])).
thf(f219,plain,(
  ($true = ((cQ @ sK2))) | ~spl25_36),
  inference(avatar_component_clause,[],[f217])).
thf(f221,plain,(
  spl25_2 | spl25_18 | spl25_36 | spl25_27),
  inference(avatar_split_clause,[],[f58,f175,f217,f134,f68])).
thf(f233,definition,(
  spl25_39 <=> ($true = ((cQ @ sK14)))),
  introduced(definition,[new_symbols(definition,[spl25_39])],[avatar_definition])).
thf(f235,plain,(
  ($true != ((cQ @ sK14))) | spl25_39),
  inference(avatar_component_clause,[],[f233])).
thf(f236,plain,(
  ~spl25_39 | spl25_1 | ~spl25_2 | spl25_29),
  inference(avatar_split_clause,[],[f63,f183,f68,f65,f233])).
thf(f238,plain,(
  $false | (~spl25_4 | spl25_39)),
  inference(forward_subsumption_resolution,[],[f235,f76])).
thf(f239,plain,(
  ~spl25_4 | spl25_39),
  inference(avatar_contradiction_clause,[],[f238])).
thf(f240,plain,(
  $false | (~spl25_1 | ~spl25_18)),
  inference(forward_subsumption_resolution,[],[f66,f135])).
thf(f241,plain,(
  ~spl25_1 | ~spl25_18),
  inference(avatar_contradiction_clause,[],[f240])).
thf(f242,plain,(
  ($false = $true) | (~spl25_5 | ~spl25_6)),
  inference(forward_demodulation,[],[f85,f80])).
thf(f243,plain,(
  $false | (~spl25_5 | ~spl25_6)),
  inference(trivial_inequality_removal,[],[f242])).
thf(f244,plain,(
  ~spl25_5 | ~spl25_6),
  inference(avatar_contradiction_clause,[],[f243])).
thf(f249,plain,(
  ($true != $true) | (spl25_10 | ~spl25_18)),
  inference(constrained_superposition,[],[f102,f135])).
thf(f253,plain,(
  $false | (spl25_10 | ~spl25_18)),
  inference(trivial_inequality_removal,[],[f249])).
thf(f254,plain,(
  spl25_10 | ~spl25_18),
  inference(avatar_contradiction_clause,[],[f253])).
thf(f256,plain,(
  ($false = $true) | (~spl25_3 | ~spl25_9)),
  inference(forward_demodulation,[],[f98,f73])).
thf(f257,plain,(
  $false | (~spl25_3 | ~spl25_9)),
  inference(trivial_inequality_removal,[],[f256])).
thf(f258,plain,(
  ~spl25_3 | ~spl25_9),
  inference(avatar_contradiction_clause,[],[f257])).
thf(f259,plain,(
  $false | (~spl25_4 | ~spl25_19)),
  inference(forward_subsumption_resolution,[],[f138,f76])).
thf(f260,plain,(
  ~spl25_4 | ~spl25_19),
  inference(avatar_contradiction_clause,[],[f259])).
thf(f261,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $false) | ($false = $true)) ) | (~spl25_4 | ~spl25_29)),
  inference(forward_demodulation,[],[f184,f76])).
thf(f262,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $false)) ) | (~spl25_4 | ~spl25_29)),
  inference(trivial_inequality_removal,[],[f261])).
thf(f263,plain,(
  ($false = $true) | (~spl25_4 | ~spl25_29)),
  inference(forward_demodulation,[],[f262,f76])).
thf(f264,plain,(
  $false | (~spl25_4 | ~spl25_29)),
  inference(trivial_inequality_removal,[],[f263])).
thf(f265,plain,(
  ~spl25_4 | ~spl25_29),
  inference(avatar_contradiction_clause,[],[f264])).
thf(f266,plain,(
  ( ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $false) | ($false = $true)) ) | (~spl25_11 | ~spl25_18)),
  inference(forward_demodulation,[],[f105,f135])).
thf(f267,plain,(
  ( ! [X22 : $i] : ((((cP @ (sK12 @ X22))) = $false)) ) | (~spl25_11 | ~spl25_18)),
  inference(trivial_inequality_removal,[],[f266])).
thf(f272,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $true) | ($false = $true)) ) | (~spl25_3 | ~spl25_30)),
  inference(forward_demodulation,[],[f188,f73])).
thf(f273,plain,(
  ( ! [X0 : $i] : ((((cQ @ (sK13 @ X0))) = $true)) ) | (~spl25_3 | ~spl25_30)),
  inference(trivial_inequality_removal,[],[f272])).
thf(f275,plain,(
  ($false = $true) | (~spl25_11 | ~spl25_18)),
  inference(forward_demodulation,[],[f267,f135])).
thf(f276,plain,(
  $false | (~spl25_11 | ~spl25_18)),
  inference(trivial_inequality_removal,[],[f275])).
thf(f277,plain,(
  ~spl25_11 | ~spl25_18),
  inference(avatar_contradiction_clause,[],[f276])).
thf(f278,plain,(
  ($false = $true) | (~spl25_3 | ~spl25_30)),
  inference(forward_demodulation,[],[f273,f73])).
thf(f279,plain,(
  $false | (~spl25_3 | ~spl25_30)),
  inference(trivial_inequality_removal,[],[f278])).
thf(f280,plain,(
  ~spl25_3 | ~spl25_30),
  inference(avatar_contradiction_clause,[],[f279])).
thf(f283,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) = $true)) ) | (~spl25_19 | ~spl25_30)),
  inference(forward_subsumption_resolution,[],[f188,f138])).
thf(f284,plain,(
  ( ! [X16 : $i] : ((((cQ @ X16)) = $true)) ) | (~spl25_8 | ~spl25_19)),
  inference(forward_subsumption_resolution,[],[f93,f138])).
thf(f287,plain,(
  $false | (~spl25_19 | ~spl25_30)),
  inference(forward_subsumption_resolution,[],[f283,f138])).
thf(f288,plain,(
  ~spl25_19 | ~spl25_30),
  inference(avatar_contradiction_clause,[],[f287])).
thf(f289,plain,(
  $false | (~spl25_8 | ~spl25_19)),
  inference(forward_subsumption_resolution,[],[f284,f138])).
thf(f290,plain,(
  ~spl25_8 | ~spl25_19),
  inference(avatar_contradiction_clause,[],[f289])).
thf(f291,plain,(
  $false | (~spl25_18 | spl25_26)),
  inference(forward_subsumption_resolution,[],[f172,f135])).
thf(f292,plain,(
  ~spl25_18 | spl25_26),
  inference(avatar_contradiction_clause,[],[f291])).
thf(f293,plain,(
  ( ! [X4 : $i] : (($false = ((cP @ (sK3 @ X4)))) | ($false = $true)) ) | (~spl25_18 | ~spl25_25)),
  inference(forward_demodulation,[],[f168,f135])).
thf(f294,plain,(
  ( ! [X4 : $i] : (($false = ((cP @ (sK3 @ X4))))) ) | (~spl25_18 | ~spl25_25)),
  inference(trivial_inequality_removal,[],[f293])).
thf(f295,plain,(
  ($false = $true) | (~spl25_18 | ~spl25_25)),
  inference(forward_demodulation,[],[f294,f135])).
thf(f296,plain,(
  $false | (~spl25_18 | ~spl25_25)),
  inference(trivial_inequality_removal,[],[f295])).
thf(f297,plain,(
  ~spl25_18 | ~spl25_25),
  inference(avatar_contradiction_clause,[],[f296])).
thf(f298,plain,(
  ($false = $true) | (~spl25_34 | ~spl25_35)),
  inference(forward_demodulation,[],[f214,f209])).
thf(f299,plain,(
  $false | (~spl25_34 | ~spl25_35)),
  inference(trivial_inequality_removal,[],[f298])).
thf(f300,plain,(
  ~spl25_34 | ~spl25_35),
  inference(avatar_contradiction_clause,[],[f299])).
thf(f306,plain,(
  ($false = $true) | (~spl25_20 | ~spl25_28)),
  inference(constrained_superposition,[],[f142,f181])).
thf(f307,plain,(
  ($false = $true) | (~spl25_14 | ~spl25_20)),
  inference(constrained_superposition,[],[f142,f118])).
thf(f310,plain,(
  ($false = $true) | (~spl25_20 | ~spl25_28)),
  inference(constrained_superposition,[],[f181,f142])).
thf(f318,plain,(
  $false | (~spl25_20 | ~spl25_28)),
  inference(trivial_inequality_removal,[],[f310])).
thf(f319,plain,(
  ~spl25_20 | ~spl25_28),
  inference(avatar_contradiction_clause,[],[f318])).
thf(f320,plain,(
  $false | (~spl25_14 | ~spl25_20)),
  inference(trivial_inequality_removal,[],[f307])).
thf(f321,plain,(
  ~spl25_14 | ~spl25_20),
  inference(avatar_contradiction_clause,[],[f320])).
thf(f326,plain,(
  $false | (~spl25_20 | ~spl25_28)),
  inference(trivial_inequality_removal,[],[f306])).
thf(f327,plain,(
  ~spl25_20 | ~spl25_28),
  inference(avatar_contradiction_clause,[],[f326])).
thf(f328,plain,(
  ($false = $true) | (~spl25_13 | ~spl25_15)),
  inference(forward_demodulation,[],[f123,f114])).
thf(f329,plain,(
  $false | (~spl25_13 | ~spl25_15)),
  inference(trivial_inequality_removal,[],[f328])).
thf(f330,plain,(
  ~spl25_13 | ~spl25_15),
  inference(avatar_contradiction_clause,[],[f329])).
thf(f337,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) = $true) | ($false = $true)) ) | (~spl25_3 | ~spl25_8)),
  inference(constrained_superposition,[],[f73,f93])).
thf(f345,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) = $true)) ) | (~spl25_3 | ~spl25_8)),
  inference(trivial_inequality_removal,[],[f337])).
thf(f347,plain,(
  ($false = $true) | (~spl25_3 | ~spl25_8)),
  inference(forward_demodulation,[],[f345,f73])).
thf(f348,plain,(
  $false | (~spl25_3 | ~spl25_8)),
  inference(trivial_inequality_removal,[],[f347])).
thf(f349,plain,(
  ~spl25_3 | ~spl25_8),
  inference(avatar_contradiction_clause,[],[f348])).
thf(f360,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) = $false) | ($false = $true)) ) | (~spl25_4 | ~spl25_7)),
  inference(constrained_superposition,[],[f89,f76])).
thf(f363,plain,(
  ($true != $true) | (~spl25_4 | spl25_24)),
  inference(constrained_superposition,[],[f161,f76])).
thf(f369,plain,(
  $false | (~spl25_4 | spl25_24)),
  inference(trivial_inequality_removal,[],[f363])).
thf(f370,plain,(
  ~spl25_4 | spl25_24),
  inference(avatar_contradiction_clause,[],[f369])).
thf(f372,plain,(
  ( ! [X0 : $i] : ((((cQ @ X0)) = $false)) ) | (~spl25_4 | ~spl25_7)),
  inference(trivial_inequality_removal,[],[f360])).
thf(f376,plain,(
  ($false = $true) | (~spl25_4 | ~spl25_7)),
  inference(forward_demodulation,[],[f372,f76])).
thf(f377,plain,(
  $false | (~spl25_4 | ~spl25_7)),
  inference(trivial_inequality_removal,[],[f376])).
thf(f378,plain,(
  ~spl25_4 | ~spl25_7),
  inference(avatar_contradiction_clause,[],[f377])).
thf(f379,plain,(
  ($false = $true) | (~spl25_20 | ~spl25_23)),
  inference(forward_demodulation,[],[f157,f142])).
thf(f380,plain,(
  $false | (~spl25_20 | ~spl25_23)),
  inference(trivial_inequality_removal,[],[f379])).
thf(f381,plain,(
  ~spl25_20 | ~spl25_23),
  inference(avatar_contradiction_clause,[],[f380])).
thf(f398,plain,(
  ($false = $true) | (~spl25_3 | ~spl25_36)),
  inference(constrained_superposition,[],[f219,f73])).
thf(f400,plain,(
  $false | (~spl25_3 | ~spl25_36)),
  inference(trivial_inequality_removal,[],[f398])).
thf(f401,plain,(
  ~spl25_3 | ~spl25_36),
  inference(avatar_contradiction_clause,[],[f400])).
thf(f439,plain,(
  $false | (~spl25_1 | ~spl25_14)),
  inference(forward_subsumption_resolution,[],[f118,f66])).
thf(f440,plain,(
  ~spl25_1 | ~spl25_14),
  inference(avatar_contradiction_clause,[],[f439])).
thf(f441,plain,(
  ( ! [X4 : $i] : (($true = ((cP @ X4)))) ) | (~spl25_1 | ~spl25_27)),
  inference(forward_subsumption_resolution,[],[f176,f66])).
thf(f442,plain,(
  $false | (~spl25_1 | ~spl25_27)),
  inference(forward_subsumption_resolution,[],[f441,f66])).
thf(f443,plain,(
  ~spl25_1 | ~spl25_27),
  inference(avatar_contradiction_clause,[],[f442])).
thf(f444,plain,(
  ( ! [X22 : $i] : (($true = ((cP @ X22)))) ) | (~spl25_1 | ~spl25_12)),
  inference(forward_subsumption_resolution,[],[f109,f66])).
thf(f452,plain,(
  $false | (~spl25_1 | ~spl25_12)),
  inference(forward_subsumption_resolution,[],[f444,f66])).
thf(f453,plain,(
  ~spl25_1 | ~spl25_12),
  inference(avatar_contradiction_clause,[],[f452])).
thf(f474,plain,(
  ($false = $true) | (~spl25_3 | ~spl25_22)),
  inference(constrained_superposition,[],[f151,f73])).
thf(f478,plain,(
  $false | (~spl25_3 | ~spl25_22)),
  inference(trivial_inequality_removal,[],[f474])).
thf(f479,plain,(
  ~spl25_3 | ~spl25_22),
  inference(avatar_contradiction_clause,[],[f478])).
thf(f480,plain,(
  ($false = $true) | (~spl25_16 | ~spl25_21)),
  inference(forward_demodulation,[],[f128,f146])).
thf(f481,plain,(
  $false | (~spl25_16 | ~spl25_21)),
  inference(trivial_inequality_removal,[],[f480])).
thf(f482,plain,(
  ~spl25_16 | ~spl25_21),
  inference(avatar_contradiction_clause,[],[f481])).
thf(f484,plain,(
  $false | (~spl25_19 | ~spl25_22)),
  inference(forward_subsumption_resolution,[],[f151,f138])).
thf(f485,plain,(
  ~spl25_19 | ~spl25_22),
  inference(avatar_contradiction_clause,[],[f484])).
cnf(s1, plain, spl25_1 | ~spl25_2 | spl25_3 | spl25_4 | spl25_5, inference(sat_conversion,[],[f81])).
cnf(s2, plain, spl25_4 | ~spl25_2 | spl25_1 | spl25_4 | spl25_6, inference(sat_conversion,[],[f86])).
cnf(s3, plain, spl25_1 | ~spl25_2 | spl25_4 | spl25_6, inference(rat,[],[s2])).
cnf(s5, plain, spl25_1 | spl25_2 | spl25_4 | spl25_8, inference(sat_conversion,[],[f94])).
cnf(s6, plain, ~spl25_2 | spl25_9 | ~spl25_10 | spl25_11, inference(sat_conversion,[],[f106])).
cnf(s8, plain, spl25_2 | spl25_3 | spl25_4 | spl25_13 | spl25_14, inference(sat_conversion,[],[f119])).
cnf(s9, plain, spl25_4 | spl25_2 | spl25_4 | spl25_14 | spl25_15, inference(sat_conversion,[],[f124])).
cnf(s10, plain, spl25_2 | spl25_4 | spl25_14 | spl25_15, inference(rat,[],[s9])).
cnf(s13, plain, spl25_18 | spl25_16 | ~spl25_2 | spl25_18 | spl25_22, inference(sat_conversion,[],[f152])).
cnf(s14, plain, ~spl25_2 | spl25_16 | spl25_18 | spl25_22, inference(rat,[],[s13])).
cnf(s15, plain, ~spl25_2 | spl25_18 | spl25_20 | spl25_21 | spl25_22, inference(sat_conversion,[],[f153])).
cnf(s16, plain, spl25_2 | spl25_7 | spl25_23 | ~spl25_24, inference(sat_conversion,[],[f162])).
cnf(s19, plain, ~spl25_2 | spl25_12 | spl25_18 | spl25_19, inference(sat_conversion,[],[f165])).
cnf(s20, plain, spl25_2 | spl25_19 | spl25_25 | ~spl25_26, inference(sat_conversion,[],[f173])).
cnf(s23, plain, ~spl25_2 | spl25_4 | spl25_28 | spl25_30, inference(sat_conversion,[],[f189])).
cnf(s28, plain, spl25_18 | spl25_2 | spl25_18 | spl25_19 | spl25_34, inference(sat_conversion,[],[f210])).
cnf(s29, plain, spl25_2 | spl25_18 | spl25_19 | spl25_34, inference(rat,[],[s28])).
cnf(s30, plain, spl25_2 | spl25_18 | spl25_19 | spl25_20 | spl25_35, inference(sat_conversion,[],[f215])).
cnf(s32, plain, spl25_2 | spl25_18 | spl25_27 | spl25_36, inference(sat_conversion,[],[f221])).
cnf(s35, plain, spl25_1 | ~spl25_2 | spl25_29 | ~spl25_39, inference(sat_conversion,[],[f236])).
cnf(s37, plain, ~spl25_4 | spl25_39, inference(sat_conversion,[],[f239])).
cnf(s38, plain, ~spl25_1 | ~spl25_18, inference(sat_conversion,[],[f241])).
cnf(s39, plain, ~spl25_5 | ~spl25_6, inference(sat_conversion,[],[f244])).
cnf(s41, plain, spl25_10 | ~spl25_18, inference(sat_conversion,[],[f254])).
cnf(s42, plain, ~spl25_3 | ~spl25_9, inference(sat_conversion,[],[f258])).
cnf(s43, plain, ~spl25_4 | ~spl25_19, inference(sat_conversion,[],[f260])).
cnf(s44, plain, ~spl25_4 | ~spl25_29, inference(sat_conversion,[],[f265])).
cnf(s46, plain, ~spl25_11 | ~spl25_18, inference(sat_conversion,[],[f277])).
cnf(s47, plain, ~spl25_3 | ~spl25_30, inference(sat_conversion,[],[f280])).
cnf(s50, plain, ~spl25_19 | ~spl25_30, inference(sat_conversion,[],[f288])).
cnf(s51, plain, ~spl25_8 | ~spl25_19, inference(sat_conversion,[],[f290])).
cnf(s52, plain, ~spl25_18 | spl25_26, inference(sat_conversion,[],[f292])).
cnf(s53, plain, ~spl25_18 | ~spl25_25, inference(sat_conversion,[],[f297])).
cnf(s54, plain, ~spl25_34 | ~spl25_35, inference(sat_conversion,[],[f300])).
cnf(s58, plain, ~spl25_20 | ~spl25_28, inference(sat_conversion,[],[f319])).
cnf(s59, plain, ~spl25_14 | ~spl25_20, inference(sat_conversion,[],[f321])).
cnf(s62, plain, ~spl25_20 | ~spl25_28, inference(sat_conversion,[],[f327])).
cnf(s63, plain, ~spl25_13 | ~spl25_15, inference(sat_conversion,[],[f330])).
cnf(s65, plain, ~spl25_3 | ~spl25_8, inference(sat_conversion,[],[f349])).
cnf(s71, plain, ~spl25_4 | spl25_24, inference(sat_conversion,[],[f370])).
cnf(s73, plain, ~spl25_4 | ~spl25_7, inference(sat_conversion,[],[f378])).
cnf(s74, plain, ~spl25_20 | ~spl25_23, inference(sat_conversion,[],[f381])).
cnf(s77, plain, ~spl25_3 | ~spl25_36, inference(sat_conversion,[],[f401])).
cnf(s87, plain, ~spl25_1 | ~spl25_14, inference(sat_conversion,[],[f440])).
cnf(s88, plain, ~spl25_1 | ~spl25_27, inference(sat_conversion,[],[f443])).
cnf(s92, plain, ~spl25_1 | ~spl25_12, inference(sat_conversion,[],[f453])).
cnf(s98, plain, ~spl25_3 | ~spl25_22, inference(sat_conversion,[],[f479])).
cnf(s99, plain, ~spl25_16 | ~spl25_21, inference(sat_conversion,[],[f482])).
cnf(s100, plain, ~spl25_19 | ~spl25_22, inference(sat_conversion,[],[f485])).
cnf(s101, plain, spl25_14 | spl25_4 | spl25_3 | spl25_2, inference(rat,[],[s63,s8,s10])).
cnf(s102, plain, spl25_18 | spl25_20 | spl25_19 | spl25_2, inference(rat,[],[s54,s30,s29])).
cnf(s103, plain, spl25_20 | spl25_19 | spl25_2, inference(rat,[],[s20,s52,s53,s102])).
cnf(s104, plain, spl25_4 | spl25_3 | spl25_2 | spl25_1, inference(rat,[],[s103,s59,s101,s51,s5])).
cnf(s105, plain, ~spl25_4 | spl25_2, inference(rat,[],[s74,s103,s16,s43,s71,s73])).
cnf(s106, plain, spl25_4 | spl25_2 | spl25_1, inference(rat,[],[s65,s104,s5])).
cnf(s107, plain, spl25_2 | spl25_1, inference(rat,[],[s106,s105])).
cnf(s108, plain, spl25_18 | spl25_20 | spl25_22 | ~spl25_2, inference(rat,[],[s99,s15,s14])).
cnf(s109, plain, spl25_5 | spl25_4 | ~spl25_2 | spl25_1, inference(rat,[],[s6,s41,s46,s108,s62,s23,s42,s47,s98,s1])).
cnf(s110, plain, spl25_4 | ~spl25_2 | spl25_1, inference(rat,[],[s109,s39,s3])).
cnf(s111, plain, ~spl25_2 | spl25_1, inference(rat,[],[s35,s37,s44,s110])).
cnf(s112, plain, spl25_1, inference(rat,[],[s111,s107])).
cnf(s113, plain, ~spl25_12, inference(rat,[],[s92,s112])).
cnf(s115, plain, ~spl25_27, inference(rat,[],[s88,s112])).
cnf(s116, plain, ~spl25_14, inference(rat,[],[s87,s112])).
cnf(s117, plain, ~spl25_18, inference(rat,[],[s38,s112])).
cnf(s118, plain, ~spl25_2, inference(rat,[],[s58,s23,s108,s43,s50,s100,s19,s117,s113])).
cnf(s119, plain, ~spl25_4, inference(rat,[],[s105,s118])).
cnf(s120, plain, spl25_36, inference(rat,[],[s32,s115,s117,s118])).
cnf(s122, plain, spl25_3, inference(rat,[],[s101,s118,s116,s119])).
cnf(s123, plain, $false, inference(rat,[],[s77,s120,s122])).
thf(f487,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s123])).
% SZS output end Proof for theBenchmark