%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, c: $tType).
thf(type_def_6, type, b: $tType).
thf(type_def_7, type, a: $tType).
thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, c_starc: (c > c > c)).
thf(func_def_1, type, c_starb: (b > b > b)).
thf(func_def_2, type, c_stara: (a > a > a)).
thf(func_def_6, type, sK0: (b > c)).
thf(func_def_7, type, sK1: (a > b)).
thf(func_def_8, type, sK2: (a > c)).
thf(func_def_9, type, sK3: (b > a)).
thf(func_def_10, type, sK4: b).
thf(func_def_11, type, sK5: (c > $o)).
thf(func_def_12, type, sK6: b).
thf(func_def_13, type, vNOT: ($o > $o)).
thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X1 : (a > c),X2 : (b > c),X0 : (a > b)] : ((! [X5 : (b > $o),X3 : a,X4 : a] : ((X5 @ (X0 @ (c_stara @ X3 @ X4))) => (X5 @ (c_starb @ (X0 @ X3) @ (X0 @ X4)))) & ! [X4 : a,X5 : (c > $o),X3 : a] : ((X5 @ (X1 @ (c_stara @ X3 @ X4))) => (X5 @ (c_starc @ (X1 @ X3) @ (X1 @ X4)))) & ! [X4 : b] : ? [X3 : a] : ! [X5 : (b > $o)] : ((X5 @ (X0 @ X3)) => (X5 @ X4)) & ! [X3 : a,X5 : (c > $o)] : ((X5 @ (X2 @ (X0 @ X3))) => (X5 @ (X1 @ X3)))) => ! [X5 : (c > $o),X3 : b,X4 : b] : ((X5 @ (X2 @ (c_starb @ X3 @ X4))) => (X5 @ (c_starc @ (X2 @ X3) @ (X2 @ X4)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM270_INST)).
thf(f2,negated_conjecture,(
  ~ ! [X1 : (a > c),X2 : (b > c),X0 : (a > b)] : ((! [X5 : (b > $o),X3 : a,X4 : a] : ((X5 @ (X0 @ (c_stara @ X3 @ X4))) => (X5 @ (c_starb @ (X0 @ X3) @ (X0 @ X4)))) & ! [X4 : a,X5 : (c > $o),X3 : a] : ((X5 @ (X1 @ (c_stara @ X3 @ X4))) => (X5 @ (c_starc @ (X1 @ X3) @ (X1 @ X4)))) & ! [X4 : b] : ? [X3 : a] : ! [X5 : (b > $o)] : ((X5 @ (X0 @ X3)) => (X5 @ X4)) & ! [X3 : a,X5 : (c > $o)] : ((X5 @ (X2 @ (X0 @ X3))) => (X5 @ (X1 @ X3)))) => ! [X5 : (c > $o),X3 : b,X4 : b] : ((X5 @ (X2 @ (c_starb @ X3 @ X4))) => (X5 @ (c_starc @ (X2 @ X3) @ (X2 @ X4)))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (a > c),X1 : (b > c),X2 : (a > b)] : ((! [X3 : (b > $o),X4 : a,X5 : a] : ((X3 @ (X2 @ (c_stara @ X4 @ X5))) => (X3 @ (c_starb @ (X2 @ X4) @ (X2 @ X5)))) & ! [X6 : a,X7 : (c > $o),X8 : a] : ((X7 @ (X0 @ (c_stara @ X8 @ X6))) => (X7 @ (c_starc @ (X0 @ X8) @ (X0 @ X6)))) & ! [X9 : b] : ? [X10 : a] : ! [X11 : (b > $o)] : ((X11 @ (X2 @ X10)) => (X11 @ X9)) & ! [X12 : a,X13 : (c > $o)] : ((X13 @ (X1 @ (X2 @ X12))) => (X13 @ (X0 @ X12)))) => ! [X14 : (c > $o),X15 : b,X16 : b] : ((X14 @ (X1 @ (c_starb @ X15 @ X16))) => (X14 @ (c_starc @ (X1 @ X15) @ (X1 @ X16)))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X2 : (a > b),X0 : (a > c),X1 : (b > c)] : ((! [X13 : (c > $o),X12 : a] : ((((X13 @ (X1 @ (X2 @ X12)))) = $true) => (((X13 @ (X0 @ X12))) = $true)) & ! [X5 : a,X4 : a,X3 : (b > $o)] : ((((X3 @ (X2 @ (c_stara @ X4 @ X5)))) = $true) => (((X3 @ (c_starb @ (X2 @ X4) @ (X2 @ X5)))) = $true)) & ! [X9 : b] : ? [X10 : a] : ! [X11 : (b > $o)] : (($true = ((X11 @ (X2 @ X10)))) => (((X11 @ X9)) = $true)) & ! [X6 : a,X7 : (c > $o),X8 : a] : ((((X7 @ (X0 @ (c_stara @ X8 @ X6)))) = $true) => (((X7 @ (c_starc @ (X0 @ X8) @ (X0 @ X6)))) = $true))) => ! [X16 : b,X14 : (c > $o),X15 : b] : ((((X14 @ (X1 @ (c_starb @ X15 @ X16)))) = $true) => (((X14 @ (c_starc @ (X1 @ X15) @ (X1 @ X16)))) = $true)))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X2 : (a > b),X0 : (a > c),X1 : (b > c)] : (? [X15 : b,X14 : (c > $o),X16 : b] : ((((X14 @ (c_starc @ (X1 @ X15) @ (X1 @ X16)))) != $true) & (((X14 @ (X1 @ (c_starb @ X15 @ X16)))) = $true)) & (! [X13 : (c > $o),X12 : a] : ((((X13 @ (X0 @ X12))) = $true) | (((X13 @ (X1 @ (X2 @ X12)))) != $true)) & ! [X3 : (b > $o),X5 : a,X4 : a] : ((((X3 @ (X2 @ (c_stara @ X4 @ X5)))) != $true) | (((X3 @ (c_starb @ (X2 @ X4) @ (X2 @ X5)))) = $true)) & ! [X9 : b] : ? [X10 : a] : ! [X11 : (b > $o)] : ((((X11 @ X9)) = $true) | ($true != ((X11 @ (X2 @ X10))))) & ! [X7 : (c > $o),X8 : a,X6 : a] : ((((X7 @ (c_starc @ (X0 @ X8) @ (X0 @ X6)))) = $true) | (((X7 @ (X0 @ (c_stara @ X8 @ X6)))) != $true))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X1 : (b > c),X2 : (a > b),X0 : (a > c)] : (! [X9 : b] : ? [X10 : a] : ! [X11 : (b > $o)] : ((((X11 @ X9)) = $true) | ($true != ((X11 @ (X2 @ X10))))) & ! [X7 : (c > $o),X8 : a,X6 : a] : ((((X7 @ (c_starc @ (X0 @ X8) @ (X0 @ X6)))) = $true) | (((X7 @ (X0 @ (c_stara @ X8 @ X6)))) != $true)) & ? [X15 : b,X14 : (c > $o),X16 : b] : ((((X14 @ (c_starc @ (X1 @ X15) @ (X1 @ X16)))) != $true) & (((X14 @ (X1 @ (c_starb @ X15 @ X16)))) = $true)) & ! [X3 : (b > $o),X5 : a,X4 : a] : ((((X3 @ (X2 @ (c_stara @ X4 @ X5)))) != $true) | (((X3 @ (c_starb @ (X2 @ X4) @ (X2 @ X5)))) = $true)) & ! [X13 : (c > $o),X12 : a] : ((((X13 @ (X0 @ X12))) = $true) | (((X13 @ (X1 @ (X2 @ X12)))) != $true)))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : (b > c),X1 : (a > b),X2 : (a > c)] : (! [X3 : b] : ? [X4 : a] : ! [X5 : (b > $o)] : ((((X5 @ X3)) = $true) | ($true != ((X5 @ (X1 @ X4))))) & ! [X6 : (c > $o),X7 : a,X8 : a] : (($true = ((X6 @ (c_starc @ (X2 @ X7) @ (X2 @ X8))))) | (((X6 @ (X2 @ (c_stara @ X7 @ X8)))) != $true)) & ? [X9 : b,X10 : (c > $o),X11 : b] : ((((X10 @ (c_starc @ (X0 @ X9) @ (X0 @ X11)))) != $true) & (((X10 @ (X0 @ (c_starb @ X9 @ X11)))) = $true)) & ! [X12 : (b > $o),X13 : a,X14 : a] : ((((X12 @ (X1 @ (c_stara @ X14 @ X13)))) != $true) | ($true = ((X12 @ (c_starb @ (X1 @ X14) @ (X1 @ X13)))))) & ! [X15 : (c > $o),X16 : a] : ((((X15 @ (X2 @ X16))) = $true) | (((X15 @ (X0 @ (X1 @ X16)))) != $true)))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X3 : b] : ! [X5 : (b > $o)] : ((((X5 @ X3)) = $true) | (((X5 @ (sK1 @ (sK3 @ X3)))) != $true)) & ! [X6 : (c > $o),X7 : a,X8 : a] : ((((X6 @ (c_starc @ (sK2 @ X7) @ (sK2 @ X8)))) = $true) | (((X6 @ (sK2 @ (c_stara @ X7 @ X8)))) != $true)) & ((((sK5 @ (c_starc @ (sK0 @ sK4) @ (sK0 @ sK6)))) != $true) & ($true = ((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6)))))) & ! [X12 : (b > $o),X13 : a,X14 : a] : ((((X12 @ (sK1 @ (c_stara @ X14 @ X13)))) != $true) | (((X12 @ (c_starb @ (sK1 @ X14) @ (sK1 @ X13)))) = $true)) & ! [X15 : (c > $o),X16 : a] : ((((X15 @ (sK2 @ X16))) = $true) | (((X15 @ (sK0 @ (sK1 @ X16)))) != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,sK4,sK5,sK6]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X4,$thf(sK3 @ X3)),skolemize(X9,$thf(sK4)),skolemize(X10,$thf(sK5)),skolemize(X11,$thf(sK6))],[f7])).
thf(f9,plain,(
  ( ! [X16 : a,X15 : (c > $o)] : ((((X15 @ (sK0 @ (sK1 @ X16)))) != $true) | (((X15 @ (sK2 @ X16))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f10,plain,(
  ( ! [X14 : a,X12 : (b > $o),X13 : a] : ((((X12 @ (c_starb @ (sK1 @ X14) @ (sK1 @ X13)))) = $true) | (((X12 @ (sK1 @ (c_stara @ X14 @ X13)))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f11,plain,(
  ($true = ((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6)))))),
  inference(cnf_transformation,[],[f8])).
thf(f12,plain,(
  (((sK5 @ (c_starc @ (sK0 @ sK4) @ (sK0 @ sK6)))) != $true)),
  inference(cnf_transformation,[],[f8])).
thf(f13,plain,(
  ( ! [X8 : a,X6 : (c > $o),X7 : a] : ((((X6 @ (c_starc @ (sK2 @ X7) @ (sK2 @ X8)))) = $true) | (((X6 @ (sK2 @ (c_stara @ X7 @ X8)))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X3 : b,X5 : (b > $o)] : ((((X5 @ (sK1 @ (sK3 @ X3)))) != $true) | (((X5 @ X3)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X0 : b] : ((((sK1 @ (sK3 @ X0))) = X0)) )),
  inference(leibniz_equality_elimination,[],[f14])).
thf(f67,plain,(
  ( ! [X0 : a] : ((((sK0 @ (sK1 @ X0))) = ((sK2 @ X0)))) )),
  inference(leibniz_equality_elimination,[],[f9])).
thf(f80,plain,(
  ( ! [X0 : b] : ((((sK2 @ (sK3 @ X0))) = ((sK0 @ X0)))) )),
  inference(superposition,[],[f67,f16])).
thf(f83,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK1 @ (c_stara @ X0 @ X1))) = ((c_starb @ (sK1 @ X0) @ (sK1 @ X1))))) )),
  inference(leibniz_equality_elimination,[],[f10])).
thf(f125,plain,(
  ( ! [X0 : b,X1 : a] : ((((c_starb @ (sK1 @ X1) @ X0)) = ((sK1 @ (c_stara @ X1 @ (sK3 @ X0)))))) )),
  inference(superposition,[],[f83,f16])).
thf(f128,plain,(
  ( ! [X0 : a,X1 : a] : ((((c_starc @ (sK2 @ X0) @ (sK2 @ X1))) = ((sK2 @ (c_stara @ X0 @ X1))))) )),
  inference(leibniz_equality_elimination,[],[f13])).
thf(f141,plain,(
  ( ! [X0 : b,X1 : a] : ((((sK2 @ (c_stara @ (sK3 @ X0) @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK2 @ X1))))) )),
  inference(superposition,[],[f128,f80])).
thf(f147,plain,(
  ( ! [X0 : a,X1 : b] : ((((sK0 @ (c_starb @ (sK1 @ X0) @ X1))) = ((sK2 @ (c_stara @ X0 @ (sK3 @ X1)))))) )),
  inference(superposition,[],[f67,f125])).
thf(f177,plain,(
  ( ! [X0 : b,X1 : b] : ((((sK0 @ (c_starb @ (sK1 @ (sK3 @ X0)) @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK2 @ (sK3 @ X1)))))) )),
  inference(superposition,[],[f141,f147])).
thf(f183,plain,(
  ( ! [X0 : b,X1 : b] : ((((sK0 @ (c_starb @ (sK1 @ (sK3 @ X0)) @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK0 @ X1))))) )),
  inference(forward_demodulation,[],[f177,f80])).
thf(f185,plain,(
  ( ! [X0 : b,X1 : b] : ((((sK0 @ (c_starb @ X0 @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK0 @ X1))))) )),
  inference(forward_demodulation,[],[f183,f16])).
thf(f190,plain,(
  ($true != ((sK5 @ (sK0 @ (c_starb @ sK4 @ sK6)))))),
  inference(superposition,[],[f12,f185])).
thf(f191,plain,(
  $false),
  inference(forward_subsumption_resolution,[],[f190,f11])).
% SZS output end Proof for theBenchmark