%----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_3, type, sK0: (a > a > $o)).
thf(func_def_4, type, sK1: ((a > $o) > a)).
thf(func_def_5, type, sK2: (a > (a > $o) > a)).
thf(func_def_6, type, sK3: (a > a)).
thf(func_def_7, type, sF4: ((a > $o) > a)).
thf(func_def_8, type, sF5: (a > (a > $o) > $o)).
thf(func_def_9, type, sF6: ((a > $o) > a > a)).
thf(func_def_10, type, sF7: (a > (a > $o) > $o)).
thf(func_def_11, type, sF8: (a > (a > $o) > $o)).
thf(func_def_12, type, sF9: ((a > $o) > a > $o)).
thf(func_def_13, type, sF10: (a > (a > $o) > $o)).
thf(func_def_14, type, sF11: (a > a > $o)).
thf(func_def_15, type, sF12: (a > a)).
thf(func_def_16, type, sF13: (a > a > $o)).
thf(func_def_17, type, sF14: (a > $o)).
thf(func_def_18, type, sF15: (a > $o)).
thf(func_def_19, type, vNOT: ($o > $o)).
thf(func_def_20, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(f1,conjecture,(
  ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : (? [X3 : a,X2 : a,X4 : a] : (((X0 @ X3 @ X4) | (X0 @ X3 @ X4)) & (~(X0 @ X2 @ X4) | ~(X0 @ X2 @ X4)) & ((X0 @ X2 @ X3) | (X0 @ X2 @ X3))) | ? [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((X0 @ X7 @ X6) | ~(X5 @ X7) | ~(X5 @ X7) | (X0 @ X7 @ X6)) & (~(X0 @ (X1 @ X5) @ X6) | ~(X0 @ (X1 @ X5) @ X6))) | ? [X8 : a] : (((X5 @ X8) | (X5 @ X8)) & (~(X0 @ X8 @ (X1 @ X5)) | ~(X0 @ X8 @ (X1 @ X5))))) | ! [X9 : (a > a)] : (? [X10 : a] : (((X0 @ (X9 @ X10) @ X10) | (X0 @ (X9 @ X10) @ X10)) & ((X0 @ X10 @ (X9 @ X10)) | (X0 @ X10 @ (X9 @ X10)))) | ? [X11 : a,X12 : a] : (((X0 @ X11 @ X12) | (X0 @ X11 @ X12)) & (~(X0 @ (X9 @ X11) @ (X9 @ X12)) | ~(X0 @ (X9 @ X11) @ (X9 @ X12))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cT145_DOUBLE)).
thf(f2,negated_conjecture,(
  ~ ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : (? [X3 : a,X2 : a,X4 : a] : (((X0 @ X3 @ X4) | (X0 @ X3 @ X4)) & (~(X0 @ X2 @ X4) | ~(X0 @ X2 @ X4)) & ((X0 @ X2 @ X3) | (X0 @ X2 @ X3))) | ? [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((X0 @ X7 @ X6) | ~(X5 @ X7) | ~(X5 @ X7) | (X0 @ X7 @ X6)) & (~(X0 @ (X1 @ X5) @ X6) | ~(X0 @ (X1 @ X5) @ X6))) | ? [X8 : a] : (((X5 @ X8) | (X5 @ X8)) & (~(X0 @ X8 @ (X1 @ X5)) | ~(X0 @ X8 @ (X1 @ X5))))) | ! [X9 : (a > a)] : (? [X10 : a] : (((X0 @ (X9 @ X10) @ X10) | (X0 @ (X9 @ X10) @ X10)) & ((X0 @ X10 @ (X9 @ X10)) | (X0 @ X10 @ (X9 @ X10)))) | ? [X11 : a,X12 : a] : (((X0 @ X11 @ X12) | (X0 @ X11 @ X12)) & (~(X0 @ (X9 @ X11) @ (X9 @ X12)) | ~(X0 @ (X9 @ X11) @ (X9 @ X12))))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X2 : a,X3 : a,X4 : a] : (((X1 @ X2 @ X4) | (X1 @ X2 @ X4)) & (~(X1 @ X3 @ X4) | ~(X1 @ X3 @ X4)) & ((X1 @ X3 @ X2) | (X1 @ X3 @ X2))) | ? [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((X1 @ X7 @ X6) | ~(X5 @ X7) | ~(X5 @ X7) | (X1 @ X7 @ X6)) & (~(X1 @ (X0 @ X5) @ X6) | ~(X1 @ (X0 @ X5) @ X6))) | ? [X8 : a] : (((X5 @ X8) | (X5 @ X8)) & (~(X1 @ X8 @ (X0 @ X5)) | ~(X1 @ X8 @ (X0 @ X5))))) | ! [X9 : (a > a)] : (? [X10 : a] : (((X1 @ (X9 @ X10) @ X10) | (X1 @ (X9 @ X10) @ X10)) & ((X1 @ X10 @ (X9 @ X10)) | (X1 @ X10 @ (X9 @ X10)))) | ? [X11 : a,X12 : a] : (((X1 @ X11 @ X12) | (X1 @ X11 @ X12)) & (~(X1 @ (X9 @ X11) @ (X9 @ X12)) | ~(X1 @ (X9 @ X11) @ (X9 @ X12))))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X2 : a,X3 : a,X4 : a] : ((($true = ((X1 @ X2 @ X4))) | ($true = ((X1 @ X2 @ X4)))) & (~ ($true = ((X1 @ X3 @ X4))) | ~ ($true = ((X1 @ X3 @ X4)))) & (($true = ((X1 @ X3 @ X2))) | ($true = ((X1 @ X3 @ X2))))) | ? [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((((X1 @ X7 @ X6)) = $true) | ~ (((X5 @ X7)) = $true) | ~ (((X5 @ X7)) = $true) | (((X1 @ X7 @ X6)) = $true)) & (~ (((X1 @ (X0 @ X5) @ X6)) = $true) | ~ (((X1 @ (X0 @ X5) @ X6)) = $true))) | ? [X8 : a] : (((((X5 @ X8)) = $true) | (((X5 @ X8)) = $true)) & (~ (((X1 @ X8 @ (X0 @ X5))) = $true) | ~ (((X1 @ X8 @ (X0 @ X5))) = $true)))) | ! [X9 : (a > a)] : (? [X10 : a] : ((($true = ((X1 @ (X9 @ X10) @ X10))) | ($true = ((X1 @ (X9 @ X10) @ X10)))) & (($true = ((X1 @ X10 @ (X9 @ X10)))) | ($true = ((X1 @ X10 @ (X9 @ X10)))))) | ? [X11 : a,X12 : a] : ((($true = ((X1 @ X11 @ X12))) | ($true = ((X1 @ X11 @ X12)))) & (~ (((X1 @ (X9 @ X11) @ (X9 @ X12))) = $true) | ~ (((X1 @ (X9 @ X11) @ (X9 @ X12))) = $true)))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X3 : a,X4 : a,X2 : a] : ((($true = ((X1 @ X3 @ X2))) | ($true = ((X1 @ X3 @ X2)))) & (($true = ((X1 @ X2 @ X4))) | ($true = ((X1 @ X2 @ X4)))) & (($true != ((X1 @ X3 @ X4))) | ($true != ((X1 @ X3 @ X4))))) | ! [X9 : (a > a)] : (? [X10 : a] : ((($true = ((X1 @ (X9 @ X10) @ X10))) | ($true = ((X1 @ (X9 @ X10) @ X10)))) & (($true = ((X1 @ X10 @ (X9 @ X10)))) | ($true = ((X1 @ X10 @ (X9 @ X10)))))) | ? [X11 : a,X12 : a] : (((((X1 @ (X9 @ X11) @ (X9 @ X12))) != $true) | (((X1 @ (X9 @ X11) @ (X9 @ X12))) != $true)) & (($true = ((X1 @ X11 @ X12))) | ($true = ((X1 @ X11 @ X12)))))) | ? [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((((X1 @ X7 @ X6)) = $true) | (((X5 @ X7)) != $true) | (((X5 @ X7)) != $true) | (((X1 @ X7 @ X6)) = $true)) & ((((X1 @ (X0 @ X5) @ X6)) != $true) | (((X1 @ (X0 @ X5) @ X6)) != $true))) | ? [X8 : a] : (((((X1 @ X8 @ (X0 @ X5))) != $true) | (((X1 @ X8 @ (X0 @ X5))) != $true)) & ((((X5 @ X8)) = $true) | (((X5 @ X8)) = $true)))))),
  inference(flattening,[],[f4])).
thf(f6,plain,(
  ? [X1 : (a > a > $o),X0 : ((a > $o) > a)] : (! [X5 : (a > $o)] : (! [X6 : a] : (((((X1 @ (X0 @ X5) @ X6)) = $true) & (((X1 @ (X0 @ X5) @ X6)) = $true)) | ? [X7 : a] : ((((X5 @ X7)) = $true) & (((X1 @ X7 @ X6)) != $true) & (((X1 @ X7 @ X6)) != $true) & (((X5 @ X7)) = $true))) & ! [X8 : a] : (((((X1 @ X8 @ (X0 @ X5))) = $true) & (((X1 @ X8 @ (X0 @ X5))) = $true)) | ((((X5 @ X8)) != $true) & (((X5 @ X8)) != $true)))) & ? [X9 : (a > a)] : (! [X12 : a,X11 : a] : ((($true != ((X1 @ X11 @ X12))) & ($true != ((X1 @ X11 @ X12)))) | ((((X1 @ (X9 @ X11) @ (X9 @ X12))) = $true) & (((X1 @ (X9 @ X11) @ (X9 @ X12))) = $true))) & ! [X10 : a] : ((($true != ((X1 @ (X9 @ X10) @ X10))) & ($true != ((X1 @ (X9 @ X10) @ X10)))) | (($true != ((X1 @ X10 @ (X9 @ X10)))) & ($true != ((X1 @ X10 @ (X9 @ X10))))))) & ! [X4 : a,X2 : a,X3 : a] : ((($true != ((X1 @ X3 @ X2))) & ($true != ((X1 @ X3 @ X2)))) | (($true != ((X1 @ X2 @ X4))) & ($true != ((X1 @ X2 @ X4)))) | (($true = ((X1 @ X3 @ X4))) & ($true = ((X1 @ X3 @ X4))))))),
  inference(ennf_transformation,[],[f5])).
thf(f7,plain,(
  ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (! [X2 : (a > $o)] : (! [X3 : a] : ((($true = ((X0 @ (X1 @ X2) @ X3))) & ($true = ((X0 @ (X1 @ X2) @ X3)))) | ? [X4 : a] : ((((X2 @ X4)) = $true) & (((X0 @ X4 @ X3)) != $true) & (((X0 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true))) & ! [X5 : a] : (((((X0 @ X5 @ (X1 @ X2))) = $true) & (((X0 @ X5 @ (X1 @ X2))) = $true)) | (($true != ((X2 @ X5))) & ($true != ((X2 @ X5)))))) & ? [X6 : (a > a)] : (! [X7 : a,X8 : a] : ((($true != ((X0 @ X8 @ X7))) & ($true != ((X0 @ X8 @ X7)))) | (($true = ((X0 @ (X6 @ X8) @ (X6 @ X7)))) & ($true = ((X0 @ (X6 @ X8) @ (X6 @ X7)))))) & ! [X9 : a] : ((($true != ((X0 @ (X6 @ X9) @ X9))) & ($true != ((X0 @ (X6 @ X9) @ X9)))) | ((((X0 @ X9 @ (X6 @ X9))) != $true) & (((X0 @ X9 @ (X6 @ X9))) != $true)))) & ! [X10 : a,X11 : a,X12 : a] : ((($true != ((X0 @ X12 @ X11))) & ($true != ((X0 @ X12 @ X11)))) | ((((X0 @ X11 @ X10)) != $true) & (((X0 @ X11 @ X10)) != $true)) | (($true = ((X0 @ X12 @ X10))) & ($true = ((X0 @ X12 @ X10))))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  ! [X2 : (a > $o)] : (! [X3 : a] : (((((sK0 @ (sK1 @ X2) @ X3)) = $true) & (((sK0 @ (sK1 @ X2) @ X3)) = $true)) | ((((X2 @ (sK2 @ X3 @ X2))) = $true) & (((sK0 @ (sK2 @ X3 @ X2) @ X3)) != $true) & (((sK0 @ (sK2 @ X3 @ X2) @ X3)) != $true) & (((X2 @ (sK2 @ X3 @ X2))) = $true))) & ! [X5 : a] : ((($true = ((sK0 @ X5 @ (sK1 @ X2)))) & ($true = ((sK0 @ X5 @ (sK1 @ X2))))) | (($true != ((X2 @ X5))) & ($true != ((X2 @ X5)))))) & (! [X7 : a,X8 : a] : (((((sK0 @ X8 @ X7)) != $true) & (((sK0 @ X8 @ X7)) != $true)) | (($true = ((sK0 @ (sK3 @ X8) @ (sK3 @ X7)))) & ($true = ((sK0 @ (sK3 @ X8) @ (sK3 @ X7)))))) & ! [X9 : a] : (((((sK0 @ (sK3 @ X9) @ X9)) != $true) & (((sK0 @ (sK3 @ X9) @ X9)) != $true)) | ((((sK0 @ X9 @ (sK3 @ X9))) != $true) & (((sK0 @ X9 @ (sK3 @ X9))) != $true)))) & ! [X10 : a,X11 : a,X12 : a] : ((($true != ((sK0 @ X12 @ X11))) & ($true != ((sK0 @ X12 @ X11)))) | ((((sK0 @ X11 @ X10)) != $true) & (((sK0 @ X11 @ X10)) != $true)) | ((((sK0 @ X12 @ X10)) = $true) & (((sK0 @ X12 @ X10)) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X4,$thf(sK2 @ X3 @ X2)),skolemize(X6,$thf(sK3))],[f7])).
thf(f9,plain,(
  ( ! [X10 : a,X11 : a,X12 : a] : (($true != ((sK0 @ X12 @ X11))) | (((sK0 @ X11 @ X10)) != $true) | (((sK0 @ X12 @ X10)) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f20,plain,(
  ( ! [X9 : a] : ((((sK0 @ (sK3 @ X9) @ X9)) != $true) | (((sK0 @ X9 @ (sK3 @ X9))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f23,plain,(
  ( ! [X8 : a,X7 : a] : ((((sK0 @ X8 @ X7)) != $true) | ($true = ((sK0 @ (sK3 @ X8) @ (sK3 @ X7))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f28,plain,(
  ( ! [X2 : (a > $o),X5 : a] : (($true = ((sK0 @ X5 @ (sK1 @ X2)))) | ($true != ((X2 @ X5)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f34,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sK0 @ (sK1 @ X2) @ X3)) = $true) | (((sK0 @ (sK2 @ X3 @ X2) @ X3)) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f36,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sK0 @ (sK1 @ X2) @ X3)) = $true) | (((X2 @ (sK2 @ X3 @ X2))) = $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f39,definition,(
  ( ! [X2 : (a > $o)] : ((((sF4 @ X2)) = ((sK1 @ X2)))) )),
  introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
thf(f40,definition,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF5 @ X3 @ X2)) = ((sK0 @ (sF4 @ X2) @ X3)))) )),
  introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
thf(f41,definition,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF6 @ X2 @ X3)) = ((sK2 @ X3 @ X2)))) )),
  introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
thf(f42,definition,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF7 @ X3 @ X2)) = ((X2 @ (sF6 @ X2 @ X3))))) )),
  introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
thf(f43,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((X2 @ (sF6 @ X2 @ X3))) = ((sF7 @ X3 @ X2)))) )),
  inference(reorient_equations,[],[f42])).
thf(f44,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF5 @ X3 @ X2)) = $true) | ($true = ((sF7 @ X3 @ X2)))) )),
  inference(definition_folding,[],[f36,f43,f41,f40,f39])).
thf(f45,definition,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF8 @ X3 @ X2)) = ((sK0 @ (sF6 @ X2 @ X3) @ X3)))) )),
  introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
thf(f46,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sK0 @ (sF6 @ X2 @ X3) @ X3)) = ((sF8 @ X3 @ X2)))) )),
  inference(reorient_equations,[],[f45])).
thf(f48,plain,(
  ( ! [X2 : (a > $o),X3 : a] : ((((sF8 @ X3 @ X2)) != $true) | (((sF5 @ X3 @ X2)) = $true)) )),
  inference(definition_folding,[],[f34,f46,f41,f40,f39])).
thf(f54,definition,(
  ( ! [X2 : (a > $o),X5 : a] : ((((sF9 @ X2 @ X5)) = ((sK0 @ X5 @ (sF4 @ X2))))) )),
  introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
thf(f55,plain,(
  ( ! [X2 : (a > $o),X5 : a] : ((((sK0 @ X5 @ (sF4 @ X2))) = ((sF9 @ X2 @ X5)))) )),
  inference(reorient_equations,[],[f54])).
thf(f56,definition,(
  ( ! [X2 : (a > $o),X5 : a] : ((((sF10 @ X5 @ X2)) = ((X2 @ X5)))) )),
  introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
thf(f57,plain,(
  ( ! [X2 : (a > $o),X5 : a] : (($true != ((sF10 @ X5 @ X2))) | ($true = ((sF9 @ X2 @ X5)))) )),
  inference(definition_folding,[],[f28,f56,f55,f39])).
thf(f61,definition,(
  ( ! [X8 : a,X7 : a] : ((((sF11 @ X7 @ X8)) = ((sK0 @ X8 @ X7)))) )),
  introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
thf(f62,plain,(
  ( ! [X8 : a,X7 : a] : ((((sK0 @ X8 @ X7)) = ((sF11 @ X7 @ X8)))) )),
  inference(reorient_equations,[],[f61])).
thf(f63,definition,(
  ( ! [X8 : a] : ((((sF12 @ X8)) = ((sK3 @ X8)))) )),
  introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
thf(f64,definition,(
  ( ! [X8 : a,X7 : a] : ((((sF13 @ X7 @ X8)) = ((sK0 @ (sF12 @ X8) @ (sF12 @ X7))))) )),
  introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
thf(f65,plain,(
  ( ! [X8 : a,X7 : a] : ((((sK0 @ (sF12 @ X8) @ (sF12 @ X7))) = ((sF13 @ X7 @ X8)))) )),
  inference(reorient_equations,[],[f64])).
thf(f67,plain,(
  ( ! [X8 : a,X7 : a] : (($true != ((sF11 @ X7 @ X8))) | ($true = ((sF13 @ X7 @ X8)))) )),
  inference(definition_folding,[],[f23,f65,f63,f63,f62])).
thf(f70,definition,(
  ( ! [X9 : a] : ((((sF14 @ X9)) = ((sK0 @ (sF12 @ X9) @ X9)))) )),
  introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
thf(f71,definition,(
  ( ! [X9 : a] : ((((sF15 @ X9)) = ((sK0 @ X9 @ (sF12 @ X9))))) )),
  introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
thf(f72,plain,(
  ( ! [X9 : a] : ((((sF15 @ X9)) != $true) | (((sF14 @ X9)) != $true)) )),
  inference(definition_folding,[],[f20,f71,f63,f70,f63])).
thf(f83,plain,(
  ( ! [X10 : a,X11 : a,X12 : a] : (($true != ((sF11 @ X11 @ X12))) | ($true = ((sF11 @ X10 @ X12))) | (((sF11 @ X10 @ X11)) != $true)) )),
  inference(definition_folding,[],[f9,f62,f62,f62])).
thf(f98,plain,(
  ( ! [X0 : a,X1 : a] : (($true != ((sK0 @ X0 @ X1))) | (((sF13 @ X1 @ X0)) = $true)) )),
  inference(superposition,[],[f67,f62])).
thf(f101,plain,(
  ( ! [X0 : a] : ((((sF15 @ X0)) != $true) | (((sF13 @ (sF12 @ X0) @ X0)) = $true)) )),
  inference(superposition,[],[f98,f71])).
thf(f103,plain,(
  ( ! [X0 : (a > $o)] : ((((sF9 @ X0 @ (sF12 @ (sF4 @ X0)))) = ((sF14 @ (sF4 @ X0))))) )),
  inference(superposition,[],[f55,f70])).
thf(f106,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((sF9 @ X0 @ X1)) != $true) | (((sF13 @ (sF4 @ X0) @ X1)) = $true)) )),
  inference(superposition,[],[f98,f55])).
thf(f108,plain,(
  ( ! [X0 : a] : ((((sF13 @ (sF12 @ X0) @ X0)) = ((sF15 @ (sF12 @ X0))))) )),
  inference(superposition,[],[f65,f71])).
thf(f114,plain,(
  ( ! [X0 : a,X1 : a] : ((((sF13 @ X0 @ X1)) = ((sF11 @ (sF12 @ X0) @ (sF12 @ X1))))) )),
  inference(superposition,[],[f62,f65])).
thf(f125,plain,(
  ( ! [X0 : (a > $o),X1 : a] : ((((X0 @ X1)) != $true) | (((sF9 @ X0 @ X1)) = $true)) )),
  inference(superposition,[],[f57,f56])).
thf(f157,plain,(
  ( ! [X0 : (a > $o)] : ((((sF15 @ (sF4 @ X0))) = ((sF5 @ (sF12 @ (sF4 @ X0)) @ X0)))) )),
  inference(superposition,[],[f71,f40])).
thf(f167,plain,(
  ( ! [X0 : a] : ((((sF7 @ X0 @ sF15)) != $true) | ($true = ((sF13 @ (sF12 @ (sF6 @ sF15 @ X0)) @ (sF6 @ sF15 @ X0))))) )),
  inference(superposition,[],[f101,f43])).
thf(f182,plain,(
  ( ! [X0 : a] : ((((sF7 @ X0 @ sF15)) != $true) | (((sF15 @ (sF12 @ (sF6 @ sF15 @ X0)))) = $true)) )),
  inference(forward_demodulation,[],[f167,f108])).
thf(f247,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : (($true != ((sF11 @ X2 @ X1))) | ($true != ((sK0 @ X0 @ X1))) | ($true = ((sF11 @ X2 @ X0)))) )),
  inference(superposition,[],[f83,f62])).
thf(f478,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : ((((sF8 @ X0 @ X1)) = ((sF11 @ X0 @ (sF6 @ X1 @ X0))))) )),
  inference(superposition,[],[f62,f46])).
thf(f483,plain,(
  ( ! [X0 : (a > $o)] : (($true = ((sF7 @ (sF12 @ (sF4 @ X0)) @ X0))) | (((sF15 @ (sF4 @ X0))) = $true)) )),
  inference(superposition,[],[f44,f157])).
thf(f690,plain,(
  ( ! [X2 : a,X0 : a,X1 : a] : (($true != ((sK0 @ X2 @ X0))) | ($true != ((sK0 @ X0 @ X1))) | (((sF11 @ X1 @ X2)) = $true)) )),
  inference(superposition,[],[f247,f62])).
thf(f775,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK0 @ (sF12 @ X0) @ X1)) != $true) | ($true = ((sF11 @ X1 @ X0))) | (((sF15 @ X0)) != $true)) )),
  inference(superposition,[],[f690,f71])).
thf(f785,plain,(
  ( ! [X0 : a,X1 : a] : (($true != ((sF13 @ X0 @ X1))) | ($true = ((sF11 @ (sF12 @ X0) @ X1))) | ($true != ((sF15 @ X1)))) )),
  inference(superposition,[],[f775,f65])).
thf(f1249,plain,(
  (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | (((sF15 @ (sF4 @ sF15))) = $true) | ($true != $true)),
  inference(superposition,[],[f182,f483])).
thf(f1250,plain,(
  (((sF15 @ (sF4 @ sF15))) = $true) | (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true)),
  inference(trivial_inequality_removal,[],[f1249])).
thf(f1252,definition,(
  spl16_8 <=> (((sF15 @ (sF4 @ sF15))) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition])).
thf(f1253,plain,(
  (((sF15 @ (sF4 @ sF15))) != $true) | spl16_8),
  inference(avatar_component_clause,[],[f1252])).
thf(f1254,plain,(
  (((sF15 @ (sF4 @ sF15))) = $true) | ~spl16_8),
  inference(avatar_component_clause,[],[f1252])).
thf(f1256,definition,(
  spl16_9 <=> (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition])).
thf(f1258,plain,(
  (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | ~spl16_9),
  inference(avatar_component_clause,[],[f1256])).
thf(f1259,plain,(
  spl16_8 | spl16_9),
  inference(avatar_split_clause,[],[f1250,f1256,f1252])).
thf(f1263,plain,(
  ($true != $true) | ($true = ((sF13 @ (sF12 @ (sF4 @ sF15)) @ (sF4 @ sF15)))) | ~spl16_8),
  inference(superposition,[],[f101,f1254])).
thf(f1264,plain,(
  (((sF14 @ (sF4 @ sF15))) != $true) | ($true != $true) | ~spl16_8),
  inference(superposition,[],[f72,f1254])).
thf(f1269,plain,(
  ($true = ((sF13 @ (sF12 @ (sF4 @ sF15)) @ (sF4 @ sF15)))) | ~spl16_8),
  inference(trivial_inequality_removal,[],[f1263])).
thf(f1270,plain,(
  (((sF14 @ (sF4 @ sF15))) != $true) | ~spl16_8),
  inference(trivial_inequality_removal,[],[f1264])).
thf(f1274,plain,(
  (((sF15 @ (sF12 @ (sF4 @ sF15)))) = $true) | ~spl16_8),
  inference(forward_demodulation,[],[f1269,f108])).
thf(f1285,plain,(
  (((sF9 @ sF15 @ (sF12 @ (sF4 @ sF15)))) = $true) | ($true != $true) | ~spl16_8),
  inference(superposition,[],[f125,f1274])).
thf(f1287,plain,(
  (((sF9 @ sF15 @ (sF12 @ (sF4 @ sF15)))) = $true) | ~spl16_8),
  inference(trivial_inequality_removal,[],[f1285])).
thf(f1297,plain,(
  (((sF14 @ (sF4 @ sF15))) = $true) | ~spl16_8),
  inference(forward_demodulation,[],[f1287,f103])).
thf(f1301,plain,(
  $false | ~spl16_8),
  inference(forward_subsumption_resolution,[],[f1297,f1270])).
thf(f1302,plain,(
  ~spl16_8),
  inference(avatar_contradiction_clause,[],[f1301])).
thf(f1312,plain,(
  (((sF9 @ sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | ($true != $true) | ~spl16_9),
  inference(superposition,[],[f125,f1258])).
thf(f1320,plain,(
  (((sF9 @ sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | ~spl16_9),
  inference(trivial_inequality_removal,[],[f1312])).
thf(f1331,definition,(
  spl16_11 <=> (((sF7 @ (sF12 @ (sF4 @ sF15)) @ sF15)) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition])).
thf(f1332,plain,(
  (((sF7 @ (sF12 @ (sF4 @ sF15)) @ sF15)) = $true) | ~spl16_11),
  inference(avatar_component_clause,[],[f1331])).
thf(f1333,plain,(
  (((sF7 @ (sF12 @ (sF4 @ sF15)) @ sF15)) != $true) | spl16_11),
  inference(avatar_component_clause,[],[f1331])).
thf(f1335,plain,(
  (((sF15 @ (sF4 @ sF15))) = $true) | ($true != $true) | spl16_11),
  inference(superposition,[],[f1333,f483])).
thf(f1336,plain,(
  (((sF15 @ (sF4 @ sF15))) = $true) | spl16_11),
  inference(trivial_inequality_removal,[],[f1335])).
thf(f1337,plain,(
  $false | (spl16_8 | spl16_11)),
  inference(forward_subsumption_resolution,[],[f1336,f1253])).
thf(f1338,plain,(
  spl16_8 | spl16_11),
  inference(avatar_contradiction_clause,[],[f1337])).
thf(f1365,plain,(
  (((sF13 @ (sF4 @ sF15) @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | ($true != $true) | ~spl16_9),
  inference(superposition,[],[f106,f1320])).
thf(f1370,plain,(
  (((sF13 @ (sF4 @ sF15) @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) = $true) | ~spl16_9),
  inference(trivial_inequality_removal,[],[f1365])).
thf(f1401,plain,(
  ($true != $true) | (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) != $true) | ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15))))))) | ~spl16_9),
  inference(superposition,[],[f785,f1370])).
thf(f1406,plain,(
  (((sF15 @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) != $true) | ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15))))))) | ~spl16_9),
  inference(trivial_inequality_removal,[],[f1401])).
thf(f1411,plain,(
  ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF12 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15))))))) | ~spl16_9),
  inference(forward_subsumption_resolution,[],[f1406,f1258])).
thf(f1413,plain,(
  (((sF13 @ (sF4 @ sF15) @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15))))) = $true) | ~spl16_9),
  inference(forward_demodulation,[],[f1411,f114])).
thf(f1414,plain,(
  ($true != ((sF15 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | ($true != $true) | ~spl16_9),
  inference(superposition,[],[f785,f1413])).
thf(f1420,plain,(
  ($true != ((sF15 @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | ~spl16_9),
  inference(trivial_inequality_removal,[],[f1414])).
thf(f1424,plain,(
  ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | (((sF7 @ (sF12 @ (sF4 @ sF15)) @ sF15)) != $true) | ~spl16_9),
  inference(forward_demodulation,[],[f1420,f43])).
thf(f1426,plain,(
  ($true = ((sF11 @ (sF12 @ (sF4 @ sF15)) @ (sF6 @ sF15 @ (sF12 @ (sF4 @ sF15)))))) | (~spl16_9 | ~spl16_11)),
  inference(forward_subsumption_resolution,[],[f1424,f1332])).
thf(f1427,plain,(
  (((sF8 @ (sF12 @ (sF4 @ sF15)) @ sF15)) = $true) | (~spl16_9 | ~spl16_11)),
  inference(forward_demodulation,[],[f1426,f478])).
thf(f1554,plain,(
  (((sF5 @ (sF12 @ (sF4 @ sF15)) @ sF15)) = $true) | ($true != $true) | (~spl16_9 | ~spl16_11)),
  inference(superposition,[],[f48,f1427])).
thf(f1555,plain,(
  (((sF5 @ (sF12 @ (sF4 @ sF15)) @ sF15)) = $true) | (~spl16_9 | ~spl16_11)),
  inference(trivial_inequality_removal,[],[f1554])).
thf(f1556,plain,(
  (((sF15 @ (sF4 @ sF15))) = $true) | (~spl16_9 | ~spl16_11)),
  inference(forward_demodulation,[],[f1555,f157])).
thf(f1557,plain,(
  $false | (spl16_8 | ~spl16_9 | ~spl16_11)),
  inference(forward_subsumption_resolution,[],[f1556,f1253])).
thf(f1558,plain,(
  spl16_8 | ~spl16_9 | ~spl16_11),
  inference(avatar_contradiction_clause,[],[f1557])).
cnf(s5, plain, spl16_8 | spl16_9, inference(sat_conversion,[],[f1259])).
cnf(s6, plain, ~spl16_8, inference(sat_conversion,[],[f1302])).
cnf(s8, plain, spl16_8 | spl16_11, inference(sat_conversion,[],[f1338])).
cnf(s10, plain, spl16_8 | ~spl16_9 | ~spl16_11, inference(sat_conversion,[],[f1558])).
cnf(s11, plain, spl16_11, inference(rat,[],[s8,s6])).
cnf(s12, plain, ~spl16_9, inference(rat,[],[s10,s6,s11])).
cnf(s13, plain, $false, inference(rat,[],[s5,s12,s6])).
thf(f1559,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s13])).
% SZS output end Proof for theBenchmark