%----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 > $o) > a)).
thf(func_def_4, type, sK1: (a > a > $o)).
thf(func_def_5, type, sK2: (a > a)).
thf(func_def_6, type, sK3: (a > (a > $o) > a)).
thf(func_def_7, type, sF4: (a > a)).
thf(func_def_8, type, sF5: (a > $o)).
thf(func_def_9, type, sF6: (a > $o)).
thf(func_def_10, type, sF7: (a > a > $o)).
thf(func_def_11, type, sF8: (a > a > $o)).
thf(func_def_12, type, sF9: ((a > $o) > a)).
thf(func_def_13, type, sF10: ((a > $o) > a > $o)).
thf(func_def_14, type, sF11: (a > (a > $o) > $o)).
thf(func_def_15, type, sF12: (a > (a > $o) > $o)).
thf(func_def_16, type, sF13: ((a > $o) > a > a)).
thf(func_def_17, type, sF14: (a > (a > $o) > $o)).
thf(func_def_18, type, sF15: (a > (a > $o) > $o)).
thf(func_def_19, type, vNOT: ($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)] : ((! [X6 : (a > $o)] : (! [X7 : a] : ((X6 @ X7) => (X0 @ X7 @ (X1 @ X6))) & ! [X8 : a] : (! [X9 : a] : (((X6 @ X9) & (X6 @ X9)) => (X0 @ X9 @ X8)) => ((X0 @ (X1 @ X6) @ X8) & (X0 @ (X1 @ X6) @ X8)))) & ! [X3 : a,X7 : a,X4 : a] : (((X0 @ X4 @ X7) & (X0 @ X3 @ X4)) => (X0 @ X3 @ X7))) => ! [X2 : (a > a)] : (! [X3 : a,X4 : a] : ((X0 @ X3 @ X4) => (X0 @ (X2 @ X3) @ (X2 @ X4))) => ? [X5 : a] : ((X0 @ X5 @ (X2 @ X5)) & (X0 @ (X2 @ X5) @ X5))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM145_C_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X1 : ((a > $o) > a),X0 : (a > a > $o)] : ((! [X6 : (a > $o)] : (! [X7 : a] : ((X6 @ X7) => (X0 @ X7 @ (X1 @ X6))) & ! [X8 : a] : (! [X9 : a] : (((X6 @ X9) & (X6 @ X9)) => (X0 @ X9 @ X8)) => ((X0 @ (X1 @ X6) @ X8) & (X0 @ (X1 @ X6) @ X8)))) & ! [X3 : a,X7 : a,X4 : a] : (((X0 @ X4 @ X7) & (X0 @ X3 @ X4)) => (X0 @ X3 @ X7))) => ! [X2 : (a > a)] : (! [X3 : a,X4 : a] : ((X0 @ X3 @ X4) => (X0 @ (X2 @ X3) @ (X2 @ X4))) => ? [X5 : a] : ((X0 @ X5 @ (X2 @ X5)) & (X0 @ (X2 @ X5) @ X5))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : ((a > $o) > a),X1 : (a > a > $o)] : ((! [X2 : (a > $o)] : (! [X3 : a] : ((X2 @ X3) => (X1 @ X3 @ (X0 @ X2))) & ! [X4 : a] : (! [X5 : a] : (((X2 @ X5) & (X2 @ X5)) => (X1 @ X5 @ X4)) => ((X1 @ (X0 @ X2) @ X4) & (X1 @ (X0 @ X2) @ X4)))) & ! [X6 : a,X7 : a,X8 : a] : (((X1 @ X8 @ X7) & (X1 @ X6 @ X8)) => (X1 @ X6 @ X7))) => ! [X9 : (a > a)] : (! [X10 : a,X11 : a] : ((X1 @ X10 @ X11) => (X1 @ (X9 @ X10) @ (X9 @ X11))) => ? [X12 : a] : ((X1 @ X12 @ (X9 @ X12)) & (X1 @ (X9 @ X12) @ X12))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X1 : (a > a > $o),X0 : ((a > $o) > a)] : ((! [X6 : a,X7 : a,X8 : a] : (((((X1 @ X8 @ X7)) = $true) & ($true = ((X1 @ X6 @ X8)))) => (((X1 @ X6 @ X7)) = $true)) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true = ((X2 @ X3))) => (((X1 @ X3 @ (X0 @ X2))) = $true)) & ! [X4 : a] : (! [X5 : a] : ((($true = ((X2 @ X5))) & ($true = ((X2 @ X5)))) => ($true = ((X1 @ X5 @ X4)))) => (($true = ((X1 @ (X0 @ X2) @ X4))) & ($true = ((X1 @ (X0 @ X2) @ X4))))))) => ! [X9 : (a > a)] : (! [X11 : a,X10 : a] : (($true = ((X1 @ X10 @ X11))) => (((X1 @ (X9 @ X10) @ (X9 @ X11))) = $true)) => ? [X12 : a] : (($true = ((X1 @ (X9 @ X12) @ X12))) & ($true = ((X1 @ X12 @ (X9 @ X12)))))))),
  inference(fool_elimination,[],[f3])).
thf(f5,plain,(
  ? [X1 : (a > a > $o),X0 : ((a > $o) > a)] : (? [X9 : (a > a)] : (! [X12 : a] : (($true != ((X1 @ (X9 @ X12) @ X12))) | ($true != ((X1 @ X12 @ (X9 @ X12))))) & ! [X10 : a,X11 : a] : ((((X1 @ (X9 @ X10) @ (X9 @ X11))) = $true) | ($true != ((X1 @ X10 @ X11))))) & (! [X6 : a,X7 : a,X8 : a] : ((((X1 @ X6 @ X7)) = $true) | ((((X1 @ X8 @ X7)) != $true) | ($true != ((X1 @ X6 @ X8))))) & ! [X2 : (a > $o)] : (! [X3 : a] : ((((X1 @ X3 @ (X0 @ X2))) = $true) | ($true != ((X2 @ X3)))) & ! [X4 : a] : ((($true = ((X1 @ (X0 @ X2) @ X4))) & ($true = ((X1 @ (X0 @ X2) @ X4)))) | ? [X5 : a] : (($true != ((X1 @ X5 @ X4))) & (($true = ((X2 @ X5))) & ($true = ((X2 @ X5)))))))))),
  inference(ennf_transformation,[],[f4])).
thf(f6,plain,(
  ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X9 : (a > a)] : (! [X12 : a] : (($true != ((X1 @ (X9 @ X12) @ X12))) | ($true != ((X1 @ X12 @ (X9 @ X12))))) & ! [X10 : a,X11 : a] : ((((X1 @ (X9 @ X10) @ (X9 @ X11))) = $true) | ($true != ((X1 @ X10 @ X11))))) & ! [X7 : a,X8 : a,X6 : a] : ((((X1 @ X6 @ X7)) = $true) | ($true != ((X1 @ X6 @ X8))) | (((X1 @ X8 @ X7)) != $true)) & ! [X2 : (a > $o)] : (! [X3 : a] : ((((X1 @ X3 @ (X0 @ X2))) = $true) | ($true != ((X2 @ X3)))) & ! [X4 : a] : ((($true = ((X1 @ (X0 @ X2) @ X4))) & ($true = ((X1 @ (X0 @ X2) @ X4)))) | ? [X5 : a] : (($true = ((X2 @ X5))) & ($true != ((X1 @ X5 @ X4))) & ($true = ((X2 @ X5)))))))),
  inference(flattening,[],[f5])).
thf(f7,plain,(
  ? [X0 : ((a > $o) > a),X1 : (a > a > $o)] : (? [X2 : (a > a)] : (! [X3 : a] : (($true != ((X1 @ (X2 @ X3) @ X3))) | (((X1 @ X3 @ (X2 @ X3))) != $true)) & ! [X4 : a,X5 : a] : ((((X1 @ (X2 @ X4) @ (X2 @ X5))) = $true) | ($true != ((X1 @ X4 @ X5))))) & ! [X6 : a,X7 : a,X8 : a] : (($true = ((X1 @ X8 @ X6))) | (((X1 @ X8 @ X7)) != $true) | ($true != ((X1 @ X7 @ X6)))) & ! [X9 : (a > $o)] : (! [X10 : a] : (($true = ((X1 @ X10 @ (X0 @ X9)))) | ($true != ((X9 @ X10)))) & ! [X11 : a] : ((($true = ((X1 @ (X0 @ X9) @ X11))) & ($true = ((X1 @ (X0 @ X9) @ X11)))) | ? [X12 : a] : ((((X9 @ X12)) = $true) & ($true != ((X1 @ X12 @ X11))) & (((X9 @ X12)) = $true)))))),
  inference(rectify,[],[f6])).
thf(f8,plain,(
  (! [X3 : a] : ((((sK1 @ (sK2 @ X3) @ X3)) != $true) | (((sK1 @ X3 @ (sK2 @ X3))) != $true)) & ! [X4 : a,X5 : a] : ((((sK1 @ (sK2 @ X4) @ (sK2 @ X5))) = $true) | ($true != ((sK1 @ X4 @ X5))))) & ! [X6 : a,X7 : a,X8 : a] : (($true = ((sK1 @ X8 @ X6))) | ($true != ((sK1 @ X8 @ X7))) | ($true != ((sK1 @ X7 @ X6)))) & ! [X9 : (a > $o)] : (! [X10 : a] : ((((sK1 @ X10 @ (sK0 @ X9))) = $true) | ($true != ((X9 @ X10)))) & ! [X11 : a] : ((($true = ((sK1 @ (sK0 @ X9) @ X11))) & ($true = ((sK1 @ (sK0 @ X9) @ X11)))) | (($true = ((X9 @ (sK3 @ X11 @ X9)))) & ($true != ((sK1 @ (sK3 @ X11 @ X9) @ X11))) & ($true = ((X9 @ (sK3 @ X11 @ X9)))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X12,$thf(sK3 @ X11 @ X9))],[f7])).
thf(f13,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : (($true = ((sK1 @ (sK0 @ X9) @ X11))) | ($true != ((sK1 @ (sK3 @ X11 @ X9) @ X11)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f14,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : (($true = ((sK1 @ (sK0 @ X9) @ X11))) | ($true = ((X9 @ (sK3 @ X11 @ X9))))) )),
  inference(cnf_transformation,[],[f8])).
thf(f15,plain,(
  ( ! [X10 : a,X9 : (a > $o)] : ((((sK1 @ X10 @ (sK0 @ X9))) = $true) | ($true != ((X9 @ X10)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f16,plain,(
  ( ! [X8 : a,X6 : a,X7 : a] : (($true = ((sK1 @ X8 @ X6))) | ($true != ((sK1 @ X8 @ X7))) | ($true != ((sK1 @ X7 @ X6)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f17,plain,(
  ( ! [X4 : a,X5 : a] : ((((sK1 @ (sK2 @ X4) @ (sK2 @ X5))) = $true) | ($true != ((sK1 @ X4 @ X5)))) )),
  inference(cnf_transformation,[],[f8])).
thf(f18,plain,(
  ( ! [X3 : a] : ((((sK1 @ (sK2 @ X3) @ X3)) != $true) | (((sK1 @ X3 @ (sK2 @ X3))) != $true)) )),
  inference(cnf_transformation,[],[f8])).
thf(f21,definition,(
  ( ! [X3 : a] : ((((sF4 @ X3)) = ((sK2 @ X3)))) )),
  introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
thf(f22,plain,(
  ( ! [X3 : a] : ((((sK2 @ X3)) = ((sF4 @ X3)))) )),
  inference(reorient_equations,[],[f21])).
thf(f23,definition,(
  ( ! [X3 : a] : ((((sF5 @ X3)) = ((sK1 @ (sF4 @ X3) @ X3)))) )),
  introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
thf(f24,definition,(
  ( ! [X3 : a] : ((((sF6 @ X3)) = ((sK1 @ X3 @ (sF4 @ X3))))) )),
  introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
thf(f25,plain,(
  ( ! [X3 : a] : ((((sK1 @ X3 @ (sF4 @ X3))) = ((sF6 @ X3)))) )),
  inference(reorient_equations,[],[f24])).
thf(f26,plain,(
  ( ! [X3 : a] : ((((sF6 @ X3)) != $true) | (((sF5 @ X3)) != $true)) )),
  inference(definition_folding,[],[f18,f25,f22,f23,f22])).
thf(f27,definition,(
  ( ! [X4 : a,X5 : a] : ((((sF7 @ X5 @ X4)) = ((sK1 @ (sF4 @ X4) @ (sF4 @ X5))))) )),
  introduced(definition,[new_symbols(definition,[sF7])],[function_definition])).
thf(f28,definition,(
  ( ! [X4 : a,X5 : a] : ((((sF8 @ X5 @ X4)) = ((sK1 @ X4 @ X5)))) )),
  introduced(definition,[new_symbols(definition,[sF8])],[function_definition])).
thf(f29,plain,(
  ( ! [X4 : a,X5 : a] : (($true != ((sF8 @ X5 @ X4))) | (((sF7 @ X5 @ X4)) = $true)) )),
  inference(definition_folding,[],[f17,f28,f27,f22,f22])).
thf(f30,plain,(
  ( ! [X8 : a,X6 : a,X7 : a] : ((((sF8 @ X7 @ X8)) != $true) | (((sF8 @ X6 @ X8)) = $true) | (((sF8 @ X6 @ X7)) != $true)) )),
  inference(definition_folding,[],[f16,f28,f28,f28])).
thf(f31,definition,(
  ( ! [X9 : (a > $o)] : ((((sF9 @ X9)) = ((sK0 @ X9)))) )),
  introduced(definition,[new_symbols(definition,[sF9])],[function_definition])).
thf(f32,definition,(
  ( ! [X10 : a,X9 : (a > $o)] : ((((sF10 @ X9 @ X10)) = ((sK1 @ X10 @ (sF9 @ X9))))) )),
  introduced(definition,[new_symbols(definition,[sF10])],[function_definition])).
thf(f33,definition,(
  ( ! [X10 : a,X9 : (a > $o)] : ((((sF11 @ X10 @ X9)) = ((X9 @ X10)))) )),
  introduced(definition,[new_symbols(definition,[sF11])],[function_definition])).
thf(f34,plain,(
  ( ! [X10 : a,X9 : (a > $o)] : (($true = ((sF10 @ X9 @ X10))) | ($true != ((sF11 @ X10 @ X9)))) )),
  inference(definition_folding,[],[f15,f33,f32,f31])).
thf(f35,definition,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF12 @ X11 @ X9)) = ((sK1 @ (sF9 @ X9) @ X11)))) )),
  introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
thf(f36,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sK1 @ (sF9 @ X9) @ X11)) = ((sF12 @ X11 @ X9)))) )),
  inference(reorient_equations,[],[f35])).
thf(f37,definition,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF13 @ X9 @ X11)) = ((sK3 @ X11 @ X9)))) )),
  introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
thf(f38,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sK3 @ X11 @ X9)) = ((sF13 @ X9 @ X11)))) )),
  inference(reorient_equations,[],[f37])).
thf(f39,definition,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF14 @ X11 @ X9)) = ((X9 @ (sF13 @ X9 @ X11))))) )),
  introduced(definition,[new_symbols(definition,[sF14])],[function_definition])).
thf(f40,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : (($true = ((sF12 @ X11 @ X9))) | (((sF14 @ X11 @ X9)) = $true)) )),
  inference(definition_folding,[],[f14,f39,f38,f36,f31])).
thf(f41,definition,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF15 @ X11 @ X9)) = ((sK1 @ (sF13 @ X9 @ X11) @ X11)))) )),
  introduced(definition,[new_symbols(definition,[sF15])],[function_definition])).
thf(f42,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sK1 @ (sF13 @ X9 @ X11) @ X11)) = ((sF15 @ X11 @ X9)))) )),
  inference(reorient_equations,[],[f41])).
thf(f43,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : (($true != ((sF15 @ X11 @ X9))) | ($true = ((sF12 @ X11 @ X9)))) )),
  inference(definition_folding,[],[f13,f42,f38,f36,f31])).
thf(f48,plain,(
  ( ! [X3 : a] : ((((sF5 @ X3)) = ((sK1 @ (sK2 @ X3) @ X3)))) )),
  inference(forward_demodulation,[],[f23,f22])).
thf(f49,plain,(
  ( ! [X3 : a] : ((((sF6 @ X3)) = ((sK1 @ X3 @ (sK2 @ X3))))) )),
  inference(forward_demodulation,[],[f25,f22])).
thf(f62,plain,(
  ( ! [X10 : a,X9 : (a > $o)] : (($true != ((X9 @ X10))) | ($true = ((sF10 @ X9 @ X10)))) )),
  inference(forward_demodulation,[],[f34,f33])).
thf(f81,plain,(
  ( ! [X0 : a] : ((((sF5 @ X0)) = ((sF8 @ X0 @ (sK2 @ X0))))) )),
  inference(constrained_superposition,[],[f28,f48])).
thf(f82,plain,(
  ( ! [X0 : a] : ((((sF8 @ (sK2 @ X0) @ X0)) = ((sF6 @ X0)))) )),
  inference(constrained_superposition,[],[f28,f49])).
thf(f104,plain,(
  ( ! [X0 : a,X1 : a] : ((((sF8 @ X1 @ (sK2 @ X0))) != $true) | ($true = ((sF8 @ X1 @ X0))) | ($true != ((sF6 @ X0)))) )),
  inference(constrained_superposition,[],[f30,f82])).
thf(f113,plain,(
  ( ! [X4 : a,X5 : a] : ((((sF7 @ X5 @ X4)) = ((sF8 @ (sF4 @ X5) @ (sF4 @ X4))))) )),
  inference(forward_demodulation,[],[f27,f28])).
thf(f114,plain,(
  ( ! [X4 : a,X5 : a] : ((((sF7 @ X5 @ X4)) = ((sF8 @ (sK2 @ X5) @ (sF4 @ X4))))) )),
  inference(forward_demodulation,[],[f113,f22])).
thf(f115,plain,(
  ( ! [X4 : a,X5 : a] : ((((sF7 @ X5 @ X4)) = ((sF8 @ (sK2 @ X5) @ (sK2 @ X4))))) )),
  inference(forward_demodulation,[],[f114,f22])).
thf(f116,plain,(
  ( ! [X10 : a,X9 : (a > $o)] : ((((sF8 @ (sF9 @ X9) @ X10)) = ((sF10 @ X9 @ X10)))) )),
  inference(forward_demodulation,[],[f32,f28])).
thf(f117,plain,(
  ( ! [X10 : a,X9 : (a > $o)] : ((((sF8 @ (sK0 @ X9) @ X10)) = ((sF10 @ X9 @ X10)))) )),
  inference(forward_demodulation,[],[f116,f31])).
thf(f118,plain,(
  ( ! [X0 : a] : ((((sF5 @ (sK2 @ X0))) = ((sF7 @ X0 @ (sK2 @ X0))))) )),
  inference(constrained_superposition,[],[f115,f81])).
thf(f119,plain,(
  ( ! [X0 : a] : ((((sF7 @ (sK2 @ X0) @ X0)) = ((sF6 @ (sK2 @ X0))))) )),
  inference(constrained_superposition,[],[f115,f82])).
thf(f128,plain,(
  ( ! [X0 : a,X1 : a] : ((((sF7 @ X0 @ X1)) != $true) | (((sF8 @ (sK2 @ X0) @ X1)) = $true) | ($true != ((sF6 @ X1)))) )),
  inference(constrained_superposition,[],[f104,f115])).
thf(f148,plain,(
  ( ! [X0 : (a > $o),X1 : a] : (($true != ((sF10 @ X0 @ X1))) | ($true = ((sF7 @ (sK0 @ X0) @ X1)))) )),
  inference(constrained_superposition,[],[f29,f117])).
thf(f1034,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF8 @ X11 @ (sF9 @ X9))) = ((sF12 @ X11 @ X9)))) )),
  inference(forward_demodulation,[],[f36,f28])).
thf(f1035,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF8 @ X11 @ (sK0 @ X9))) = ((sF12 @ X11 @ X9)))) )),
  inference(forward_demodulation,[],[f1034,f31])).
thf(f2620,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true != ((sF14 @ X0 @ X1))) | ($true = ((sF10 @ X1 @ (sF13 @ X1 @ X0))))) )),
  inference(constrained_superposition,[],[f62,f39])).
thf(f4548,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : ((((sF12 @ X0 @ X1)) != $true) | ($true = ((sF7 @ X0 @ (sK0 @ X1))))) )),
  inference(constrained_superposition,[],[f29,f1035])).
thf(f4976,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true = ((sF7 @ X0 @ (sK0 @ X1)))) | ($true != $true) | ($true = ((sF14 @ X0 @ X1)))) )),
  inference(constrained_superposition,[],[f4548,f40])).
thf(f4977,plain,(
  ( ! [X0 : a,X1 : (a > $o)] : (($true = ((sF7 @ X0 @ (sK0 @ X1)))) | ($true = ((sF14 @ X0 @ X1)))) )),
  inference(trivial_inequality_removal,[],[f4976])).
thf(f4978,plain,(
  ( ! [X0 : (a > $o)] : (($true = ((sF14 @ (sK2 @ (sK0 @ X0)) @ X0))) | ($true = ((sF6 @ (sK2 @ (sK0 @ X0)))))) )),
  inference(constrained_superposition,[],[f4977,f119])).
thf(f5964,plain,(
  ( ! [X11 : a,X9 : (a > $o)] : ((((sF8 @ X11 @ (sF13 @ X9 @ X11))) = ((sF15 @ X11 @ X9)))) )),
  inference(forward_demodulation,[],[f42,f28])).
thf(f6455,definition,(
  spl16_135 <=> (((sF6 @ (sK2 @ (sK0 @ sF6)))) = $true)),
  introduced(definition,[new_symbols(definition,[spl16_135])],[avatar_definition])).
thf(f6456,plain,(
  (((sF6 @ (sK2 @ (sK0 @ sF6)))) != $true) | spl16_135),
  inference(avatar_component_clause,[],[f6455])).
thf(f6457,plain,(
  (((sF6 @ (sK2 @ (sK0 @ sF6)))) = $true) | ~spl16_135),
  inference(avatar_component_clause,[],[f6455])).
thf(f6464,plain,(
  ($true != ((sF5 @ (sK2 @ (sK0 @ sF6))))) | ($true != $true) | ~spl16_135),
  inference(constrained_superposition,[],[f26,f6457])).
thf(f6479,plain,(
  ($true = ((sF10 @ sF6 @ (sK2 @ (sK0 @ sF6))))) | ($true != $true) | ~spl16_135),
  inference(constrained_superposition,[],[f62,f6457])).
thf(f6491,plain,(
  ($true != ((sF5 @ (sK2 @ (sK0 @ sF6))))) | ~spl16_135),
  inference(trivial_inequality_removal,[],[f6464])).
thf(f6511,plain,(
  ($true = ((sF10 @ sF6 @ (sK2 @ (sK0 @ sF6))))) | ~spl16_135),
  inference(trivial_inequality_removal,[],[f6479])).
thf(f6735,plain,(
  ($true = ((sF7 @ (sK0 @ sF6) @ (sK2 @ (sK0 @ sF6))))) | ($true != $true) | ~spl16_135),
  inference(constrained_superposition,[],[f148,f6511])).
thf(f6743,plain,(
  ($true = ((sF7 @ (sK0 @ sF6) @ (sK2 @ (sK0 @ sF6))))) | ~spl16_135),
  inference(trivial_inequality_removal,[],[f6735])).
thf(f6746,plain,(
  ($true = ((sF5 @ (sK2 @ (sK0 @ sF6))))) | ~spl16_135),
  inference(forward_demodulation,[],[f6743,f118])).
thf(f6747,plain,(
  $false | ~spl16_135),
  inference(forward_subsumption_resolution,[],[f6746,f6491])).
thf(f6748,plain,(
  ~spl16_135),
  inference(avatar_contradiction_clause,[],[f6747])).
thf(f7063,definition,(
  spl16_141 <=> ($true = ((sF14 @ (sK2 @ (sK0 @ sF6)) @ sF6)))),
  introduced(definition,[new_symbols(definition,[spl16_141])],[avatar_definition])).
thf(f7064,plain,(
  ($true = ((sF14 @ (sK2 @ (sK0 @ sF6)) @ sF6))) | ~spl16_141),
  inference(avatar_component_clause,[],[f7063])).
thf(f7065,plain,(
  ($true != ((sF14 @ (sK2 @ (sK0 @ sF6)) @ sF6))) | spl16_141),
  inference(avatar_component_clause,[],[f7063])).
thf(f7071,plain,(
  (((sF6 @ (sK2 @ (sK0 @ sF6)))) = $true) | ($true != $true) | spl16_141),
  inference(constrained_superposition,[],[f7065,f4978])).
thf(f7072,plain,(
  (((sF6 @ (sK2 @ (sK0 @ sF6)))) = $true) | spl16_141),
  inference(trivial_inequality_removal,[],[f7071])).
thf(f7073,plain,(
  $false | (spl16_135 | spl16_141)),
  inference(forward_subsumption_resolution,[],[f7072,f6456])).
thf(f7074,plain,(
  spl16_135 | spl16_141),
  inference(avatar_contradiction_clause,[],[f7073])).
thf(f7075,plain,(
  ($true != $true) | ($true = ((sF10 @ sF6 @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6)))))) | ~spl16_141),
  inference(constrained_superposition,[],[f2620,f7064])).
thf(f7077,plain,(
  ($true = ((sF10 @ sF6 @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6)))))) | ~spl16_141),
  inference(trivial_inequality_removal,[],[f7075])).
thf(f7550,plain,(
  ($true != $true) | (((sF7 @ (sK0 @ sF6) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | ~spl16_141),
  inference(constrained_superposition,[],[f148,f7077])).
thf(f7553,plain,(
  (((sF7 @ (sK0 @ sF6) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | ~spl16_141),
  inference(trivial_inequality_removal,[],[f7550])).
thf(f8331,plain,(
  ($true != $true) | (((sF8 @ (sK2 @ (sK0 @ sF6)) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | (((sF6 @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) != $true) | ~spl16_141),
  inference(constrained_superposition,[],[f128,f7553])).
thf(f8339,plain,(
  (((sF6 @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) != $true) | (((sF8 @ (sK2 @ (sK0 @ sF6)) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | ~spl16_141),
  inference(trivial_inequality_removal,[],[f8331])).
thf(f8348,plain,(
  (((sF8 @ (sK2 @ (sK0 @ sF6)) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | ($true != ((sF14 @ (sK2 @ (sK0 @ sF6)) @ sF6))) | ~spl16_141),
  inference(forward_demodulation,[],[f8339,f39])).
thf(f8349,plain,(
  (((sF8 @ (sK2 @ (sK0 @ sF6)) @ (sF13 @ sF6 @ (sK2 @ (sK0 @ sF6))))) = $true) | ~spl16_141),
  inference(forward_subsumption_resolution,[],[f8348,f7064])).
thf(f8350,plain,(
  (((sF15 @ (sK2 @ (sK0 @ sF6)) @ sF6)) = $true) | ~spl16_141),
  inference(forward_demodulation,[],[f8349,f5964])).
thf(f8351,plain,(
  ($true != $true) | ($true = ((sF12 @ (sK2 @ (sK0 @ sF6)) @ sF6))) | ~spl16_141),
  inference(constrained_superposition,[],[f43,f8350])).
thf(f8352,plain,(
  ($true = ((sF12 @ (sK2 @ (sK0 @ sF6)) @ sF6))) | ~spl16_141),
  inference(trivial_inequality_removal,[],[f8351])).
thf(f8355,plain,(
  ($true != $true) | ($true = ((sF7 @ (sK2 @ (sK0 @ sF6)) @ (sK0 @ sF6)))) | ~spl16_141),
  inference(constrained_superposition,[],[f4548,f8352])).
thf(f8356,plain,(
  ($true = ((sF7 @ (sK2 @ (sK0 @ sF6)) @ (sK0 @ sF6)))) | ~spl16_141),
  inference(trivial_inequality_removal,[],[f8355])).
thf(f8359,plain,(
  (((sF6 @ (sK2 @ (sK0 @ sF6)))) = $true) | ~spl16_141),
  inference(forward_demodulation,[],[f8356,f119])).
thf(f8360,plain,(
  $false | (spl16_135 | ~spl16_141)),
  inference(forward_subsumption_resolution,[],[f8359,f6456])).
thf(f8361,plain,(
  spl16_135 | ~spl16_141),
  inference(avatar_contradiction_clause,[],[f8360])).
cnf(s82, plain, ~spl16_135, inference(sat_conversion,[],[f6748])).
cnf(s84, plain, spl16_135 | spl16_141, inference(sat_conversion,[],[f7074])).
cnf(s101, plain, spl16_135 | ~spl16_141, inference(sat_conversion,[],[f8361])).
cnf(s103, plain, ~spl16_141, inference(rat,[],[s101,s82])).
cnf(s104, plain, $false, inference(rat,[],[s84,s103,s82])).
thf(f8362,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s104])).
% SZS output end Proof for theBenchmark