YES 0SSplusSxxplus0x0y0plusxyplus0x1y1plusxyplus0xjyjplusxyplus1x1yjplus1Splusxyplusjxjy1plusjSplusxyplus1xjy0plusxyoppSSopp0x0oppxopp1xjoppxoppjx1oppxminusxyplusoppyxtimesSxStimes0xy0timesxytimes1xyplus0timesxyytimesjxyminus0timesxyysignxif_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSyplustimesplustimes2.1plusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyzplusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyzplusplusxyzplusyztimestimesxyztimesyzplus0x0y0plusxyplus0x0yplusxyplus0x1yplusxyplus0xjyplusxyplus1x1yplus1Splusxyplus1x1yplusxyplusjxjyplusjSplusxyplusjxjyplusxyplus1xjy0plusxyplus1xjyplusxyopp0x0oppxopp0xoppxopp1xoppxoppjxoppxminusxyplusoppyxminusxyoppytimes0xy0timesxytimes0xytimesxytimes1xyplus0timesxyytimes1xy0timesxytimes1xytimesxytimesjxyminus0timesxyytimesjxy0timesxytimesjxytimesxysignxif_signxSif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxjSoppxminxyif_minminusabsyabsxxySminxyminusabsyabsxminxyabsyminxyabsxmin'xyif_minminusabs1yabs1xxySmin'xyminusabs1yabs1xmin'xyabs1ymin'xyabs1xmin''xyif_minminusabsjyabsjxxySmin''xyminusabsjyabsjxmin''xyabsjymin''xyabsjxif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x0yext0plusxyplusplus0x0yextplusxyplusplus0x1yextplus1plusxyextplusplus0x1yextplusxyplusplus0xjyextplusjplusxyextplusplus0xjyextplusxyplusplus1x1yextplusjplus1Splusxyextplusplus1x1yextplus1Splusxyplusplus1x1yextplusxyplusplusjxjyextplus1plusjSplusxyextplusplusjxjyextplusjSplusxyplusplusjxjyextplusxyplusplus1xjyextplus0plusxyextplusplus1xjyext0plusxyplusplus1xjyextplusxytimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes0xyext0timesxytimestimes0xyexttimesxytimestimes1xyexttimesplus0timesxyyexttimestimes1xyextplus0timesxyytimestimes1xyext0timesxytimestimes1xyexttimesxytimestimesjxyexttimesminus0timesxyyexttimestimesjxyextminus0timesxyytimestimesjxyext0timesxytimestimesjxyexttimesxyplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus1x1yextplusjplus1Splusxyextplusplusjxjyextplus1plusjSplusxyextplusplus1xjyextplus0plusxyexttimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyexttimes1xytimesxytimes0xytimesxytimesjxytimesxytimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes0xyexttimesxytimestimes1xyexttimesplus0timesxyyexttimestimes1xyexttimesxytimestimesjxyexttimesminus0timesxyyexttimestimesjxyexttimesxytimestimesxyztimesyztimesxytimesyxtimestimesxyztimesxtimesyztrue2times21211112times212111120111j1111minus211211S0011111plus21211opp1111timestimesjxyexttimesxytimestimes1xyexttimesplus0timesxyyexttimes1xytimesxytimesjxytimesxytimestimes1xyexttimesxyplusplus1x1yextplusjplus1Splusxyextplusplus0xjyextplusjplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x0y0plusxyplusjxjy1plusjSplusxyplusplus0x1yextplus1plusxyextplusplusjxjyextplus1plusjSplusxyextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxxminusxyplusoppyx0SStimesSxStimestimesSxexttimesSexttimes1xyplus0timesxyytimestimes0xyexttimes0timesxyexttimesjxyminus0timesxyytimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyexttimes0xy0timesxyopp1xjoppxopp0x0oppxoppSSoppjx1oppxplusplusxyzplusxplusyzplusxyplusyxtimesxytimesyxtimestimesxyztimesxtimesyz2times21211112times212111120111j1111minus21211S00plus21211opp11111111timestimesjxyexttimesminus0timesxyyextminusxyplusoppyxplusplus1x1yextplusjplus1Splusxyextplusplus0xjyextplusjplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x0y0plusxyplusjxjy1plusjSplusxyplusplus0x1yextplus1plusxyextplusplusjxjyextplus1plusjSplusxyextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxxopp1xjoppxopp0x0oppxoppSSoppjx1oppxtimesSxStimestimesSxexttimesSexttimes1xyplus0timesxyytimestimes0xyexttimes0timesxyexttimesjxyminus0timesxyytimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyexttimes0xy0timesxy0SSplusplusxyzplusxplusyzplusxyplusyxtimesxytimesyxtimestimesxyztimesxtimesyz2times21211112times2121111201111S0011111plus21211j1111minus21211opp111timestimes0xyexttimesxytimes0xytimesxy0SStimesSxStimestimesSxexttimesSexttimes1xyplus0timesxyytimestimes0xyexttimes0timesxyexttimesjxyminus0timesxyytimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyexttimes0xy0timesxyplusplus1x1yextplusjplus1Splusxyextplusplus0xjyextplusjplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x0y0plusxyplusjxjy1plusjSplusxyplusplus0x1yextplus1plusxyextplusplusjxjyextplus1plusjSplusxyextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxxminusxyplusoppyxopp1xjoppxopp0x0oppxoppSSoppjx1oppxtimesxytimesyxtimestimesxyztimesxtimesyzplusplusxyzplusxplusyzplusxyplusyx1times23132times231112S00013minus211112plus21112opp1111111j12timestimesxyztimesyztimestimesSxexttimesSexttimestimes0xyexttimes0timesxyextminusxyplusoppyxopp1xjoppxopp0x0oppxoppSSoppjx1oppx0SStimesSxStimestimesSxexttimesSexttimes1xyplus0timesxyytimestimes0xyexttimes0timesxyexttimesjxyminus0timesxyytimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyexttimes0xy0timesxyplusplus1x1yextplusjplus1Splusxyextplusplus0xjyextplusjplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x0y0plusxyplusjxjy1plusjSplusxyplusplus0x1yextplus1plusxyextplusplusjxjyextplus1plusjSplusxyextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxxtimesxytimesyxtimestimesxyztimesxtimesyzplusplusxyzplusxplusyzplusxyplusyxtimesjxyminus0timesxyyfalseminxyminusabsyabsxfalsemin'xyminusabs1yabs1xfalsemin''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_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSytimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyextplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplusjxjyextplus1plusjSplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxx0SSplus0x0y0plusxyplusplusxyzplusxplusyzplusxyplusyx1plus21112plus21112times21112j111111111S0001111plusplus0x0yextplus0plusxyextplusplus1xjyextplusxyplusplusjxjyextplusjSplusxyplus1x1yplusxyplus0x1yplusxyplusplus0x1yextplusxyplusjxjyplusxyplusplus1xjyextplus0plusxyextplusplus1x1yextplus1Splusxyplusplusjxjyextplusxyplus0x0yplusxyplusplus0x0yextplusxyplusplus1x1yextplusxyplusplus0x1yextplus1plusxyextplusjxjyplusjSplusxyplus1x1yplus1Splusxyplusplus0xjyextplusjplusxyextplus0xjyplusxyplus1xjyplusxyplusplus0xjyextplusxyplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus0x0yextplus0plusxyextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxy0SSplus0x0y0plusxyplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplusjxjyextplus1plusjSplusxyextplusplus0x0yextplus0plusxyextplusplusSxextplusxextplus0x1y1plusxyplus1xjy0plusxyplusplus1xjyextplus0plusxyextplus0xjyjplusxyplus1x1yjplus1SplusxyplusSxx0SSplus0x0y0plusxyplusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyz1plus22122plus21112j10110S01plusplusSxextplusxextplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplus1x1yjplus1Splusxyplusplusjxjyextplus1plusjSplusxyextplusSxxplusplusSxextplusxextplusplusxyzplusxplusyzplusxyplusyx1plus22122plus21112j11112S00plusplus1x1yextplusjplus1Splusxyextplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplus1x1yjplus1Splusxyplusplusjxjyextplus1plusjSplusxyextplusSxxplusplusSxextplusxextplusplusxyzplusxplusyzplusxyplusyx1plus21112plus211112j10111S00plusplusxyzplusyzplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplus1x1yjplus1Splusxyplusplusjxjyextplus1plusjSplusxyextplusSxxplusplusSxextplusxextplusplusxyzplusxplusyzplusxyplusyx1plus21112plus21112j11111S00plusplusjxjyextplus1plusjSplusxyextplusjxjy1plusjSplusxyplusplus1x1yextplusjplus1Splusxyextplus1x1yjplus1Splusxyplusplusjxjyextplus1plusjSplusxyextplusSxxplusplusSxextplusxextplusplusxyzplusxplusyzplusxyplusyxplus0x0y0plusxyfalseplus1xjy0plusxyfalseminusxyoppyfalseminxyabsyfalseminxyabsxfalsemin'xyabs1yfalsemin'xyabs1xfalsemin''xyabsjyfalsemin''xyabsjxfalseabsxif_absxxSfalseif_abs1xyzif_absxy1Sif_abs0xyzif_absxyzif_absjxyzif_absxyjStrue1if_abs31112131111S00j1210131if_abs0xyzif_absxyz0SSplusSxxplus0x0y0plusxyplus0x1y1plusxyplus0xjyjplusxyplus1x1yjplus1Splusxyplusjxjy1plusjSplusxyplus1xjy0plusxyoppSSopp0x0oppxopp1xjoppxoppjx1oppxminusxyplusoppyxtimesSxStimes0xy0timesxytimes1xyplus0timesxyytimesjxyminus0timesxyysignxif_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSyplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus1x1yextplusjplus1Splusxyextplusplusjxjyextplus1plusjSplusxyextplusplus1xjyextplus0plusxyexttimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyext1plus21112times21112if_abs33112231111S00j1321if_absjxyzif_absxyjSplusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyz1plus21112times21112if_abs331121311321S01if_abs1xyzif_absxy1Splusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyzif_absSxjSoppxfalseopp1xoppxopp0xoppxoppjxoppxtrue1opp121j13101311111oppjxoppxopp0xoppxopp1xoppx0SSplusSxxplus0x0y0plusxyplus0x1y1plusxyplus0xjyjplusxyplus1x1yjplus1Splusxyplusjxjy1plusjSplusxyplus1xjy0plusxyoppSSopp0x0oppxopp1xjoppxoppjx1oppxminusxyplusoppyxtimesSxStimes0xy0timesxytimes1xyplus0timesxyytimesjxyminus0timesxyysignxif_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSyplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus1x1yextplusjplus1Splusxyextplusplusjxjyextplus1plusjSplusxyextplusplus1xjyextplus0plusxyexttimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyextopp0x0oppxfalsetimes0xy0timesxyfalsetimes1xy0timesxyfalsetimesjxy0timesxyfalsesignxif_signxSfalseif_sign1xyif_signx1Sif_sign0xyif_signxyif_signjxyif_signxjStrue1if_sign2111201311111S00j111if_sign0xyif_signxy0SSplusSxxplus0x0y0plusxyplus0x1y1plusxyplus0xjyjplusxyplus1x1yjplus1Splusxyplusjxjy1plusjSplusxyplus1xjy0plusxyoppSSopp0x0oppxopp1xjoppxoppjx1oppxminusxyplusoppyxtimesSxStimes0xy0timesxytimes1xyplus0timesxyytimesjxyminus0timesxyysignxif_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSyplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus1x1yextplusjplus1Splusxyextplusplusjxjyextplus1plusjSplusxyextplusplus1xjyextplus0plusxyexttimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyext1plus21112times21112if_sign231221111S00j1321if_signjxyif_signxjSplusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyz1plus21112times21112if_sign2311211321S01if_sign1xyif_signx1Splusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyzminxyif_minminusabsyabsxxySfalsemin'xyif_minminusabs1yabs1xxySfalsemin''xyif_minminusabsjyabsjxxySfalseif_min1xyzuif_minxyz1Sif_min0xyzuif_minxyzuif_minjxyzuif_minxyzjStrue1if_min4111213141111S00j1110131if_min0xyzuif_minxyzu0SSplusSxxplus0x0y0plusxyplus0x1y1plusxyplus0xjyjplusxyplus1x1yjplus1Splusxyplusjxjy1plusjSplusxyplus1xjy0plusxyoppSSopp0x0oppxopp1xjoppxoppjx1oppxminusxyplusoppyxtimesSxStimes0xy0timesxytimes1xyplus0timesxyytimesjxyminus0timesxyysignxif_signxSif_signSxxif_sign0xyif_signxyif_sign1xyif_signx1Sif_signjxyif_signxjSabsxif_absxxSif_abs0xyzif_absxyzif_abs1xyzif_absxy1Sif_absjxyzif_absxyjSif_absSxSSif_absSx1Sxif_absSxjSoppxminxyif_minminusabsyabsxxySmin'xyif_minminusabs1yabs1xxySmin''xyif_minminusabsjyabsjxxySif_min0xyzuif_minxyzuif_min1xyzuif_minxyz1Sif_minjxyzuif_minxyzjSif_minSxySxif_minSxy1Sxif_minSxyjSyplusplusSxextplusxextplusplus0x0yextplus0plusxyextplusplus0x1yextplus1plusxyextplusplus0xjyextplusjplusxyextplusplus1x1yextplusjplus1Splusxyextplusplusjxjyextplus1plusjSplusxyextplusplus1xjyextplus0plusxyexttimestimesSxexttimesSexttimestimes0xyexttimes0timesxyexttimestimes1xyexttimesplus0timesxyyexttimestimesjxyexttimesminus0timesxyyext1plus21112times21112if_min4311213241111S00j1321if_minjxyzuif_minxyzjSplusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyz1plus21112times21112if_min43112131411321S01if_min1xyzuif_minxyz1Splusxyplusyxtimesxytimesyxplusplusxyzplusxplusyztimestimesxyztimesxtimesyzplusplus0x0yext0plusxyfalseplusplus1xjyext0plusxyfalsetimestimes0xyext0timesxyfalsetimestimes1xyext0timesxyfalsetimestimesjxyext0timesxyfalseAProVEAProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Statistics for single proof: 100.00 % (28 real / 0 unknown / 0 assumptions / 28 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe