%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL950^17 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:56 PM UTC 2026 % Result : Theorem 47.14s 47.68s % Output : Proof 47.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL950^17 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.36 % Computer : n027.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Fri Sep 4 13:58:42 UTC 2026 % 0.09/0.37 % CPUTime : % 47.14/47.68 % SZS status Theorem % 47.14/47.68 % Mode: mode484 % 47.14/47.68 % Inferences: 11715 % 47.14/47.68 % SZS output start Proof % 47.14/47.68 thf(ty_mworld, type, mworld : $tType). % 47.14/47.68 thf(ty_eigen__6, type, eigen__6 : mworld). % 47.14/47.68 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)). % 47.14/47.68 thf(ty_eigen__2, type, eigen__2 : mworld). % 47.14/47.68 thf(ty_eigen__7, type, eigen__7 : mworld). % 47.14/47.68 thf(ty_eigen__1, type, eigen__1 : $i). % 47.14/47.68 thf(ty_eigen__0, type, eigen__0 : mworld). % 47.14/47.68 thf(ty_member, type, member : ($i>$i>mworld>$o)). % 47.14/47.68 thf(ty_eigen__4, type, eigen__4 : mworld). % 47.14/47.68 thf(ty_eigen__5, type, eigen__5 : $i). % 47.14/47.68 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 47.14/47.68 thf(ty_eigen__3, type, eigen__3 : $i). % 47.14/47.68 thf(ty_mactual, type, mactual : mworld). % 47.14/47.68 thf(ty_intersect, type, intersect : ($i>$i>mworld>$o)). % 47.14/47.68 thf(sP1,plain,sP1 <=> (((eiw_di @ eigen__3) @ mactual) => (![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__3) @ eigen__5) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 47.14/47.68 thf(sP2,plain,sP2 <=> ((mrel @ eigen__6) @ eigen__7),introduced(definition,[new_symbols(definition,[sP2])])). % 47.14/47.68 thf(sP3,plain,sP3 <=> (![X1:mworld]:(![X2:$i]:((~((((eiw_di @ X2) @ eigen__0) => (~(((mrel @ eigen__0) @ X1)))))) => ((eiw_di @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 47.14/47.68 thf(sP4,plain,sP4 <=> (![X1:$i]:((~((((eiw_di @ X1) @ eigen__0) => (~(((mrel @ eigen__0) @ eigen__2)))))) => ((eiw_di @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP4])])). % 47.14/47.68 thf(sP5,plain,sP5 <=> ((![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((member @ eigen__1) @ eigen__5) @ X1))) => (~((![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((member @ eigen__1) @ eigen__3) @ X1)))))),introduced(definition,[new_symbols(definition,[sP5])])). % 47.14/47.68 thf(sP6,plain,sP6 <=> ((mrel @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP6])])). % 47.14/47.68 thf(sP7,plain,sP7 <=> ((![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((intersect @ eigen__5) @ eigen__3) @ X1))) => (![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((intersect @ eigen__3) @ eigen__5) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])])). % 47.14/47.68 thf(sP8,plain,sP8 <=> (![X1:$i]:((~((((eiw_di @ X1) @ eigen__0) => (~(((mrel @ eigen__0) @ mactual)))))) => ((eiw_di @ X1) @ mactual))),introduced(definition,[new_symbols(definition,[sP8])])). % 47.14/47.68 thf(sP9,plain,sP9 <=> ((eiw_di @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])). % 47.14/47.68 thf(sP10,plain,sP10 <=> ((eiw_di @ eigen__3) @ eigen__0),introduced(definition,[new_symbols(definition,[sP10])])). % 47.14/47.68 thf(sP11,plain,sP11 <=> ((~((((mrel @ eigen__4) @ eigen__2) => (~(((mrel @ eigen__4) @ eigen__6)))))) => ((mrel @ eigen__2) @ eigen__6)),introduced(definition,[new_symbols(definition,[sP11])])). % 47.14/47.68 thf(sP12,plain,sP12 <=> ((~((((mrel @ mactual) @ eigen__0) => (~(((mrel @ mactual) @ mactual)))))) => ((mrel @ eigen__0) @ mactual)),introduced(definition,[new_symbols(definition,[sP12])])). % 47.14/47.68 thf(sP13,plain,sP13 <=> (((mrel @ eigen__0) @ eigen__2) => (~(((mrel @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP13])])). % 47.14/47.68 thf(sP14,plain,sP14 <=> (![X1:$i]:((~((((eiw_di @ X1) @ eigen__2) => (~(((mrel @ eigen__2) @ eigen__0)))))) => ((eiw_di @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP14])])). % 47.14/47.68 thf(sP15,plain,sP15 <=> ((mrel @ eigen__4) @ eigen__6),introduced(definition,[new_symbols(definition,[sP15])])). % 47.14/47.68 thf(sP16,plain,sP16 <=> (![X1:mworld]:(![X2:$i]:((~((((eiw_di @ X2) @ eigen__2) => (~(((mrel @ eigen__2) @ X1)))))) => ((eiw_di @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP16])])). % 47.14/47.68 thf(sP17,plain,sP17 <=> (![X1:mworld]:(![X2:$i]:((~((((eiw_di @ X2) @ eigen__4) => (~(((mrel @ eigen__4) @ X1)))))) => ((eiw_di @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP17])])). % 47.14/47.68 thf(sP18,plain,sP18 <=> ((~((sP9 => (~(((mrel @ eigen__0) @ eigen__2)))))) => ((eiw_di @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP18])])). % 47.14/47.68 thf(sP19,plain,sP19 <=> ((~((((eiw_di @ eigen__3) @ eigen__2) => (~(((mrel @ eigen__2) @ eigen__0)))))) => sP10),introduced(definition,[new_symbols(definition,[sP19])])). % 47.14/47.68 thf(sP20,plain,sP20 <=> ((~((((mrel @ eigen__0) @ mactual) => (~(((mrel @ eigen__0) @ eigen__2)))))) => ((mrel @ mactual) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP20])])). % 47.14/47.68 thf(sP21,plain,sP21 <=> ((~((sP6 => (~(((mrel @ eigen__2) @ eigen__2)))))) => ((mrel @ eigen__4) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP21])])). % 47.14/47.68 thf(sP22,plain,sP22 <=> (((eiw_di @ eigen__5) @ eigen__4) => (~(((mrel @ eigen__4) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP22])])). % 47.14/47.68 thf(sP23,plain,sP23 <=> (((mrel @ mactual) @ eigen__0) => (~(((mrel @ mactual) @ mactual)))),introduced(definition,[new_symbols(definition,[sP23])])). % 47.14/47.68 thf(sP24,plain,sP24 <=> ((mrel @ eigen__4) @ eigen__2),introduced(definition,[new_symbols(definition,[sP24])])). % 47.14/47.68 thf(sP25,plain,sP25 <=> (sP9 => (~(((mrel @ eigen__0) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP25])])). % 47.14/47.68 thf(sP26,plain,sP26 <=> ((mrel @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP26])])). % 47.14/47.68 thf(sP27,plain,sP27 <=> (((mrel @ eigen__2) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => (~(((![X2:mworld]:(((mrel @ mactual) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3))) => (~((![X3:$i]:(((eiw_di @ X3) @ X2) => ((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ eigen__5) @ X4))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ X1) @ X4))))))))))))) => (~((![X2:mworld]:(((mrel @ mactual) @ X2) => ((~((![X3:$i]:(((eiw_di @ X3) @ X2) => ((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ eigen__5) @ X4))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ X1) @ X4)))))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 47.14/47.68 thf(sP28,plain,sP28 <=> (((eiw_di @ eigen__5) @ eigen__2) => (![X1:mworld]:(((mrel @ eigen__2) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__5) @ X2) @ X4))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ X2) @ eigen__5) @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 47.14/47.68 thf(sP29,plain,sP29 <=> (![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((intersect @ eigen__5) @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP29])])). % 47.14/47.68 thf(sP30,plain,sP30 <=> (sP2 => (((intersect @ eigen__3) @ eigen__5) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP30])])). % 47.14/47.68 thf(sP31,plain,sP31 <=> (((mrel @ mactual) @ eigen__2) => (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5))) => (~((![X5:$i]:(((eiw_di @ X5) @ X4) => ((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X1) @ X6))) => (~((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X3) @ X6))))))))))))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => ((~((![X5:$i]:(((eiw_di @ X5) @ X4) => ((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X1) @ X6))) => (~((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X3) @ X6)))))))))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 47.14/47.68 thf(sP32,plain,sP32 <=> ((mrel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP32])])). % 47.14/47.68 thf(sP33,plain,sP33 <=> ((mrel @ mactual) @ eigen__6),introduced(definition,[new_symbols(definition,[sP33])])). % 47.14/47.68 thf(sP34,plain,sP34 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X3) @ X1) @ X5)))))))))))),introduced(definition,[new_symbols(definition,[sP34])])). % 47.14/47.68 thf(sP35,plain,sP35 <=> (![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((intersect @ eigen__3) @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP35])])). % 47.14/47.68 thf(sP36,plain,sP36 <=> ((~((((mrel @ eigen__2) @ mactual) => (~(((mrel @ eigen__2) @ eigen__6)))))) => sP33),introduced(definition,[new_symbols(definition,[sP36])])). % 47.14/47.68 thf(sP37,plain,sP37 <=> ((eiw_di @ eigen__5) @ eigen__4),introduced(definition,[new_symbols(definition,[sP37])])). % 47.14/47.68 thf(sP38,plain,sP38 <=> ((~(sP22)) => ((eiw_di @ eigen__5) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP38])])). % 47.14/47.68 thf(sP39,plain,sP39 <=> (sP10 => (~(((mrel @ eigen__0) @ mactual)))),introduced(definition,[new_symbols(definition,[sP39])])). % 47.14/47.68 thf(sP40,plain,sP40 <=> (![X1:mworld]:(((mrel @ eigen__2) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (~(((![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__5) @ X2) @ X4))) => (~((![X4:$i]:(((eiw_di @ X4) @ X3) => ((![X5:mworld]:(((mrel @ X3) @ X5) => (((member @ X4) @ eigen__5) @ X5))) => (~((![X5:mworld]:(((mrel @ X3) @ X5) => (((member @ X4) @ X2) @ X5))))))))))))) => (~((![X3:mworld]:(((mrel @ X1) @ X3) => ((~((![X4:$i]:(((eiw_di @ X4) @ X3) => ((![X5:mworld]:(((mrel @ X3) @ X5) => (((member @ X4) @ eigen__5) @ X5))) => (~((![X5:mworld]:(((mrel @ X3) @ X5) => (((member @ X4) @ X2) @ X5)))))))))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__5) @ X2) @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP40])])). % 47.14/47.68 thf(sP41,plain,sP41 <=> (![X1:mworld]:(![X2:mworld]:((~((((mrel @ eigen__4) @ X2) => (~(((mrel @ eigen__4) @ X1)))))) => ((mrel @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP41])])). % 47.14/47.68 thf(sP42,plain,sP42 <=> ((mrel @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP42])])). % 47.14/47.68 thf(sP43,plain,sP43 <=> (![X1:mworld]:(![X2:mworld]:((~((((mrel @ eigen__0) @ X2) => (~(((mrel @ eigen__0) @ X1)))))) => ((mrel @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP43])])). % 47.14/47.68 thf(sP44,plain,sP44 <=> (![X1:mworld]:(((mrel @ eigen__2) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__5) @ X2) @ X4))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ X2) @ eigen__5) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP44])])). % 47.14/47.68 thf(sP45,plain,sP45 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP45])])). % 47.14/47.68 thf(sP46,plain,sP46 <=> (![X1:mworld]:((~((((mrel @ eigen__2) @ X1) => (~(((mrel @ eigen__2) @ eigen__6)))))) => ((mrel @ X1) @ eigen__6))),introduced(definition,[new_symbols(definition,[sP46])])). % 47.14/47.68 thf(sP47,plain,sP47 <=> (((mrel @ eigen__2) @ mactual) => (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:mworld]:(((mrel @ mactual) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ X1) @ eigen__5) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP47])])). % 47.14/47.68 thf(sP48,plain,sP48 <=> (((mrel @ mactual) @ eigen__2) => sP34),introduced(definition,[new_symbols(definition,[sP48])])). % 47.14/47.68 thf(sP49,plain,sP49 <=> (![X1:mworld]:((~((((mrel @ eigen__2) @ X1) => (~(((mrel @ eigen__2) @ eigen__2)))))) => ((mrel @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP49])])). % 47.14/47.68 thf(sP50,plain,sP50 <=> ((~(sP39)) => ((eiw_di @ eigen__3) @ mactual)),introduced(definition,[new_symbols(definition,[sP50])])). % 47.14/47.68 thf(sP51,plain,sP51 <=> ((eiw_di @ eigen__1) @ eigen__6),introduced(definition,[new_symbols(definition,[sP51])])). % 47.14/47.68 thf(sP52,plain,sP52 <=> (((mrel @ eigen__0) @ mactual) => (~(((mrel @ eigen__0) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP52])])). % 47.14/47.68 thf(sP53,plain,sP53 <=> (![X1:$i]:((~((((eiw_di @ X1) @ eigen__2) => (~(((mrel @ eigen__2) @ eigen__6)))))) => ((eiw_di @ X1) @ eigen__6))),introduced(definition,[new_symbols(definition,[sP53])])). % 47.14/47.68 thf(sP54,plain,sP54 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (~(((![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X2) @ X4) @ X6))) => (~((![X6:$i]:(((eiw_di @ X6) @ X5) => ((![X7:mworld]:(((mrel @ X5) @ X7) => (((member @ X6) @ X2) @ X7))) => (~((![X7:mworld]:(((mrel @ X5) @ X7) => (((member @ X6) @ X4) @ X7))))))))))))) => (~((![X5:mworld]:(((mrel @ X3) @ X5) => ((~((![X6:$i]:(((eiw_di @ X6) @ X5) => ((![X7:mworld]:(((mrel @ X5) @ X7) => (((member @ X6) @ X2) @ X7))) => (~((![X7:mworld]:(((mrel @ X5) @ X7) => (((member @ X6) @ X4) @ X7)))))))))) => (![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X2) @ X4) @ X6))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP54])])). % 47.14/47.68 thf(sP55,plain,sP55 <=> (![X1:mworld]:((~((((mrel @ eigen__0) @ X1) => (~(sP32))))) => ((mrel @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP55])])). % 47.14/47.68 thf(sP56,plain,sP56 <=> (((eiw_di @ eigen__3) @ eigen__2) => (~(sP26))),introduced(definition,[new_symbols(definition,[sP56])])). % 47.14/47.68 thf(sP57,plain,sP57 <=> ((mrel @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP57])])). % 47.14/47.68 thf(sP58,plain,sP58 <=> (sP33 => sP7),introduced(definition,[new_symbols(definition,[sP58])])). % 47.14/47.68 thf(sP59,plain,sP59 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP59])])). % 47.14/47.68 thf(sP60,plain,sP60 <=> (![X1:mworld]:((~((((mrel @ mactual) @ X1) => (~(sP42))))) => ((mrel @ X1) @ mactual))),introduced(definition,[new_symbols(definition,[sP60])])). % 47.14/47.68 thf(sP61,plain,sP61 <=> ((mrel @ mactual) @ eigen__2),introduced(definition,[new_symbols(definition,[sP61])])). % 47.14/47.68 thf(sP62,plain,sP62 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5))) => (~((![X5:$i]:(((eiw_di @ X5) @ X4) => ((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X1) @ X6))) => (~((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X3) @ X6))))))))))))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => ((~((![X5:$i]:(((eiw_di @ X5) @ X4) => ((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X1) @ X6))) => (~((![X6:mworld]:(((mrel @ X4) @ X6) => (((member @ X5) @ X3) @ X6)))))))))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5))))))))))))))))),introduced(definition,[new_symbols(definition,[sP62])])). % 47.14/47.68 thf(sP63,plain,sP63 <=> (((eiw_di @ eigen__3) @ mactual) => (~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2))) => (~((![X2:$i]:(((eiw_di @ X2) @ X1) => ((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__5) @ X3))) => (~((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__3) @ X3))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((~((![X2:$i]:(((eiw_di @ X2) @ X1) => ((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__5) @ X3))) => (~((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__3) @ X3)))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 47.14/47.68 thf(sP64,plain,sP64 <=> (![X1:mworld]:(![X2:mworld]:(![X3:mworld]:((~((((mrel @ X1) @ X3) => (~(((mrel @ X1) @ X2)))))) => ((mrel @ X3) @ X2))))),introduced(definition,[new_symbols(definition,[sP64])])). % 47.14/47.68 thf(sP65,plain,sP65 <=> (![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((member @ eigen__1) @ eigen__5) @ X1))),introduced(definition,[new_symbols(definition,[sP65])])). % 47.14/47.68 thf(sP66,plain,sP66 <=> ((~((((eiw_di @ eigen__1) @ eigen__2) => (~(((mrel @ eigen__2) @ eigen__6)))))) => sP51),introduced(definition,[new_symbols(definition,[sP66])])). % 47.14/47.68 thf(sP67,plain,sP67 <=> (((eiw_di @ eigen__5) @ eigen__2) => sP40),introduced(definition,[new_symbols(definition,[sP67])])). % 47.14/47.68 thf(sP68,plain,sP68 <=> (((intersect @ eigen__3) @ eigen__5) @ eigen__7),introduced(definition,[new_symbols(definition,[sP68])])). % 47.14/47.68 thf(sP69,plain,sP69 <=> ((mrel @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP69])])). % 47.14/47.68 thf(sP70,plain,sP70 <=> (![X1:mworld]:(![X2:mworld]:((~((((mrel @ mactual) @ X2) => (~(((mrel @ mactual) @ X1)))))) => ((mrel @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP70])])). % 47.14/47.68 thf(sP71,plain,sP71 <=> ((eiw_di @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP71])])). % 47.14/47.68 thf(sP72,plain,sP72 <=> (sP57 => (~(sP32))),introduced(definition,[new_symbols(definition,[sP72])])). % 47.14/47.68 thf(sP73,plain,sP73 <=> (sP33 => ((~((![X1:$i]:(((eiw_di @ X1) @ eigen__6) => ((![X2:mworld]:(((mrel @ eigen__6) @ X2) => (((member @ X1) @ eigen__5) @ X2))) => (~((![X2:mworld]:(((mrel @ eigen__6) @ X2) => (((member @ X1) @ eigen__3) @ X2)))))))))) => sP29)),introduced(definition,[new_symbols(definition,[sP73])])). % 47.14/47.68 thf(sP74,plain,sP74 <=> ((~(sP13)) => sP69),introduced(definition,[new_symbols(definition,[sP74])])). % 47.14/47.68 thf(sP75,plain,sP75 <=> (![X1:$i]:((~((((eiw_di @ X1) @ eigen__4) => (~(sP24))))) => ((eiw_di @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP75])])). % 47.14/47.68 thf(sP76,plain,sP76 <=> ((~(sP72)) => sP26),introduced(definition,[new_symbols(definition,[sP76])])). % 47.14/47.68 thf(sP77,plain,sP77 <=> (![X1:mworld]:((~((((mrel @ eigen__4) @ X1) => (~(sP15))))) => ((mrel @ X1) @ eigen__6))),introduced(definition,[new_symbols(definition,[sP77])])). % 47.14/47.68 thf(sP78,plain,sP78 <=> ((eiw_di @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP78])])). % 47.14/47.68 thf(sP79,plain,sP79 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X2) @ X4) @ X6))) => (![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X4) @ X2) @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP79])])). % 47.14/47.68 thf(sP80,plain,sP80 <=> (sP6 => (~(((mrel @ eigen__2) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP80])])). % 47.14/47.68 thf(sP81,plain,sP81 <=> ((eiw_di @ eigen__5) @ eigen__2),introduced(definition,[new_symbols(definition,[sP81])])). % 47.14/47.68 thf(sP82,plain,sP82 <=> ((mrel @ eigen__2) @ eigen__6),introduced(definition,[new_symbols(definition,[sP82])])). % 47.14/47.68 thf(sP83,plain,sP83 <=> (![X1:mworld]:(![X2:mworld]:((~((((mrel @ eigen__2) @ X2) => (~(((mrel @ eigen__2) @ X1)))))) => ((mrel @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP83])])). % 47.14/47.68 thf(sP84,plain,sP84 <=> (sP51 => sP5),introduced(definition,[new_symbols(definition,[sP84])])). % 47.14/47.68 thf(sP85,plain,sP85 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__3) @ eigen__5) @ X2)))))),introduced(definition,[new_symbols(definition,[sP85])])). % 47.14/47.68 thf(sP86,plain,sP86 <=> (![X1:mworld]:((~((((mrel @ eigen__0) @ X1) => (~(sP57))))) => ((mrel @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP86])])). % 47.14/47.68 thf(sP87,plain,sP87 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => ((~((![X2:$i]:(((eiw_di @ X2) @ X1) => ((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__5) @ X3))) => (~((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__3) @ X3)))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2)))))),introduced(definition,[new_symbols(definition,[sP87])])). % 47.14/47.68 thf(sP88,plain,sP88 <=> ((mrel @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP88])])). % 47.14/47.68 thf(sP89,plain,sP89 <=> (![X1:mworld]:(![X2:mworld]:(![X3:$i]:((~((((eiw_di @ X3) @ X1) => (~(((mrel @ X1) @ X2)))))) => ((eiw_di @ X3) @ X2))))),introduced(definition,[new_symbols(definition,[sP89])])). % 47.14/47.68 thf(sP90,plain,sP90 <=> ((eiw_di @ eigen__3) @ mactual),introduced(definition,[new_symbols(definition,[sP90])])). % 47.14/47.68 thf(sP91,plain,sP91 <=> ((mrel @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP91])])). % 47.14/47.68 thf(sP92,plain,sP92 <=> (![X1:mworld]:((~((((mrel @ eigen__0) @ X1) => (~(sP88))))) => ((mrel @ X1) @ mactual))),introduced(definition,[new_symbols(definition,[sP92])])). % 47.14/47.68 thf(sP93,plain,sP93 <=> (sP69 => (~(sP82))),introduced(definition,[new_symbols(definition,[sP93])])). % 47.14/47.68 thf(sP94,plain,sP94 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__6) => ((![X2:mworld]:(((mrel @ eigen__6) @ X2) => (((member @ X1) @ eigen__5) @ X2))) => (~((![X2:mworld]:(((mrel @ eigen__6) @ X2) => (((member @ X1) @ eigen__3) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP94])])). % 47.14/47.68 thf(sP95,plain,sP95 <=> (sP71 => (~(sP82))),introduced(definition,[new_symbols(definition,[sP95])])). % 47.14/47.68 thf(sP96,plain,sP96 <=> (![X1:mworld]:(((mrel @ eigen__6) @ X1) => (((member @ eigen__1) @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP96])])). % 47.14/47.68 thf(sP97,plain,sP97 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (~(((![X2:mworld]:(((mrel @ mactual) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3))) => (~((![X3:$i]:(((eiw_di @ X3) @ X2) => ((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ eigen__5) @ X4))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ X1) @ X4))))))))))))) => (~((![X2:mworld]:(((mrel @ mactual) @ X2) => ((~((![X3:$i]:(((eiw_di @ X3) @ X2) => ((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ eigen__5) @ X4))) => (~((![X4:mworld]:(((mrel @ X2) @ X4) => (((member @ X3) @ X1) @ X4)))))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3))))))))))))),introduced(definition,[new_symbols(definition,[sP97])])). % 47.14/47.68 thf(sP98,plain,sP98 <=> (![X1:$i]:(((eiw_di @ X1) @ mactual) => (![X2:mworld]:(((mrel @ mactual) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__5) @ X1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ X1) @ eigen__5) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP98])])). % 47.14/47.68 thf(sP99,plain,sP99 <=> (sP24 => (~(sP15))),introduced(definition,[new_symbols(definition,[sP99])])). % 47.14/47.68 thf(sP100,plain,sP100 <=> ((~(sP94)) => sP29),introduced(definition,[new_symbols(definition,[sP100])])). % 47.14/47.68 thf(sP101,plain,sP101 <=> ((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__5) @ eigen__3) @ X2))) => (~((![X2:$i]:(((eiw_di @ X2) @ X1) => ((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__5) @ X3))) => (~((![X3:mworld]:(((mrel @ X1) @ X3) => (((member @ X2) @ eigen__3) @ X3))))))))))))) => (~(sP87))),introduced(definition,[new_symbols(definition,[sP101])])). % 47.14/47.68 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 47.14/47.68 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 47.14/47.68 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 47.14/47.68 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 47.14/47.68 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 47.14/47.68 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 47.14/47.68 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 47.14/47.68 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 47.14/47.68 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 47.14/47.68 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))). % 47.14/47.68 thf(prove_th13,conjecture,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => (![X6:$i]:(((eiw_di @ X6) @ X5) => (![X7:mworld]:(((mrel @ X5) @ X7) => ((~(((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X4) @ X8))) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X6) @ X8)))))))) => (![X8:mworld]:(((mrel @ X7) @ X8) => (((intersect @ X4) @ X6) @ X8))))))))))))))))))). % 47.14/47.68 thf(h0,negated_conjecture,(~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => (![X6:$i]:(((eiw_di @ X6) @ X5) => (![X7:mworld]:(((mrel @ X5) @ X7) => ((~(((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X4) @ X8))) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X6) @ X8)))))))) => (![X8:mworld]:(((mrel @ X7) @ X8) => (((intersect @ X4) @ X6) @ X8)))))))))))))))))))),inference(assume_negation,[status(cth)],[prove_th13])). % 47.14/47.68 thf(h1,assumption,(~((sP59 => (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((~(((![X7:mworld]:(((mrel @ X6) @ X7) => (((member @ X1) @ X3) @ X7))) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((member @ X1) @ X5) @ X7)))))))) => (![X7:mworld]:(((mrel @ X6) @ X7) => (((intersect @ X3) @ X5) @ X7))))))))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h2,assumption,sP59,introduced(assumption,[])). % 47.14/47.68 thf(h3,assumption,(~((![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((~(((![X7:mworld]:(((mrel @ X6) @ X7) => (((member @ X1) @ X3) @ X7))) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((member @ X1) @ X5) @ X7)))))))) => (![X7:mworld]:(((mrel @ X6) @ X7) => (((intersect @ X3) @ X5) @ X7)))))))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h4,assumption,(~((sP9 => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (((member @ eigen__1) @ X2) @ X6))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((member @ eigen__1) @ X4) @ X6)))))))) => (![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X2) @ X4) @ X6))))))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h5,assumption,sP9,introduced(assumption,[])). % 47.14/47.68 thf(h6,assumption,(~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (((member @ eigen__1) @ X2) @ X6))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((member @ eigen__1) @ X4) @ X6)))))))) => (![X6:mworld]:(((mrel @ X5) @ X6) => (((intersect @ X2) @ X4) @ X6)))))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h7,assumption,(~((sP57 => (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((~(((![X5:mworld]:(((mrel @ X4) @ X5) => (((member @ eigen__1) @ X1) @ X5))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((member @ eigen__1) @ X3) @ X5)))))))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5))))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h8,assumption,sP57,introduced(assumption,[])). % 47.14/47.68 thf(h9,assumption,(~((![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((~(((![X5:mworld]:(((mrel @ X4) @ X5) => (((member @ eigen__1) @ X1) @ X5))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((member @ eigen__1) @ X3) @ X5)))))))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((intersect @ X1) @ X3) @ X5)))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h10,assumption,(~((sP78 => (![X1:mworld]:(((mrel @ eigen__2) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((~(((![X4:mworld]:(((mrel @ X3) @ X4) => (((member @ eigen__1) @ eigen__3) @ X4))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((member @ eigen__1) @ X2) @ X4)))))))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__3) @ X2) @ X4))))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h11,assumption,sP78,introduced(assumption,[])). % 47.14/47.68 thf(h12,assumption,(~((![X1:mworld]:(((mrel @ eigen__2) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((~(((![X4:mworld]:(((mrel @ X3) @ X4) => (((member @ eigen__1) @ eigen__3) @ X4))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((member @ eigen__1) @ X2) @ X4)))))))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((intersect @ eigen__3) @ X2) @ X4)))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h13,assumption,(~((sP6 => (![X1:$i]:(((eiw_di @ X1) @ eigen__4) => (![X2:mworld]:(((mrel @ eigen__4) @ X2) => ((~(((![X3:mworld]:(((mrel @ X2) @ X3) => (((member @ eigen__1) @ eigen__3) @ X3))) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((member @ eigen__1) @ X1) @ X3)))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__3) @ X1) @ X3))))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h14,assumption,sP6,introduced(assumption,[])). % 47.14/47.68 thf(h15,assumption,(~((![X1:$i]:(((eiw_di @ X1) @ eigen__4) => (![X2:mworld]:(((mrel @ eigen__4) @ X2) => ((~(((![X3:mworld]:(((mrel @ X2) @ X3) => (((member @ eigen__1) @ eigen__3) @ X3))) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((member @ eigen__1) @ X1) @ X3)))))))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((intersect @ eigen__3) @ X1) @ X3)))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h16,assumption,(~((sP37 => (![X1:mworld]:(((mrel @ eigen__4) @ X1) => ((~(((![X2:mworld]:(((mrel @ X1) @ X2) => (((member @ eigen__1) @ eigen__3) @ X2))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((member @ eigen__1) @ eigen__5) @ X2)))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__3) @ eigen__5) @ X2))))))))),introduced(assumption,[])). % 47.14/47.68 thf(h17,assumption,sP37,introduced(assumption,[])). % 47.14/47.68 thf(h18,assumption,(~((![X1:mworld]:(((mrel @ eigen__4) @ X1) => ((~(((![X2:mworld]:(((mrel @ X1) @ X2) => (((member @ eigen__1) @ eigen__3) @ X2))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((member @ eigen__1) @ eigen__5) @ X2)))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((intersect @ eigen__3) @ eigen__5) @ X2)))))))),introduced(assumption,[])). % 47.14/47.68 thf(h19,assumption,(~((sP15 => ((~((sP96 => (~(sP65))))) => sP35)))),introduced(assumption,[])). % 47.14/47.68 thf(h20,assumption,sP15,introduced(assumption,[])). % 47.14/47.68 thf(h21,assumption,(~(((~((sP96 => (~(sP65))))) => sP35))),introduced(assumption,[])). % 47.14/47.68 thf(h22,assumption,(~((sP96 => (~(sP65))))),introduced(assumption,[])). % 47.14/47.68 thf(h23,assumption,(~(sP35)),introduced(assumption,[])). % 47.14/47.68 thf(h24,assumption,sP96,introduced(assumption,[])). % 47.14/47.68 thf(h25,assumption,sP65,introduced(assumption,[])). % 47.14/47.68 thf(h26,assumption,(~(sP30)),introduced(assumption,[])). % 47.14/47.68 thf(h27,assumption,sP2,introduced(assumption,[])). % 47.14/47.68 thf(h28,assumption,(~(sP68)),introduced(assumption,[])). % 47.14/47.68 thf(1,plain,((~(sP5) | ~(sP65)) | ~(sP96)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(2,plain,((~(sP30) | ~(sP2)) | sP68),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(3,plain,((~(sP84) | ~(sP51)) | sP5),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(4,plain,(~(sP35) | sP30),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(5,plain,(~(sP94) | sP84),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(6,plain,((~(sP100) | sP94) | sP29),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(7,plain,((~(sP7) | ~(sP29)) | sP35),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(8,plain,((~(sP73) | ~(sP33)) | sP100),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(9,plain,((~(sP58) | ~(sP33)) | sP7),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(10,plain,(~(sP87) | sP73),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(11,plain,(sP101 | sP87),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(12,plain,(~(sP85) | sP58),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(13,plain,((~(sP63) | ~(sP90)) | ~(sP101)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(14,plain,((~(sP1) | ~(sP90)) | sP85),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(15,plain,(~(sP97) | sP63),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(16,plain,(~(sP98) | sP1),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(17,plain,((~(sP27) | ~(sP69)) | sP97),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(18,plain,((~(sP47) | ~(sP69)) | sP98),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(19,plain,(~(sP40) | sP27),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(20,plain,((~(sP99) | ~(sP24)) | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(21,plain,((~(sP93) | ~(sP69)) | ~(sP82)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(22,plain,((~(sP80) | ~(sP6)) | ~(sP91)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(23,plain,((~(sP52) | ~(sP88)) | ~(sP57)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(24,plain,((~(sP72) | ~(sP57)) | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(25,plain,((~(sP13) | ~(sP57)) | ~(sP88)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(26,plain,((~(sP23) | ~(sP59)) | ~(sP42)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(27,plain,((~(sP22) | ~(sP37)) | ~(sP24)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(28,plain,((~(sP95) | ~(sP71)) | ~(sP82)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(29,plain,((~(sP56) | ~(sP78)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(30,plain,((~(sP25) | ~(sP9)) | ~(sP57)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(31,plain,((~(sP39) | ~(sP10)) | ~(sP88)),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(32,plain,(~(sP44) | sP47),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(33,plain,((~(sP11) | sP99) | sP82),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(34,plain,((~(sP36) | sP93) | sP33),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(35,plain,((~(sP21) | sP80) | sP24),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(36,plain,((~(sP20) | sP52) | sP61),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(37,plain,((~(sP76) | sP72) | sP26),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(38,plain,((~(sP74) | sP13) | sP69),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(39,plain,((~(sP12) | sP23) | sP88),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(40,plain,((~(sP38) | sP22) | sP81),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(41,plain,((~(sP66) | sP95) | sP51),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(42,plain,((~(sP19) | sP56) | sP10),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(43,plain,((~(sP18) | sP25) | sP71),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(44,plain,((~(sP50) | sP39) | sP90),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(45,plain,((~(sP67) | ~(sP81)) | sP40),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(46,plain,((~(sP28) | ~(sP81)) | sP44),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(47,plain,(~(sP77) | sP11),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(48,plain,(~(sP46) | sP36),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(49,plain,(~(sP49) | sP21),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(50,plain,(~(sP86) | sP20),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(51,plain,(~(sP55) | sP76),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(52,plain,(~(sP92) | sP74),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(53,plain,(~(sP60) | sP12),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(54,plain,(~(sP75) | sP38),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(55,plain,(~(sP53) | sP66),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(56,plain,(~(sP14) | sP19),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(57,plain,(~(sP4) | sP18),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(58,plain,(~(sP8) | sP50),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(59,plain,(~(sP62) | sP67),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(60,plain,(~(sP34) | sP28),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(61,plain,(~(sP41) | sP77),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(62,plain,(~(sP83) | sP46),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(63,plain,(~(sP83) | sP49),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(64,plain,(~(sP43) | sP86),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(65,plain,(~(sP43) | sP55),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(66,plain,(~(sP43) | sP92),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(67,plain,(~(sP70) | sP60),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(68,plain,(~(sP17) | sP75),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(69,plain,(~(sP16) | sP53),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(70,plain,(~(sP16) | sP14),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(71,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(72,plain,(~(sP3) | sP8),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(73,plain,((~(sP31) | ~(sP61)) | sP62),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(74,plain,((~(sP48) | ~(sP61)) | sP34),inference(prop_rule,[status(thm)],[])). % 47.14/47.68 thf(75,plain,(~(sP45) | sP91),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(76,plain,(~(sP45) | sP32),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(77,plain,(~(sP45) | sP42),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(78,plain,(~(sP64) | sP41),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(79,plain,(~(sP64) | sP83),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(80,plain,(~(sP64) | sP43),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(81,plain,(~(sP64) | sP70),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(82,plain,(~(sP89) | sP17),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(83,plain,(~(sP89) | sP16),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(84,plain,(~(sP89) | sP3),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(85,plain,(~(sP54) | sP31),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(86,plain,(~(sP79) | sP48),inference(all_rule,[status(thm)],[])). % 47.14/47.68 thf(mrel_reflexive,axiom,sP45). % 47.14/47.68 thf(mrel_euclidean,axiom,sP64). % 47.14/47.68 thf(eiw_di_cumul,axiom,sP89). % 47.14/47.68 thf(intersect_defn,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:((mand @ (mbox @ ((mimplies @ (mbox @ ((intersect @ X1) @ X2))) @ (mexists_di @ (^[X3:$i]:((mand @ (mbox @ ((member @ X3) @ X1))) @ (mbox @ ((member @ X3) @ X2)))))))) @ (mbox @ ((mimplies @ (mexists_di @ (^[X3:$i]:((mand @ (mbox @ ((member @ X3) @ X1))) @ (mbox @ ((member @ X3) @ X2)))))) @ (mbox @ ((intersect @ X1) @ X2))))))))))))). % 47.14/47.68 thf(87,plain,sP54,inference(preprocess,[status(thm)],[intersect_defn]). % 47.14/47.68 thf(symmetry_of_intersect,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ ((mimplies @ (mbox @ ((intersect @ X1) @ X2))) @ (mbox @ ((intersect @ X2) @ X1)))))))))))). % 47.14/47.68 thf(88,plain,sP79,inference(preprocess,[status(thm)],[symmetry_of_intersect]). % 47.14/47.68 thf(89,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,mrel_reflexive,mrel_euclidean,eiw_di_cumul,87,88,h2,h5,h8,h11,h14,h17,h20,h24,h25,h27,h28])). % 47.14/47.68 thf(90,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,89,h27,h28])). % 47.14/47.68 thf(91,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[h23,90,h26])). % 47.14/47.68 thf(92,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h22,91,h24,h25])). % 47.14/47.68 thf(93,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h21,h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,92,h22,h23])). % 47.14/47.68 thf(94,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,93,h20,h21])). % 47.14/47.68 thf(95,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h18,h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,94,h19])). % 47.14/47.68 thf(96,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,95,h17,h18])). % 47.14/47.68 thf(97,plain,$false,inference(tab_negall,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h15,96,h16])). % 47.14/47.68 thf(98,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,97,h14,h15])). % 47.14/47.68 thf(99,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,98,h13])). % 47.14/47.68 thf(100,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,99,h11,h12])). % 47.14/47.68 thf(101,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,100,h10])). % 47.14/47.68 thf(102,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,101,h8,h9])). % 47.14/47.68 thf(103,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,102,h7])). % 47.14/47.68 thf(104,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,103,h5,h6])). % 47.14/47.68 thf(105,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,104,h4])). % 47.14/47.68 thf(106,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,105,h2,h3])). % 47.14/47.68 thf(107,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,106,h1])). % 47.14/47.68 thf(0,theorem,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => (![X6:$i]:(((eiw_di @ X6) @ X5) => (![X7:mworld]:(((mrel @ X5) @ X7) => ((~(((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X4) @ X8))) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (((member @ X2) @ X6) @ X8)))))))) => (![X8:mworld]:(((mrel @ X7) @ X8) => (((intersect @ X4) @ X6) @ X8)))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[107,h0])). % 47.14/47.68 % SZS output end Proof %------------------------------------------------------------------------------