%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM667^4 : TPTP v9.2.0. Released v7.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 02:11:43 PM UTC 2025 % Result : Theorem 196.51s 196.53s % Output : Proof 196.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.11 % Problem : NUM667^4 : TPTP v9.2.0. Released v7.1.0. % 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n031.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Oct 8 22:07:38 EDT 2025 % 0.12/0.33 % CPUTime : % 196.51/196.53 % SZS status Theorem % 196.51/196.53 % Mode: mode449:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 % 196.51/196.53 % Inferences: 5830 % 196.51/196.53 % SZS output start Proof % 196.51/196.53 thf(ty_d_not, type, d_not : ($o>$o)). % 196.51/196.53 thf(ty_eigen__2, type, eigen__2 : $i). % 196.51/196.53 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 196.51/196.53 thf(ty_d_29_ii, type, d_29_ii : ($i>$i>$o)). % 196.51/196.53 thf(ty_eigen__1, type, eigen__1 : $i). % 196.51/196.53 thf(ty_eigen__0, type, eigen__0 : $i). % 196.51/196.53 thf(ty_d_Sep, type, d_Sep : ($i>($i>$o)>$i)). % 196.51/196.53 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 196.51/196.53 thf(ty_emptyset, type, emptyset : $i). % 196.51/196.53 thf(ty_omega, type, omega : $i). % 196.51/196.53 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 196.51/196.53 thf(ty_in, type, in : ($i>$i>$o)). % 196.51/196.53 thf(ty_iii, type, iii : ($i>$i>$o)). % 196.51/196.53 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 196.51/196.53 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((l_or @ ((iii @ eigen__0) @ X2)) @ ((n_is @ eigen__0) @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 196.51/196.53 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((d_Sep @ omega) @ (^[X5:$i]:(~((X5 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => (((l_or @ ((iii @ X2) @ X3)) @ ((n_is @ X2) @ X3)) => ((l_or @ ((iii @ X1) @ X3)) @ ((n_is @ X1) @ X3))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 196.51/196.53 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)) => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 196.51/196.53 thf(sP1,plain,sP1 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => (((iii @ X1) @ X2) => ((iii @ eigen__1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 196.51/196.53 thf(sP2,plain,sP2 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((l_or @ ((iii @ eigen__0) @ X2)) @ ((n_is @ eigen__0) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 196.51/196.53 thf(sP3,plain,sP3 <=> (((iii @ eigen__2) @ eigen__2) => (((l_or @ ((iii @ eigen__2) @ eigen__0)) @ ((n_is @ eigen__2) @ eigen__0)) => ((iii @ eigen__2) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP3])])). % 196.51/196.53 thf(sP4,plain,sP4 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((d_29_ii @ eigen__0) @ eigen__2) => ((iii @ eigen__2) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP4])])). % 196.51/196.53 thf(sP5,plain,sP5 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((l_or @ ((iii @ eigen__0) @ X2)) @ ((n_is @ eigen__0) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 196.51/196.53 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => (d_not @ ((d_29_ii @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP6])])). % 196.51/196.53 thf(sP7,plain,sP7 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((d_Sep @ omega) @ (^[X5:$i]:(~((X5 = emptyset)))))))) => (((iii @ X1) @ X2) => (((l_or @ ((iii @ X2) @ X3)) @ ((n_is @ X2) @ X3)) => ((iii @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 196.51/196.53 thf(sP8,plain,sP8 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((d_29_ii @ eigen__0) @ X1) => ((iii @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP8])])). % 196.51/196.53 thf(sP9,plain,sP9 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__2) => (((l_or @ ((iii @ eigen__2) @ X1)) @ ((n_is @ eigen__2) @ X1)) => ((iii @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 196.51/196.53 thf(sP10,plain,sP10 <=> (((iii @ eigen__0) @ eigen__2) => ((d_29_ii @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP10])])). % 196.51/196.53 thf(sP11,plain,sP11 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ X1) => ((d_29_ii @ X1) @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP11])])). % 196.51/196.53 thf(sP12,plain,sP12 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)) => (((l_or @ ((iii @ eigen__1) @ eigen__2)) @ ((n_is @ eigen__1) @ eigen__2)) => ((l_or @ ((iii @ eigen__0) @ eigen__2)) @ ((n_is @ eigen__0) @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP12])])). % 196.51/196.53 thf(sP13,plain,sP13 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__0) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((iii @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 196.51/196.53 thf(sP14,plain,sP14 <=> ((l_or @ ((iii @ eigen__0) @ eigen__1)) @ ((n_is @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP14])])). % 196.51/196.53 thf(sP15,plain,sP15 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => sP3),introduced(definition,[new_symbols(definition,[sP15])])). % 196.51/196.53 thf(sP16,plain,sP16 <=> ((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 196.51/196.53 thf(sP17,plain,sP17 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__0) => ((d_29_ii @ eigen__0) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP17])])). % 196.51/196.53 thf(sP18,plain,sP18 <=> (sP16 => (((iii @ eigen__2) @ eigen__1) => (((l_or @ ((iii @ eigen__1) @ eigen__2)) @ ((n_is @ eigen__1) @ eigen__2)) => ((iii @ eigen__2) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP18])])). % 196.51/196.53 thf(sP19,plain,sP19 <=> ((l_or @ ((iii @ eigen__1) @ eigen__2)) @ ((n_is @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP19])])). % 196.51/196.53 thf(sP20,plain,sP20 <=> (sP16 => (((d_29_ii @ eigen__1) @ eigen__2) => ((iii @ eigen__2) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP20])])). % 196.51/196.53 thf(sP21,plain,sP21 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP14 => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP21])])). % 196.51/196.53 thf(sP22,plain,sP22 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (sP19 => (((iii @ eigen__2) @ eigen__1) => ((iii @ eigen__1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP22])])). % 196.51/196.53 thf(sP23,plain,sP23 <=> (((d_29_ii @ eigen__0) @ eigen__2) => ((iii @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP23])])). % 196.51/196.53 thf(sP24,plain,sP24 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__0) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => ((iii @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP24])])). % 196.51/196.53 thf(sP25,plain,sP25 <=> (((l_or @ ((iii @ eigen__2) @ eigen__0)) @ ((n_is @ eigen__2) @ eigen__0)) => ((iii @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP25])])). % 196.51/196.53 thf(sP26,plain,sP26 <=> (sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ eigen__2) @ X1) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((iii @ eigen__2) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 196.51/196.53 thf(sP27,plain,sP27 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((d_29_ii @ eigen__1) @ X1) => ((iii @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP27])])). % 196.51/196.53 thf(sP28,plain,sP28 <=> (d_not @ ((d_29_ii @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP28])])). % 196.51/196.53 thf(sP29,plain,sP29 <=> (((iii @ eigen__1) @ eigen__1) => (sP19 => ((iii @ eigen__1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP29])])). % 196.51/196.53 thf(sP30,plain,sP30 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => ((d_not @ ((d_29_ii @ X1) @ X2)) => ((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 196.51/196.53 thf(sP31,plain,sP31 <=> ((iii @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP31])])). % 196.51/196.53 thf(sP32,plain,sP32 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => (d_not @ ((d_29_ii @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP32])])). % 196.51/196.53 thf(sP33,plain,sP33 <=> (sP16 => (sP19 => sP28)),introduced(definition,[new_symbols(definition,[sP33])])). % 196.51/196.53 thf(sP34,plain,sP34 <=> (((iii @ eigen__2) @ eigen__0) => ((d_29_ii @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP34])])). % 196.51/196.53 thf(sP35,plain,sP35 <=> ((d_not @ ((d_29_ii @ eigen__0) @ eigen__2)) => ((l_or @ sP31) @ ((n_is @ eigen__0) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP35])])). % 196.51/196.53 thf(sP36,plain,sP36 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 196.51/196.53 thf(sP37,plain,sP37 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__0) => (sP14 => ((iii @ eigen__2) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP37])])). % 196.51/196.53 thf(sP38,plain,sP38 <=> (sP36 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((d_not @ ((d_29_ii @ eigen__0) @ X1)) => ((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP38])])). % 196.51/196.53 thf(sP39,plain,sP39 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ eigen__1) => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((iii @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP39])])). % 196.51/196.53 thf(sP40,plain,sP40 <=> (((iii @ eigen__2) @ eigen__0) => (sP14 => ((iii @ eigen__2) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP40])])). % 196.51/196.53 thf(sP41,plain,sP41 <=> ((iii @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP41])])). % 196.51/196.53 thf(sP42,plain,sP42 <=> ((iii @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP42])])). % 196.51/196.53 thf(sP43,plain,sP43 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ eigen__1) @ X1) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((iii @ eigen__1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP43])])). % 196.51/196.53 thf(sP44,plain,sP44 <=> (d_not @ ((d_29_ii @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP44])])). % 196.51/196.53 thf(sP45,plain,sP45 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))) => sP27),introduced(definition,[new_symbols(definition,[sP45])])). % 196.51/196.53 thf(sP46,plain,sP46 <=> ((iii @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP46])])). % 196.51/196.53 thf(sP47,plain,sP47 <=> (sP41 => (sP19 => ((iii @ eigen__2) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP47])])). % 196.51/196.53 thf(sP48,plain,sP48 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => (((iii @ X1) @ X2) => ((iii @ eigen__1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP48])])). % 196.51/196.53 thf(sP49,plain,sP49 <=> (sP36 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__0) @ X1) => ((d_29_ii @ X1) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP49])])). % 196.51/196.53 thf(sP50,plain,sP50 <=> (((d_29_ii @ eigen__1) @ eigen__2) = ((d_29_ii @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP50])])). % 196.51/196.53 thf(sP51,plain,sP51 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP41 => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((iii @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP51])])). % 196.51/196.53 thf(sP52,plain,sP52 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((d_29_ii @ eigen__0) @ X1) => ((iii @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP52])])). % 196.51/196.53 thf(sP53,plain,sP53 <=> (sP16 => sP29),introduced(definition,[new_symbols(definition,[sP53])])). % 196.51/196.53 thf(sP54,plain,sP54 <=> (sP36 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => (((iii @ X1) @ X2) => ((iii @ eigen__0) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP54])])). % 196.51/196.53 thf(sP55,plain,sP55 <=> (sP14 => (((iii @ eigen__1) @ eigen__2) => sP31)),introduced(definition,[new_symbols(definition,[sP55])])). % 196.51/196.53 thf(sP56,plain,sP56 <=> ((l_or @ sP46) @ ((n_is @ eigen__2) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP56])])). % 196.51/196.53 thf(sP57,plain,sP57 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ ((d_Sep @ omega) @ (^[X2:$i]:(~((X2 = emptyset)))))))),introduced(definition,[new_symbols(definition,[sP57])])). % 196.51/196.53 thf(sP58,plain,sP58 <=> (sP57 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP42 => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((iii @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP58])])). % 196.51/196.53 thf(sP59,plain,sP59 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ eigen__2) @ X1) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => ((iii @ eigen__2) @ X2))))))),introduced(definition,[new_symbols(definition,[sP59])])). % 196.51/196.53 thf(sP60,plain,sP60 <=> (((iii @ eigen__1) @ eigen__2) => sP31),introduced(definition,[new_symbols(definition,[sP60])])). % 196.51/196.53 thf(sP61,plain,sP61 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__0) @ X1) => ((d_29_ii @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP61])])). % 196.51/196.53 thf(sP62,plain,sP62 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1)) => (((iii @ X1) @ X2) => ((iii @ eigen__0) @ X2))))))),introduced(definition,[new_symbols(definition,[sP62])])). % 196.51/196.53 thf(sP63,plain,sP63 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((d_not @ ((d_29_ii @ eigen__2) @ X1)) => ((l_or @ ((iii @ eigen__2) @ X1)) @ ((n_is @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP63])])). % 196.51/196.53 thf(sP64,plain,sP64 <=> (sP16 => sP10),introduced(definition,[new_symbols(definition,[sP64])])). % 196.51/196.53 thf(sP65,plain,sP65 <=> (sP57 => (sP41 => ((d_29_ii @ eigen__1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP65])])). % 196.51/196.53 thf(sP66,plain,sP66 <=> (sP41 => sP42),introduced(definition,[new_symbols(definition,[sP66])])). % 196.51/196.53 thf(sP67,plain,sP67 <=> (sP16 => sP55),introduced(definition,[new_symbols(definition,[sP67])])). % 196.51/196.53 thf(sP68,plain,sP68 <=> (sP36 => (sP44 => sP56)),introduced(definition,[new_symbols(definition,[sP68])])). % 196.51/196.53 thf(sP69,plain,sP69 <=> ((l_or @ sP31) @ ((n_is @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP69])])). % 196.51/196.53 thf(sP70,plain,sP70 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (((iii @ eigen__2) @ X1) => ((d_29_ii @ X1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP70])])). % 196.51/196.53 thf(sP71,plain,sP71 <=> ((iii @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP71])])). % 196.51/196.53 thf(sP72,plain,sP72 <=> (sP14 => sP41),introduced(definition,[new_symbols(definition,[sP72])])). % 196.51/196.53 thf(sP73,plain,sP73 <=> (sP57 => sP6),introduced(definition,[new_symbols(definition,[sP73])])). % 196.51/196.53 thf(sP74,plain,sP74 <=> (((d_29_ii @ eigen__1) @ eigen__2) = ((d_29_ii @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP74])])). % 196.51/196.53 thf(sP75,plain,sP75 <=> (sP57 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP14 => (((iii @ eigen__1) @ X1) => ((iii @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP75])])). % 196.51/196.53 thf(sP76,plain,sP76 <=> (sP14 => (sP19 => sP69)),introduced(definition,[new_symbols(definition,[sP76])])). % 196.51/196.53 thf(sP77,plain,sP77 <=> (sP44 => sP56),introduced(definition,[new_symbols(definition,[sP77])])). % 196.51/196.53 thf(sP78,plain,sP78 <=> (((d_29_ii @ eigen__1) @ eigen__2) => sP41),introduced(definition,[new_symbols(definition,[sP78])])). % 196.51/196.53 thf(sP79,plain,sP79 <=> ((iii @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP79])])). % 196.51/196.53 thf(sP80,plain,sP80 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((iii @ X1) @ X2) => ((d_29_ii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP80])])). % 196.51/196.53 thf(sP81,plain,sP81 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((d_Sep @ omega) @ (^[X5:$i]:(~((X5 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => (((l_or @ ((iii @ X2) @ X3)) @ ((n_is @ X2) @ X3)) => ((l_or @ ((iii @ X1) @ X3)) @ ((n_is @ X1) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP81])])). % 196.51/196.53 thf(sP82,plain,sP82 <=> ((d_29_ii @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP82])])). % 196.51/196.53 thf(sP83,plain,sP83 <=> (sP16 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP19 => (((iii @ eigen__2) @ X1) => ((iii @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP83])])). % 196.51/196.53 thf(sP84,plain,sP84 <=> (sP19 => sP69),introduced(definition,[new_symbols(definition,[sP84])])). % 196.51/196.53 thf(sP85,plain,sP85 <=> (sP19 => sP79),introduced(definition,[new_symbols(definition,[sP85])])). % 196.51/196.53 thf(sP86,plain,sP86 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP79 => (((l_or @ ((iii @ eigen__2) @ X1)) @ ((n_is @ eigen__2) @ X1)) => ((iii @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP86])])). % 196.51/196.53 thf(sP87,plain,sP87 <=> (d_not @ sP82),introduced(definition,[new_symbols(definition,[sP87])])). % 196.51/196.53 thf(sP88,plain,sP88 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (((d_29_ii @ X1) @ X2) => ((iii @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP88])])). % 196.51/196.53 thf(sP89,plain,sP89 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP14 => (((iii @ eigen__1) @ X1) => ((iii @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP89])])). % 196.51/196.53 thf(sP90,plain,sP90 <=> (sP19 => sP28),introduced(definition,[new_symbols(definition,[sP90])])). % 196.51/196.53 thf(sP91,plain,sP91 <=> ((d_29_ii @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP91])])). % 196.51/196.53 thf(sP92,plain,sP92 <=> (sP57 => sP21),introduced(definition,[new_symbols(definition,[sP92])])). % 196.51/196.53 thf(sP93,plain,sP93 <=> (sP41 => sP91),introduced(definition,[new_symbols(definition,[sP93])])). % 196.51/196.53 thf(sP94,plain,sP94 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ ((d_Sep @ omega) @ (^[X4:$i]:(~((X4 = emptyset)))))))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ ((d_Sep @ omega) @ (^[X5:$i]:(~((X5 = emptyset)))))))) => (((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)) => (((iii @ X2) @ X3) => ((iii @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP94])])). % 196.51/196.53 thf(sP95,plain,sP95 <=> (sP57 => sP43),introduced(definition,[new_symbols(definition,[sP95])])). % 196.51/196.53 thf(sP96,plain,sP96 <=> (sP19 => sP71),introduced(definition,[new_symbols(definition,[sP96])])). % 196.51/196.53 thf(sP97,plain,sP97 <=> (sP19 => sP66),introduced(definition,[new_symbols(definition,[sP97])])). % 196.51/196.53 thf(sP98,plain,sP98 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP42 => (((l_or @ ((iii @ eigen__1) @ X1)) @ ((n_is @ eigen__1) @ X1)) => ((iii @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP98])])). % 196.51/196.53 thf(sP99,plain,sP99 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => ((d_not @ ((d_29_ii @ eigen__0) @ X1)) => ((l_or @ ((iii @ eigen__0) @ X1)) @ ((n_is @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP99])])). % 196.51/196.53 thf(sP100,plain,sP100 <=> ((d_29_ii @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP100])])). % 196.51/196.53 thf(sP101,plain,sP101 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ ((d_Sep @ omega) @ (^[X3:$i]:(~((X3 = emptyset)))))))) => (sP19 => (((iii @ eigen__2) @ X1) => ((iii @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP101])])). % 196.51/196.53 thf(sP102,plain,sP102 <=> (sP16 => sP35),introduced(definition,[new_symbols(definition,[sP102])])). % 196.51/196.53 thf(sP103,plain,sP103 <=> (sP16 => sP63),introduced(definition,[new_symbols(definition,[sP103])])). % 196.51/196.53 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 196.51/196.53 thf(def_nat,definition,(nat = ((d_Sep @ omega) @ (^[X1:$i]:(~((X1 = emptyset))))))). % 196.51/196.53 thf(def_lessis,definition,(lessis = (^[X1:$i]:(^[X2:$i]:((l_or @ ((iii @ X1) @ X2)) @ ((n_is @ X1) @ X2)))))). % 196.51/196.53 thf(satz17,conjecture,sP81). % 196.51/196.53 thf(h1,negated_conjecture,(~(sP81)),inference(assume_negation,[status(cth)],[satz17])). % 196.51/196.53 thf(1,plain,(~(sP52) | sP4),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(2,plain,((~(sP4) | ~(sP16)) | sP23),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(3,plain,((~(sP23) | ~(sP82)) | sP46),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(4,plain,(~(sP27) | sP20),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(5,plain,((~(sP20) | ~(sP16)) | sP78),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(6,plain,((~(sP78) | ~(sP91)) | sP41),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(7,plain,(~(sP88) | sP45),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(8,plain,((~(sP45) | ~(sP57)) | sP27),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(9,plain,(~(sP88) | sP8),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(10,plain,((~(sP8) | ~(sP36)) | sP52),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(11,plain,(~(sP70) | sP17),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(12,plain,((~(sP17) | ~(sP36)) | sP34),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(13,plain,((~(sP34) | ~(sP46)) | sP82),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(14,plain,(~(sP70) | sP65),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(15,plain,((~(sP65) | ~(sP57)) | sP93),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(16,plain,((~(sP93) | ~(sP41)) | sP91),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(17,plain,(~(sP61) | sP64),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(18,plain,((~(sP64) | ~(sP16)) | sP10),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(19,plain,((~(sP10) | ~(sP31)) | sP100),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(20,plain,(~(sP80) | sP11),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(21,plain,((~(sP11) | ~(sP16)) | sP70),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(22,plain,(~(sP80) | sP49),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(23,plain,((~(sP49) | ~(sP36)) | sP61),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(24,plain,((sP50 | ~(sP91)) | ~(sP100)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(25,plain,((~(sP28) | sP44) | ~(sP50)),inference(mating_rule,[status(thm)],[])). % 196.51/196.53 thf(26,plain,((sP74 | ~(sP91)) | ~(sP82)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(27,plain,((sP74 | sP91) | sP82),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(28,plain,((~(sP28) | sP87) | ~(sP74)),inference(mating_rule,[status(thm)],[])). % 196.51/196.53 thf(29,plain,(~(sP6) | sP33),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(30,plain,((~(sP33) | ~(sP16)) | sP90),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(31,plain,((~(sP90) | ~(sP19)) | sP28),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(32,plain,(~(sP32) | sP73),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(33,plain,((~(sP73) | ~(sP57)) | sP6),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(34,plain,(~(sP99) | sP102),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(35,plain,((~(sP102) | ~(sP16)) | sP35),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(36,plain,((~(sP35) | ~(sP87)) | sP69),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(37,plain,(~(sP63) | sP68),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(38,plain,((~(sP68) | ~(sP36)) | sP77),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(39,plain,((~(sP77) | ~(sP44)) | sP56),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(40,plain,(~(sP30) | sP103),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(41,plain,((~(sP103) | ~(sP16)) | sP63),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(42,plain,(~(sP30) | sP38),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(43,plain,((~(sP38) | ~(sP36)) | sP99),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(44,plain,(~(sP89) | sP67),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(45,plain,((~(sP67) | ~(sP16)) | sP55),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(46,plain,((~(sP55) | ~(sP14)) | sP60),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(47,plain,((~(sP60) | ~(sP71)) | sP31),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(48,plain,(~(sP62) | sP75),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(49,plain,((~(sP75) | ~(sP57)) | sP89),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(50,plain,(~(sP101) | sP22),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(51,plain,((~(sP22) | ~(sP57)) | sP97),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(52,plain,((~(sP97) | ~(sP19)) | sP66),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(53,plain,((~(sP66) | ~(sP41)) | sP42),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(54,plain,(~(sP48) | sP83),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(55,plain,((~(sP83) | ~(sP16)) | sP101),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(56,plain,(~(sP94) | sP1),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(57,plain,((~(sP1) | ~(sP57)) | sP48),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(58,plain,(~(sP94) | sP54),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(59,plain,((~(sP54) | ~(sP36)) | sP62),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(60,plain,(~(sP98) | sP53),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(61,plain,((~(sP53) | ~(sP16)) | sP29),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(62,plain,((~(sP29) | ~(sP42)) | sP96),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(63,plain,((~(sP96) | ~(sP19)) | sP71),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(64,plain,(~(sP43) | sP58),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(65,plain,((~(sP58) | ~(sP57)) | sP98),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(66,plain,(~(sP86) | sP15),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(67,plain,((~(sP15) | ~(sP36)) | sP3),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(68,plain,((~(sP3) | ~(sP79)) | sP25),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(69,plain,((~(sP25) | ~(sP56)) | sP46),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(70,plain,(~(sP51) | sP18),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(71,plain,((~(sP18) | ~(sP16)) | sP47),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(72,plain,((~(sP47) | ~(sP41)) | sP85),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(73,plain,((~(sP85) | ~(sP19)) | sP79),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(74,plain,(~(sP24) | sP37),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(75,plain,((~(sP37) | ~(sP57)) | sP40),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(76,plain,((~(sP40) | ~(sP46)) | sP72),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(77,plain,((~(sP72) | ~(sP14)) | sP41),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(78,plain,(~(sP59) | sP9),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(79,plain,((~(sP9) | ~(sP16)) | sP86),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(80,plain,(~(sP59) | sP39),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(81,plain,((~(sP39) | ~(sP57)) | sP51),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(82,plain,(~(sP59) | sP13),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(83,plain,((~(sP13) | ~(sP36)) | sP24),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(84,plain,(~(sP7) | sP26),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(85,plain,((~(sP26) | ~(sP16)) | sP59),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(86,plain,(~(sP7) | sP95),inference(all_rule,[status(thm)],[])). % 196.51/196.53 thf(87,plain,((~(sP95) | ~(sP57)) | sP43),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(88,plain,(sP84 | ~(sP69)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(89,plain,(sP84 | sP19),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(90,plain,(sP76 | ~(sP84)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(91,plain,(sP76 | sP14),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(92,plain,(sP12 | ~(sP76)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(93,plain,(sP12 | sP16),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(94,plain,(sP21 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 196.51/196.53 thf(95,plain,(sP92 | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(96,plain,(sP92 | sP57),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(97,plain,(sP5 | ~(sP92)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 196.51/196.53 thf(98,plain,(sP2 | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(99,plain,(sP2 | sP36),inference(prop_rule,[status(thm)],[])). % 196.51/196.53 thf(100,plain,(sP81 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 196.51/196.53 thf(satz16b,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ nat))) @ (^[X3:$i]:(((iii @ X1) @ X2) => (((lessis @ X2) @ X3) => ((iii @ X1) @ X3)))))))))). % 196.51/196.53 thf(101,plain,sP7,inference(preprocess,[status(thm)],[satz16b]). % 196.51/196.53 thf(satz16a,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ nat))) @ (^[X3:$i]:(((lessis @ X1) @ X2) => (((iii @ X2) @ X3) => ((iii @ X1) @ X3)))))))))). % 196.51/196.53 thf(102,plain,sP94,inference(preprocess,[status(thm)],[satz16a]). % 196.51/196.53 thf(satz10e,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:((d_not @ ((d_29_ii @ X1) @ X2)) => ((lessis @ X1) @ X2))))))). % 196.51/196.53 thf(103,plain,sP30,inference(preprocess,[status(thm)],[satz10e]). % 196.51/196.53 thf(satz10d,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((lessis @ X1) @ X2) => (d_not @ ((d_29_ii @ X1) @ X2)))))))). % 196.51/196.53 thf(104,plain,sP32,inference(preprocess,[status(thm)],[satz10d]). % 196.51/196.53 thf(satz12,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((iii @ X1) @ X2) => ((d_29_ii @ X2) @ X1))))))). % 196.51/196.53 thf(105,plain,sP80,inference(preprocess,[status(thm)],[satz12]). % 196.51/196.53 thf(satz11,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ nat))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ nat))) @ (^[X2:$i]:(((d_29_ii @ X1) @ X2) => ((iii @ X2) @ X1))))))). % 196.51/196.53 thf(106,plain,sP88,inference(preprocess,[status(thm)],[satz11]). % 196.51/196.53 thf(107,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,h1])). % 196.51/196.53 thf(108,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[107,h0])). % 196.51/196.53 thf(0,theorem,sP81,inference(contra,[status(thm),contra(discharge,[h1])],[107,h1])). % 196.51/196.53 % SZS output end Proof %------------------------------------------------------------------------------