%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : NUM739^4 : 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 : n027.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 02:11:59 PM UTC 2025 % Result : Theorem 198.45s 198.26s % Output : Proof 198.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM739^4 : TPTP v9.2.0. Released v7.1.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 22:06:53 EDT 2025 % 0.13/0.34 % CPUTime : % 198.45/198.26 % SZS status Theorem % 198.45/198.26 % Mode: mode449:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0 % 198.45/198.26 % Inferences: 9452 % 198.45/198.26 % SZS output start Proof % 198.45/198.26 thf(ty_nat, type, nat : $i). % 198.45/198.26 thf(ty_eigen__2, type, eigen__2 : $i). % 198.45/198.26 thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)). % 198.45/198.26 thf(ty_num, type, num : ($i>$i)). % 198.45/198.26 thf(ty_eigen__1, type, eigen__1 : $i). % 198.45/198.26 thf(ty_eigen__0, type, eigen__0 : $i). % 198.45/198.26 thf(ty_l_or, type, l_or : ($o>$o>$o)). % 198.45/198.26 thf(ty_eigen__3, type, eigen__3 : $i). % 198.45/198.26 thf(ty_den, type, den : ($i>$i)). % 198.45/198.26 thf(ty_moref, type, moref : ($i>$i>$o)). % 198.45/198.26 thf(ty_n_ts, type, n_ts : ($i>$i>$i)). % 198.45/198.26 thf(ty_lessf, type, lessf : ($i>$i>$o)). % 198.45/198.26 thf(ty_pair1type, type, pair1type : ($i>$i)). % 198.45/198.26 thf(ty_n_is, type, n_is : ($i>$i>$o)). % 198.45/198.26 thf(ty_in, type, in : ($i>$i>$o)). % 198.45/198.26 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 198.45/198.26 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ eigen__1)) @ ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((l_or @ ((moref @ eigen__2) @ X1)) @ ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 198.45/198.26 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ X1)) @ ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => ((l_or @ ((moref @ X2) @ X3)) @ ((n_is @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 198.45/198.26 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (![X4:$i]:(((is_of @ X4) @ (^[X5:$i]:((in @ X5) @ (pair1type @ nat)))) => (((l_or @ ((moref @ X1) @ X2)) @ ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2))) => ((l_or @ ((moref @ X3) @ X4)) @ ((n_is @ ((n_ts @ (num @ X3)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X3)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 198.45/198.26 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ eigen__1)) @ ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__1))) => ((l_or @ ((moref @ X1) @ X2)) @ ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 198.45/198.26 thf(sP1,plain,sP1 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => ((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP1])])). % 198.45/198.26 thf(sP2,plain,sP2 <=> ((moref @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP2])])). % 198.45/198.26 thf(sP3,plain,sP3 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (![X4:$i]:(((is_of @ X4) @ (^[X5:$i]:((in @ X5) @ (pair1type @ nat)))) => (((moref @ X1) @ X2) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2))) => ((moref @ X3) @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 198.45/198.26 thf(sP4,plain,sP4 <=> (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))) => ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP4])])). % 198.45/198.26 thf(sP5,plain,sP5 <=> ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__0))),introduced(definition,[new_symbols(definition,[sP5])])). % 198.45/198.26 thf(sP6,plain,sP6 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((lessf @ eigen__3) @ eigen__2) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))) => ((lessf @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 198.45/198.26 thf(sP7,plain,sP7 <=> (((moref @ eigen__0) @ eigen__1) = sP2),introduced(definition,[new_symbols(definition,[sP7])])). % 198.45/198.26 thf(sP8,plain,sP8 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ X1) @ X2) => ((lessf @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 198.45/198.26 thf(sP9,plain,sP9 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((lessf @ eigen__3) @ X1) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__3))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => ((lessf @ X2) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 198.45/198.26 thf(sP10,plain,sP10 <=> (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((moref @ eigen__0) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP10])])). % 198.45/198.26 thf(sP11,plain,sP11 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ eigen__1)) @ ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((l_or @ sP2) @ ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2)))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 198.45/198.26 thf(sP12,plain,sP12 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 198.45/198.26 thf(sP13,plain,sP13 <=> (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3))) => sP2)),introduced(definition,[new_symbols(definition,[sP13])])). % 198.45/198.26 thf(sP14,plain,sP14 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__2) @ X1) => ((lessf @ X1) @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP14])])). % 198.45/198.26 thf(sP15,plain,sP15 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((lessf @ eigen__1) @ X1) => ((moref @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP15])])). % 198.45/198.26 thf(sP16,plain,sP16 <=> ((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__3))),introduced(definition,[new_symbols(definition,[sP16])])). % 198.45/198.26 thf(sP17,plain,sP17 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP12),introduced(definition,[new_symbols(definition,[sP17])])). % 198.45/198.26 thf(sP18,plain,sP18 <=> (((lessf @ eigen__3) @ eigen__2) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) => ((lessf @ eigen__1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP18])])). % 198.45/198.26 thf(sP19,plain,sP19 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP2 => ((lessf @ eigen__3) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP19])])). % 198.45/198.26 thf(sP20,plain,sP20 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ X1)) @ ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => ((l_or @ ((moref @ X2) @ X3)) @ ((n_is @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2))))))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 198.45/198.26 thf(sP21,plain,sP21 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP21])])). % 198.45/198.26 thf(sP22,plain,sP22 <=> ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__2))),introduced(definition,[new_symbols(definition,[sP22])])). % 198.45/198.26 thf(sP23,plain,sP23 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 198.45/198.26 thf(sP24,plain,sP24 <=> ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__0))),introduced(definition,[new_symbols(definition,[sP24])])). % 198.45/198.26 thf(sP25,plain,sP25 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((lessf @ eigen__3) @ eigen__2) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__3))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__2))) => ((lessf @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP25])])). % 198.45/198.26 thf(sP26,plain,sP26 <=> (sP2 => ((lessf @ eigen__3) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP26])])). % 198.45/198.26 thf(sP27,plain,sP27 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X2))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 198.45/198.26 thf(sP28,plain,sP28 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP22 => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2)))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 198.45/198.26 thf(sP29,plain,sP29 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP25),introduced(definition,[new_symbols(definition,[sP29])])). % 198.45/198.26 thf(sP30,plain,sP30 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__3))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2)))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 198.45/198.26 thf(sP31,plain,sP31 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__3) => sP13)),introduced(definition,[new_symbols(definition,[sP31])])). % 198.45/198.26 thf(sP32,plain,sP32 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP18),introduced(definition,[new_symbols(definition,[sP32])])). % 198.45/198.26 thf(sP33,plain,sP33 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((lessf @ X1) @ X2) => ((moref @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP33])])). % 198.45/198.26 thf(sP34,plain,sP34 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((lessf @ eigen__1) @ eigen__0) => ((moref @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP34])])). % 198.45/198.26 thf(sP35,plain,sP35 <=> ((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))),introduced(definition,[new_symbols(definition,[sP35])])). % 198.45/198.26 thf(sP36,plain,sP36 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 198.45/198.26 thf(sP37,plain,sP37 <=> (sP5 => sP10),introduced(definition,[new_symbols(definition,[sP37])])). % 198.45/198.26 thf(sP38,plain,sP38 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((moref @ eigen__0) @ eigen__1)) @ sP24) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__1))) => ((l_or @ ((moref @ X1) @ X2)) @ ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP38])])). % 198.45/198.26 thf(sP39,plain,sP39 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) => (sP24 => sP22))),introduced(definition,[new_symbols(definition,[sP39])])). % 198.45/198.26 thf(sP40,plain,sP40 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__2))))))))),introduced(definition,[new_symbols(definition,[sP40])])). % 198.45/198.26 thf(sP41,plain,sP41 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__1) => (sP5 => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((moref @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP41])])). % 198.45/198.26 thf(sP42,plain,sP42 <=> (sP22 => sP24),introduced(definition,[new_symbols(definition,[sP42])])). % 198.45/198.26 thf(sP43,plain,sP43 <=> (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP43])])). % 198.45/198.26 thf(sP44,plain,sP44 <=> (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) => (sP24 => sP22)),introduced(definition,[new_symbols(definition,[sP44])])). % 198.45/198.26 thf(sP45,plain,sP45 <=> ((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP45])])). % 198.45/198.26 thf(sP46,plain,sP46 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP15),introduced(definition,[new_symbols(definition,[sP46])])). % 198.45/198.26 thf(sP47,plain,sP47 <=> (sP24 = ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP47])])). % 198.45/198.26 thf(sP48,plain,sP48 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP48])])). % 198.45/198.26 thf(sP49,plain,sP49 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP49])])). % 198.45/198.26 thf(sP50,plain,sP50 <=> (((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP22 => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP50])])). % 198.45/198.26 thf(sP51,plain,sP51 <=> ((lessf @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP51])])). % 198.45/198.26 thf(sP52,plain,sP52 <=> (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))) => (sP35 => sP22)),introduced(definition,[new_symbols(definition,[sP52])])). % 198.45/198.26 thf(sP53,plain,sP53 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__1) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__1))) => ((moref @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP53])])). % 198.45/198.26 thf(sP54,plain,sP54 <=> ((is_of @ eigen__3) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP54])])). % 198.45/198.26 thf(sP55,plain,sP55 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ X1) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => ((moref @ X2) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP55])])). % 198.45/198.26 thf(sP56,plain,sP56 <=> (sP35 => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) => sP51)),introduced(definition,[new_symbols(definition,[sP56])])). % 198.45/198.26 thf(sP57,plain,sP57 <=> (((moref @ eigen__0) @ eigen__3) => sP13),introduced(definition,[new_symbols(definition,[sP57])])). % 198.45/198.26 thf(sP58,plain,sP58 <=> ((moref @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP58])])). % 198.45/198.26 thf(sP59,plain,sP59 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) @ ((n_ts @ (num @ eigen__1)) @ (den @ X1)))))),introduced(definition,[new_symbols(definition,[sP59])])). % 198.45/198.26 thf(sP60,plain,sP60 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))) => ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))))))),introduced(definition,[new_symbols(definition,[sP60])])). % 198.45/198.26 thf(sP61,plain,sP61 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP49),introduced(definition,[new_symbols(definition,[sP61])])). % 198.45/198.26 thf(sP62,plain,sP62 <=> (sP48 => sP38),introduced(definition,[new_symbols(definition,[sP62])])). % 198.45/198.26 thf(sP63,plain,sP63 <=> (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => sP35),introduced(definition,[new_symbols(definition,[sP63])])). % 198.45/198.26 thf(sP64,plain,sP64 <=> ((lessf @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP64])])). % 198.45/198.26 thf(sP65,plain,sP65 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((lessf @ eigen__3) @ X1) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__3))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => ((lessf @ X2) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP65])])). % 198.45/198.26 thf(sP66,plain,sP66 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__3) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__3))) => ((moref @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP66])])). % 198.45/198.26 thf(sP67,plain,sP67 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP41),introduced(definition,[new_symbols(definition,[sP67])])). % 198.45/198.26 thf(sP68,plain,sP68 <=> (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((l_or @ sP2) @ ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP68])])). % 198.45/198.26 thf(sP69,plain,sP69 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP5),introduced(definition,[new_symbols(definition,[sP69])])). % 198.45/198.26 thf(sP70,plain,sP70 <=> (sP51 => sP58),introduced(definition,[new_symbols(definition,[sP70])])). % 198.45/198.26 thf(sP71,plain,sP71 <=> ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))),introduced(definition,[new_symbols(definition,[sP71])])). % 198.45/198.26 thf(sP72,plain,sP72 <=> (sP22 => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP72])])). % 198.45/198.26 thf(sP73,plain,sP73 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP55),introduced(definition,[new_symbols(definition,[sP73])])). % 198.45/198.26 thf(sP74,plain,sP74 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ sP58) @ sP24) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((l_or @ ((moref @ eigen__2) @ X1)) @ ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))))))))),introduced(definition,[new_symbols(definition,[sP74])])). % 198.45/198.26 thf(sP75,plain,sP75 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))))))),introduced(definition,[new_symbols(definition,[sP75])])). % 198.45/198.26 thf(sP76,plain,sP76 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__3))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP76])])). % 198.45/198.26 thf(sP77,plain,sP77 <=> (sP48 => sP4),introduced(definition,[new_symbols(definition,[sP77])])). % 198.45/198.26 thf(sP78,plain,sP78 <=> ((moref @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP78])])). % 198.45/198.26 thf(sP79,plain,sP79 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ X1))))),introduced(definition,[new_symbols(definition,[sP79])])). % 198.45/198.26 thf(sP80,plain,sP80 <=> (sP16 => sP2),introduced(definition,[new_symbols(definition,[sP80])])). % 198.45/198.26 thf(sP81,plain,sP81 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP81])])). % 198.45/198.26 thf(sP82,plain,sP82 <=> (sP54 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP78 => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__3))) => ((moref @ X1) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP82])])). % 198.45/198.26 thf(sP83,plain,sP83 <=> (sP45 => sP66),introduced(definition,[new_symbols(definition,[sP83])])). % 198.45/198.26 thf(sP84,plain,sP84 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__2) @ X1) => ((lessf @ X1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP84])])). % 198.45/198.26 thf(sP85,plain,sP85 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (![X4:$i]:(((is_of @ X4) @ (^[X5:$i]:((in @ X5) @ (pair1type @ nat)))) => (((l_or @ ((moref @ X1) @ X2)) @ ((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2))) => ((l_or @ ((moref @ X3) @ X4)) @ ((n_is @ ((n_ts @ (num @ X3)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X3))))))))))))))),introduced(definition,[new_symbols(definition,[sP85])])). % 198.45/198.26 thf(sP86,plain,sP86 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP22 => (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__1))) => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP86])])). % 198.45/198.26 thf(sP87,plain,sP87 <=> (sP58 => sP37),introduced(definition,[new_symbols(definition,[sP87])])). % 198.45/198.26 thf(sP88,plain,sP88 <=> (sP45 => sP74),introduced(definition,[new_symbols(definition,[sP88])])). % 198.45/198.26 thf(sP89,plain,sP89 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP78 => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => (((n_is @ ((n_ts @ (num @ eigen__3)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ eigen__3))) => ((moref @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP89])])). % 198.45/198.26 thf(sP90,plain,sP90 <=> (sP45 => sP60),introduced(definition,[new_symbols(definition,[sP90])])). % 198.45/198.26 thf(sP91,plain,sP91 <=> ((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ eigen__2))) @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__0))),introduced(definition,[new_symbols(definition,[sP91])])). % 198.45/198.26 thf(sP92,plain,sP92 <=> (sP54 => sP87),introduced(definition,[new_symbols(definition,[sP92])])). % 198.45/198.26 thf(sP93,plain,sP93 <=> (((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))) => ((l_or @ sP2) @ ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))))),introduced(definition,[new_symbols(definition,[sP93])])). % 198.45/198.26 thf(sP94,plain,sP94 <=> ((l_or @ sP58) @ sP24),introduced(definition,[new_symbols(definition,[sP94])])). % 198.45/198.26 thf(sP95,plain,sP95 <=> (sP54 => sP63),introduced(definition,[new_symbols(definition,[sP95])])). % 198.45/198.26 thf(sP96,plain,sP96 <=> (sP35 => sP22),introduced(definition,[new_symbols(definition,[sP96])])). % 198.45/198.26 thf(sP97,plain,sP97 <=> (sP48 => sP52),introduced(definition,[new_symbols(definition,[sP97])])). % 198.45/198.26 thf(sP98,plain,sP98 <=> ((n_is @ ((n_ts @ (num @ eigen__1)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__1))),introduced(definition,[new_symbols(definition,[sP98])])). % 198.45/198.26 thf(sP99,plain,sP99 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))) => ((n_is @ ((n_ts @ (num @ X2)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ X2)))))))),introduced(definition,[new_symbols(definition,[sP99])])). % 198.45/198.26 thf(sP100,plain,sP100 <=> (sP98 => ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP100])])). % 198.45/198.26 thf(sP101,plain,sP101 <=> ((n_is @ ((n_ts @ (num @ eigen__2)) @ (den @ eigen__3))) @ ((n_ts @ (num @ eigen__3)) @ (den @ eigen__2))),introduced(definition,[new_symbols(definition,[sP101])])). % 198.45/198.26 thf(sP102,plain,sP102 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (![X4:$i]:(((is_of @ X4) @ (^[X5:$i]:((in @ X5) @ (pair1type @ nat)))) => (((lessf @ X1) @ X2) => (((n_is @ ((n_ts @ (num @ X1)) @ (den @ X3))) @ ((n_ts @ (num @ X3)) @ (den @ X1))) => (((n_is @ ((n_ts @ (num @ X2)) @ (den @ X4))) @ ((n_ts @ (num @ X4)) @ (den @ X2))) => ((lessf @ X3) @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP102])])). % 198.45/198.26 thf(sP103,plain,sP103 <=> (sP71 => sP51),introduced(definition,[new_symbols(definition,[sP103])])). % 198.45/198.26 thf(sP104,plain,sP104 <=> ((l_or @ sP2) @ sP101),introduced(definition,[new_symbols(definition,[sP104])])). % 198.45/198.26 thf(sP105,plain,sP105 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((n_is @ ((n_ts @ (num @ eigen__0)) @ (den @ X1))) @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) => ((n_is @ ((n_ts @ (num @ X1)) @ (den @ eigen__0))) @ ((n_ts @ (num @ eigen__0)) @ (den @ X1)))))),introduced(definition,[new_symbols(definition,[sP105])])). % 198.45/198.26 thf(sP106,plain,sP106 <=> (sP81 => sP20),introduced(definition,[new_symbols(definition,[sP106])])). % 198.45/198.26 thf(sP107,plain,sP107 <=> (sP48 => sP53),introduced(definition,[new_symbols(definition,[sP107])])). % 198.45/198.26 thf(sP108,plain,sP108 <=> (sP94 => sP68),introduced(definition,[new_symbols(definition,[sP108])])). % 198.45/198.26 thf(sP109,plain,sP109 <=> (sP48 => sP6),introduced(definition,[new_symbols(definition,[sP109])])). % 198.45/198.26 thf(sP110,plain,sP110 <=> (sP24 => sP22),introduced(definition,[new_symbols(definition,[sP110])])). % 198.45/198.26 thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))). % 198.45/198.26 thf(def_frac,definition,(frac = (pair1type @ nat))). % 198.45/198.26 thf(def_n_eq,definition,(n_eq = (^[X1:$i]:(^[X2:$i]:((n_is @ ((n_ts @ (num @ X1)) @ (den @ X2))) @ ((n_ts @ (num @ X2)) @ (den @ X1))))))). % 198.45/198.26 thf(def_moreq,definition,(moreq = (^[X1:$i]:(^[X2:$i]:((l_or @ ((moref @ X1) @ X2)) @ ((n_eq @ X1) @ X2)))))). % 198.45/198.26 thf(satz46,conjecture,sP85). % 198.45/198.26 thf(h1,negated_conjecture,(~(sP85)),inference(assume_negation,[status(cth)],[satz46])). % 198.45/198.26 thf(1,plain,(~(sP41) | sP92),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(2,plain,((~(sP92) | ~(sP54)) | sP87),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(3,plain,((~(sP87) | ~(sP58)) | sP37),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(4,plain,((~(sP37) | ~(sP5)) | sP10),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(5,plain,((~(sP10) | ~(sP98)) | sP78),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(6,plain,(~(sP53) | sP67),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(7,plain,((~(sP67) | ~(sP81)) | sP41),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(8,plain,(~(sP66) | sP31),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(9,plain,((~(sP31) | ~(sP54)) | sP57),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(10,plain,((~(sP57) | ~(sP78)) | sP13),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(11,plain,((~(sP13) | ~(sP91)) | sP80),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(12,plain,((~(sP80) | ~(sP16)) | sP2),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(13,plain,(~(sP89) | sP83),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(14,plain,((~(sP83) | ~(sP45)) | sP66),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(15,plain,(~(sP6) | sP32),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(16,plain,((~(sP32) | ~(sP81)) | sP18),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(17,plain,((~(sP18) | ~(sP64)) | sP56),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(18,plain,((~(sP56) | ~(sP35)) | sP103),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(19,plain,((~(sP103) | ~(sP71)) | sP51),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(20,plain,(~(sP25) | sP109),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(21,plain,((~(sP109) | ~(sP48)) | sP6),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(22,plain,(~(sP65) | sP29),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(23,plain,((~(sP29) | ~(sP45)) | sP25),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(24,plain,(~(sP55) | sP82),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(25,plain,((~(sP82) | ~(sP54)) | sP89),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(26,plain,(~(sP55) | sP107),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(27,plain,((~(sP107) | ~(sP48)) | sP53),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(28,plain,(~(sP60) | sP77),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(29,plain,((~(sP77) | ~(sP48)) | sP4),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(30,plain,((~(sP4) | ~(sP91)) | sP42),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(31,plain,((~(sP42) | ~(sP22)) | sP24),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(32,plain,(~(sP12) | sP90),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(33,plain,((~(sP90) | ~(sP45)) | sP60),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(34,plain,(~(sP86) | sP50),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(35,plain,((~(sP50) | ~(sP54)) | sP72),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(36,plain,((~(sP72) | ~(sP22)) | sP100),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(37,plain,((~(sP100) | ~(sP98)) | sP101),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(38,plain,(~(sP49) | sP39),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(39,plain,((~(sP39) | ~(sP48)) | sP44),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(40,plain,((~(sP44) | ~(sP71)) | sP110),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(41,plain,((~(sP110) | ~(sP24)) | sP22),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(42,plain,(~(sP76) | sP97),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(43,plain,((~(sP97) | ~(sP48)) | sP52),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(44,plain,((~(sP52) | ~(sP101)) | sP96),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(45,plain,((~(sP96) | ~(sP35)) | sP22),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(46,plain,(~(sP40) | sP30),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(47,plain,((~(sP30) | ~(sP54)) | sP76),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(48,plain,(~(sP40) | sP28),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(49,plain,((~(sP28) | ~(sP48)) | sP86),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(50,plain,(~(sP40) | sP61),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(51,plain,((~(sP61) | ~(sP81)) | sP49),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(52,plain,(~(sP84) | sP19),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(53,plain,((~(sP19) | ~(sP54)) | sP26),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(54,plain,((~(sP26) | ~(sP2)) | sP64),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(55,plain,(~(sP8) | sP14),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(56,plain,((~(sP14) | ~(sP45)) | sP84),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(57,plain,(~(sP15) | sP34),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(58,plain,((~(sP34) | ~(sP81)) | sP70),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(59,plain,((~(sP70) | ~(sP51)) | sP58),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(60,plain,(~(sP33) | sP46),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(61,plain,((~(sP46) | ~(sP48)) | sP15),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(62,plain,(~(sP3) | sP73),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(63,plain,((~(sP73) | ~(sP81)) | sP55),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(64,plain,(~(sP102) | sP9),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(65,plain,((~(sP9) | ~(sP54)) | sP65),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(66,plain,(~(sP79) | sP1),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(67,plain,((~(sP1) | ~(sP54)) | sP16),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(68,plain,(~(sP79) | sP69),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(69,plain,((~(sP69) | ~(sP81)) | sP5),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(70,plain,(~(sP59) | sP95),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(71,plain,((~(sP95) | ~(sP54)) | sP63),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(72,plain,((~(sP63) | ~(sP98)) | sP35),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(73,plain,(~(sP105) | sP21),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(74,plain,((~(sP21) | ~(sP45)) | sP43),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(75,plain,((~(sP43) | ~(sP91)) | sP71),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(76,plain,(~(sP99) | sP36),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(77,plain,((~(sP36) | ~(sP48)) | sP59),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(78,plain,(~(sP99) | sP75),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(79,plain,((~(sP75) | ~(sP81)) | sP105),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(80,plain,(~(sP27) | sP23),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(81,plain,((~(sP23) | ~(sP45)) | sP40),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(82,plain,(~(sP27) | sP17),inference(all_rule,[status(thm)],[])). % 198.45/198.26 thf(83,plain,((~(sP17) | ~(sP81)) | sP12),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(84,plain,((sP7 | ~(sP58)) | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(85,plain,((sP7 | sP58) | sP2),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(86,plain,((sP47 | ~(sP24)) | ~(sP101)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(87,plain,((sP47 | sP24) | sP101),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(88,plain,(((~(sP94) | sP104) | ~(sP7)) | ~(sP47)),inference(mating_rule,[status(thm)],[])). % 198.45/198.26 thf(89,plain,(sP93 | ~(sP104)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(90,plain,(sP93 | sP98),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(91,plain,(sP68 | ~(sP93)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(92,plain,(sP68 | sP91),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(93,plain,(sP108 | ~(sP68)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(94,plain,(sP108 | sP94),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(95,plain,(sP11 | ~(sP108)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(96,plain,(sP11 | sP54),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(97,plain,(sP74 | ~(sP11)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 198.45/198.26 thf(98,plain,(sP88 | ~(sP74)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(99,plain,(sP88 | sP45),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(100,plain,(sP38 | ~(sP88)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 198.45/198.26 thf(101,plain,(sP62 | ~(sP38)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(102,plain,(sP62 | sP48),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(103,plain,(sP20 | ~(sP62)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 198.45/198.26 thf(104,plain,(sP106 | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(105,plain,(sP106 | sP81),inference(prop_rule,[status(thm)],[])). % 198.45/198.26 thf(106,plain,(sP85 | ~(sP106)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 198.45/198.26 thf(satz45,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ frac))) @ (^[X3:$i]:((all_of @ (^[X4:$i]:((in @ X4) @ frac))) @ (^[X4:$i]:(((lessf @ X1) @ X2) => (((n_eq @ X1) @ X3) => (((n_eq @ X2) @ X4) => ((lessf @ X3) @ X4))))))))))))). % 198.45/198.26 thf(107,plain,sP102,inference(preprocess,[status(thm)],[satz45]). % 198.45/198.26 thf(satz44,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ frac))) @ (^[X3:$i]:((all_of @ (^[X4:$i]:((in @ X4) @ frac))) @ (^[X4:$i]:(((moref @ X1) @ X2) => (((n_eq @ X1) @ X3) => (((n_eq @ X2) @ X4) => ((moref @ X3) @ X4))))))))))))). % 198.45/198.26 thf(108,plain,sP3,inference(preprocess,[status(thm)],[satz44]). % 198.45/198.26 thf(satz43,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((lessf @ X1) @ X2) => ((moref @ X2) @ X1))))))). % 198.45/198.26 thf(109,plain,sP33,inference(preprocess,[status(thm)],[satz43]). % 198.45/198.26 thf(satz42,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((moref @ X1) @ X2) => ((lessf @ X2) @ X1))))))). % 198.45/198.26 thf(110,plain,sP8,inference(preprocess,[status(thm)],[satz42]). % 198.45/198.26 thf(satz39,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ frac))) @ (^[X3:$i]:(((n_eq @ X1) @ X2) => (((n_eq @ X2) @ X3) => ((n_eq @ X1) @ X3)))))))))). % 198.45/198.26 thf(111,plain,sP27,inference(preprocess,[status(thm)],[satz39]). % 198.45/198.26 thf(satz38,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((n_eq @ X1) @ X2) => ((n_eq @ X2) @ X1))))))). % 198.45/198.26 thf(112,plain,sP99,inference(preprocess,[status(thm)],[satz38]). % 198.45/198.26 thf(satz37,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((n_eq @ X1) @ X1)))). % 198.45/198.26 thf(113,plain,sP79,inference(preprocess,[status(thm)],[satz37]). % 198.45/198.26 thf(114,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,h1])). % 198.45/198.27 thf(115,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[114,h0])). % 198.45/198.27 thf(0,theorem,sP85,inference(contra,[status(thm),contra(discharge,[h1])],[114,h1])). % 198.45/198.27 % SZS output end Proof %------------------------------------------------------------------------------