0.02/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.09/0.30	% Computer   : n020.cluster.edu
0.09/0.30	% Model      : x86_64 x86_64
0.09/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.30	% Memory     : 8042.1875MB
0.09/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.30	% CPULimit   : 960
0.09/0.30	% WCLimit    : 120
0.09/0.30	% DateTime   : Thu Jul  2 09:26:02 EDT 2020
0.09/0.30	% CPUTime    : 
103.34/102.72	% SZS status Theorem
103.34/102.72	% Mode: mode449:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
103.34/102.72	% Inferences: 4193
103.34/102.72	% SZS output start Proof
103.34/102.72	thf(ty_n_eq, type, n_eq : ($i>$i>$o)).
103.34/102.72	thf(ty_d_not, type, d_not : ($o>$o)).
103.34/102.72	thf(ty_nat, type, nat : $i).
103.34/102.72	thf(ty_eigen__2, type, eigen__2 : $i).
103.34/102.72	thf(ty_is_of, type, is_of : ($i>($i>$o)>$o)).
103.34/102.72	thf(ty_eigen__1, type, eigen__1 : $i).
103.34/102.72	thf(ty_eigen__0, type, eigen__0 : $i).
103.34/102.72	thf(ty_l_or, type, l_or : ($o>$o>$o)).
103.34/102.72	thf(ty_moreq, type, moreq : ($i>$i>$o)).
103.34/102.72	thf(ty_moref, type, moref : ($i>$i>$o)).
103.34/102.72	thf(ty_lessf, type, lessf : ($i>$i>$o)).
103.34/102.72	thf(ty_pair1type, type, pair1type : ($i>$i)).
103.34/102.72	thf(ty_in, type, in : ($i>$i>$o)).
103.34/102.72	thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
103.34/102.72	thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ eigen__0) @ X2)) @ ((n_eq @ eigen__0) @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
103.34/102.72	thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$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:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => (((l_or @ ((lessf @ X2) @ X3)) @ ((n_eq @ X2) @ X3)) => ((l_or @ ((lessf @ X1) @ X3)) @ ((n_eq @ X1) @ X3))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
103.34/102.72	thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ eigen__1)) @ ((n_eq @ eigen__0) @ eigen__1)) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => ((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
103.34/102.72	thf(sP1,plain,sP1 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ eigen__1)) @ ((n_eq @ eigen__1) @ eigen__1)) => (((n_eq @ eigen__1) @ eigen__2) => (((n_eq @ eigen__1) @ X1) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP1])])).
103.34/102.72	thf(sP2,plain,sP2 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)) => (((n_eq @ eigen__0) @ eigen__2) => (((n_eq @ eigen__0) @ X1) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP2])])).
103.34/102.72	thf(sP3,plain,sP3 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => (d_not @ ((moref @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])).
103.34/102.72	thf(sP4,plain,sP4 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ X1) => (((moreq @ X1) @ X2) => ((moref @ eigen__0) @ X2))))))),introduced(definition,[new_symbols(definition,[sP4])])).
103.34/102.72	thf(sP5,plain,sP5 <=> ((moref @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])).
103.34/102.72	thf(sP6,plain,sP6 <=> ((d_not @ sP5) => ((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP6])])).
103.34/102.72	thf(sP7,plain,sP7 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__1) @ eigen__1)) => ((l_or @ ((lessf @ eigen__1) @ eigen__1)) @ ((n_eq @ eigen__1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP7])])).
103.34/102.72	thf(sP8,plain,sP8 <=> ((l_or @ ((lessf @ eigen__0) @ eigen__1)) @ ((n_eq @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP8])])).
103.34/102.72	thf(sP9,plain,sP9 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)) => (((n_eq @ eigen__0) @ eigen__2) => (((n_eq @ eigen__0) @ X1) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP9])])).
103.34/102.72	thf(sP10,plain,sP10 <=> (![X1:$o]:((((moref @ eigen__0) @ eigen__2) = X1) => (X1 = ((moref @ eigen__0) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP10])])).
103.34/102.72	thf(sP11,plain,sP11 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__1) => (((moreq @ eigen__1) @ X1) => ((moref @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP11])])).
103.34/102.72	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)))) => (![X3:$i]:(((is_of @ X3) @ (^[X4:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (((n_eq @ eigen__0) @ X2) => (((n_eq @ X1) @ X3) => ((l_or @ ((lessf @ X2) @ X3)) @ ((n_eq @ X2) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP12])])).
103.34/102.72	thf(sP13,plain,sP13 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ eigen__1) => (((moreq @ eigen__1) @ eigen__0) => sP5))),introduced(definition,[new_symbols(definition,[sP13])])).
103.34/102.72	thf(sP14,plain,sP14 <=> (d_not @ ((moref @ eigen__0) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP14])])).
103.34/102.72	thf(sP15,plain,sP15 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__0) @ eigen__1) => (((moreq @ eigen__1) @ X1) => ((moref @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP15])])).
103.34/102.72	thf(sP16,plain,sP16 <=> (((is_of @ eigen__0) @ (^[X1:$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)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ eigen__0) @ X2)) @ ((n_eq @ eigen__0) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP16])])).
103.34/102.72	thf(sP17,plain,sP17 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__2) @ X1)) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP17])])).
103.34/102.72	thf(sP18,plain,sP18 <=> ((d_not @ ((moref @ eigen__0) @ eigen__2)) => ((l_or @ ((lessf @ eigen__0) @ eigen__2)) @ ((n_eq @ eigen__0) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP18])])).
103.34/102.72	thf(sP19,plain,sP19 <=> (d_not @ ((moref @ eigen__2) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP19])])).
103.34/102.72	thf(sP20,plain,sP20 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ eigen__1) => (((moreq @ eigen__1) @ X1) => ((moref @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP20])])).
103.34/102.72	thf(sP21,plain,sP21 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (d_not @ ((moref @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP21])])).
103.34/102.72	thf(sP22,plain,sP22 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)) => (((n_eq @ eigen__0) @ eigen__2) => (((n_eq @ eigen__0) @ eigen__2) => ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP22])])).
103.34/102.72	thf(sP23,plain,sP23 <=> (((moreq @ eigen__1) @ eigen__0) => ((moref @ eigen__0) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP23])])).
103.34/102.72	thf(sP24,plain,sP24 <=> (((moref @ eigen__0) @ eigen__1) => sP23),introduced(definition,[new_symbols(definition,[sP24])])).
103.34/102.72	thf(sP25,plain,sP25 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0)) => (((lessf @ eigen__0) @ X1) => ((lessf @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP25])])).
103.34/102.72	thf(sP26,plain,sP26 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ eigen__2) @ X1) => (((moreq @ X1) @ X2) => ((moref @ eigen__2) @ X2))))))),introduced(definition,[new_symbols(definition,[sP26])])).
103.34/102.72	thf(sP27,plain,sP27 <=> (((lessf @ eigen__0) @ eigen__2) => ((lessf @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP27])])).
103.34/102.72	thf(sP28,plain,sP28 <=> (d_not @ ((moref @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP28])])).
103.34/102.72	thf(sP29,plain,sP29 <=> ((moreq @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP29])])).
103.34/102.72	thf(sP30,plain,sP30 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ eigen__2)) @ ((n_eq @ eigen__1) @ eigen__2)) => (d_not @ ((moref @ eigen__1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP30])])).
103.34/102.72	thf(sP31,plain,sP31 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__1) @ X1)) => ((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP31])])).
103.34/102.72	thf(sP32,plain,sP32 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)) => ((moreq @ X1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP32])])).
103.34/102.72	thf(sP33,plain,sP33 <=> (((moreq @ eigen__2) @ eigen__1) => ((moref @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP33])])).
103.34/102.72	thf(sP34,plain,sP34 <=> (sP8 => ((moreq @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP34])])).
103.34/102.72	thf(sP35,plain,sP35 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP8 => (((lessf @ eigen__1) @ X1) => ((lessf @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP35])])).
103.34/102.72	thf(sP36,plain,sP36 <=> (((moref @ eigen__1) @ eigen__2) = ((moref @ eigen__0) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP36])])).
103.34/102.72	thf(sP37,plain,sP37 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => (d_not @ ((moref @ eigen__1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP37])])).
103.34/102.72	thf(sP38,plain,sP38 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP14 => ((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP38])])).
103.34/102.72	thf(sP39,plain,sP39 <=> (((moref @ eigen__0) @ eigen__0) = sP5),introduced(definition,[new_symbols(definition,[sP39])])).
103.34/102.72	thf(sP40,plain,sP40 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (d_not @ ((moref @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP40])])).
103.34/102.72	thf(sP41,plain,sP41 <=> ((l_or @ ((lessf @ eigen__2) @ eigen__1)) @ ((n_eq @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP41])])).
103.34/102.72	thf(sP42,plain,sP42 <=> (![X1:$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:$i]:((in @ X4) @ (pair1type @ nat)))) => (((moref @ X1) @ X2) => (((moreq @ X2) @ X3) => ((moref @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP42])])).
103.34/102.72	thf(sP43,plain,sP43 <=> (((lessf @ eigen__1) @ eigen__2) => ((lessf @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP43])])).
103.34/102.72	thf(sP44,plain,sP44 <=> ((moreq @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP44])])).
103.34/102.72	thf(sP45,plain,sP45 <=> (((n_eq @ eigen__1) @ eigen__2) => (((n_eq @ eigen__1) @ eigen__2) => ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP45])])).
103.34/102.72	thf(sP46,plain,sP46 <=> (((moref @ eigen__0) @ eigen__2) = ((moref @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP46])])).
103.34/102.72	thf(sP47,plain,sP47 <=> (((moref @ eigen__1) @ eigen__2) = ((moref @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP47])])).
103.34/102.72	thf(sP48,plain,sP48 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP25),introduced(definition,[new_symbols(definition,[sP48])])).
103.34/102.72	thf(sP49,plain,sP49 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (((lessf @ X1) @ X2) => ((lessf @ eigen__0) @ X2))))))),introduced(definition,[new_symbols(definition,[sP49])])).
103.34/102.72	thf(sP50,plain,sP50 <=> (d_not @ ((moref @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP50])])).
103.34/102.72	thf(sP51,plain,sP51 <=> ((lessf @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP51])])).
103.34/102.72	thf(sP52,plain,sP52 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__0) @ X1)) => ((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP52])])).
103.34/102.72	thf(sP53,plain,sP53 <=> (((moref @ eigen__0) @ eigen__2) => (((moreq @ eigen__2) @ eigen__1) => ((moref @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP53])])).
103.34/102.72	thf(sP54,plain,sP54 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ eigen__2) => (((moreq @ eigen__2) @ X1) => ((moref @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP54])])).
103.34/102.72	thf(sP55,plain,sP55 <=> ((moref @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP55])])).
103.34/102.72	thf(sP56,plain,sP56 <=> ((l_or @ ((lessf @ eigen__1) @ eigen__1)) @ ((n_eq @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP56])])).
103.34/102.72	thf(sP57,plain,sP57 <=> (((moref @ eigen__1) @ eigen__2) = ((moref @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP57])])).
103.34/102.72	thf(sP58,plain,sP58 <=> (sP46 => (((moref @ eigen__1) @ eigen__2) = sP55)),introduced(definition,[new_symbols(definition,[sP58])])).
103.34/102.72	thf(sP59,plain,sP59 <=> ((moref @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP59])])).
103.34/102.72	thf(sP60,plain,sP60 <=> (((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP12),introduced(definition,[new_symbols(definition,[sP60])])).
103.34/102.72	thf(sP61,plain,sP61 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP53),introduced(definition,[new_symbols(definition,[sP61])])).
103.34/102.72	thf(sP62,plain,sP62 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((l_or @ sP51) @ ((n_eq @ eigen__1) @ eigen__2)) => ((moreq @ eigen__2) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP62])])).
103.34/102.72	thf(sP63,plain,sP63 <=> (((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2)) => sP19),introduced(definition,[new_symbols(definition,[sP63])])).
103.34/102.72	thf(sP64,plain,sP64 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP54),introduced(definition,[new_symbols(definition,[sP64])])).
103.34/102.72	thf(sP65,plain,sP65 <=> (![X1:$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:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => (((n_eq @ eigen__1) @ X2) => (((n_eq @ X1) @ X3) => ((l_or @ ((lessf @ X2) @ X3)) @ ((n_eq @ X2) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP65])])).
103.34/102.72	thf(sP66,plain,sP66 <=> (sP29 => sP55),introduced(definition,[new_symbols(definition,[sP66])])).
103.34/102.72	thf(sP67,plain,sP67 <=> ((moref @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP67])])).
103.34/102.72	thf(sP68,plain,sP68 <=> (((n_eq @ eigen__1) @ eigen__2) = ((n_eq @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP68])])).
103.34/102.72	thf(sP69,plain,sP69 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0)) => sP27)),introduced(definition,[new_symbols(definition,[sP69])])).
103.34/102.72	thf(sP70,plain,sP70 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => (((lessf @ X1) @ X2) => ((lessf @ eigen__1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP70])])).
103.34/102.72	thf(sP71,plain,sP71 <=> (sP8 => (d_not @ ((moref @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP71])])).
103.34/102.72	thf(sP72,plain,sP72 <=> (d_not @ sP59),introduced(definition,[new_symbols(definition,[sP72])])).
103.34/102.72	thf(sP73,plain,sP73 <=> (![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 @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => (((lessf @ X2) @ X3) => ((lessf @ X1) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP73])])).
103.34/102.72	thf(sP74,plain,sP74 <=> ((d_not @ ((moref @ eigen__1) @ eigen__1)) => sP56),introduced(definition,[new_symbols(definition,[sP74])])).
103.34/102.72	thf(sP75,plain,sP75 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP41 => sP29)),introduced(definition,[new_symbols(definition,[sP75])])).
103.34/102.72	thf(sP76,plain,sP76 <=> (((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (((moref @ eigen__2) @ eigen__2) => sP33)),introduced(definition,[new_symbols(definition,[sP76])])).
103.34/102.72	thf(sP77,plain,sP77 <=> (((l_or @ sP51) @ ((n_eq @ eigen__1) @ eigen__2)) => ((l_or @ ((lessf @ eigen__0) @ eigen__2)) @ ((n_eq @ eigen__0) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP77])])).
103.34/102.72	thf(sP78,plain,sP78 <=> (((n_eq @ eigen__0) @ eigen__2) => (((n_eq @ eigen__0) @ eigen__2) => ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP78])])).
103.34/102.72	thf(sP79,plain,sP79 <=> ((l_or @ ((lessf @ eigen__0) @ eigen__2)) @ ((n_eq @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP79])])).
103.34/102.72	thf(sP80,plain,sP80 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__1) @ X1)) => ((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP80])])).
103.34/102.72	thf(sP81,plain,sP81 <=> ((is_of @ eigen__0) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP81])])).
103.34/102.72	thf(sP82,plain,sP82 <=> (((n_eq @ eigen__0) @ eigen__2) => ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP82])])).
103.34/102.72	thf(sP83,plain,sP83 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP63),introduced(definition,[new_symbols(definition,[sP83])])).
103.34/102.72	thf(sP84,plain,sP84 <=> (((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)) => sP78),introduced(definition,[new_symbols(definition,[sP84])])).
103.34/102.72	thf(sP85,plain,sP85 <=> (((n_eq @ eigen__1) @ eigen__2) => ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP85])])).
103.34/102.72	thf(sP86,plain,sP86 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP56 => sP45)),introduced(definition,[new_symbols(definition,[sP86])])).
103.34/102.72	thf(sP87,plain,sP87 <=> (((l_or @ sP51) @ ((n_eq @ eigen__1) @ eigen__2)) => ((moreq @ eigen__2) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP87])])).
103.34/102.72	thf(sP88,plain,sP88 <=> (((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0)) => sP27),introduced(definition,[new_symbols(definition,[sP88])])).
103.34/102.72	thf(sP89,plain,sP89 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP18),introduced(definition,[new_symbols(definition,[sP89])])).
103.34/102.72	thf(sP90,plain,sP90 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => (d_not @ ((moref @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP90])])).
103.34/102.72	thf(sP91,plain,sP91 <=> (sP56 => sP45),introduced(definition,[new_symbols(definition,[sP91])])).
103.34/102.72	thf(sP92,plain,sP92 <=> (((moref @ eigen__2) @ eigen__2) => sP33),introduced(definition,[new_symbols(definition,[sP92])])).
103.34/102.72	thf(sP93,plain,sP93 <=> ((moreq @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP93])])).
103.34/102.72	thf(sP94,plain,sP94 <=> (sP81 => sP49),introduced(definition,[new_symbols(definition,[sP94])])).
103.34/102.72	thf(sP95,plain,sP95 <=> (sP51 = ((lessf @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP95])])).
103.34/102.72	thf(sP96,plain,sP96 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP56 => (((n_eq @ eigen__1) @ X1) => (((n_eq @ eigen__1) @ X2) => ((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP96])])).
103.34/102.72	thf(sP97,plain,sP97 <=> (d_not @ ((moref @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP97])])).
103.34/102.72	thf(sP98,plain,sP98 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP26),introduced(definition,[new_symbols(definition,[sP98])])).
103.34/102.72	thf(sP99,plain,sP99 <=> (sP44 => sP5),introduced(definition,[new_symbols(definition,[sP99])])).
103.34/102.72	thf(sP100,plain,sP100 <=> ((l_or @ ((lessf @ eigen__1) @ eigen__0)) @ ((n_eq @ eigen__1) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP100])])).
103.34/102.72	thf(sP101,plain,sP101 <=> ((n_eq @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP101])])).
103.34/102.72	thf(sP102,plain,sP102 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ eigen__1) => (((moreq @ eigen__1) @ X1) => ((moref @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP102])])).
103.34/102.72	thf(sP103,plain,sP103 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__0) @ X1)) => ((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP103])])).
103.34/102.72	thf(sP104,plain,sP104 <=> ((is_of @ eigen__1) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP104])])).
103.34/102.72	thf(sP105,plain,sP105 <=> (sP14 => ((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP105])])).
103.34/102.72	thf(sP106,plain,sP106 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => sP32),introduced(definition,[new_symbols(definition,[sP106])])).
103.34/102.72	thf(sP107,plain,sP107 <=> (sP59 => (sP93 => ((moref @ eigen__1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP107])])).
103.34/102.72	thf(sP108,plain,sP108 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP108])])).
103.34/102.72	thf(sP109,plain,sP109 <=> (sP104 => (sP28 => sP41)),introduced(definition,[new_symbols(definition,[sP109])])).
103.34/102.72	thf(sP110,plain,sP110 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((moref @ eigen__2) @ eigen__2) => (((moreq @ eigen__2) @ X1) => ((moref @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP110])])).
103.34/102.72	thf(sP111,plain,sP111 <=> (sP104 => sP65),introduced(definition,[new_symbols(definition,[sP111])])).
103.34/102.72	thf(sP112,plain,sP112 <=> (sP104 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => ((moreq @ X1) @ eigen__1))))),introduced(definition,[new_symbols(definition,[sP112])])).
103.34/102.72	thf(sP113,plain,sP113 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((moreq @ X2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP113])])).
103.34/102.72	thf(sP114,plain,sP114 <=> (sP104 => sP71),introduced(definition,[new_symbols(definition,[sP114])])).
103.34/102.72	thf(sP115,plain,sP115 <=> (sP104 => sP34),introduced(definition,[new_symbols(definition,[sP115])])).
103.34/102.72	thf(sP116,plain,sP116 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => ((moreq @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP116])])).
103.34/102.72	thf(sP117,plain,sP117 <=> (sP28 => sP41),introduced(definition,[new_symbols(definition,[sP117])])).
103.34/102.72	thf(sP118,plain,sP118 <=> ((moref @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP118])])).
103.34/102.72	thf(sP119,plain,sP119 <=> (sP59 = sP55),introduced(definition,[new_symbols(definition,[sP119])])).
103.34/102.72	thf(sP120,plain,sP120 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP55 => (((moreq @ eigen__2) @ X1) => ((moref @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP120])])).
103.34/102.72	thf(sP121,plain,sP121 <=> (sP93 => ((moref @ eigen__1) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP121])])).
103.34/102.72	thf(sP122,plain,sP122 <=> (sP81 => sP6),introduced(definition,[new_symbols(definition,[sP122])])).
103.34/102.72	thf(sP123,plain,sP123 <=> (sP118 => sP66),introduced(definition,[new_symbols(definition,[sP123])])).
103.34/102.72	thf(sP124,plain,sP124 <=> ((l_or @ ((lessf @ eigen__0) @ eigen__0)) @ ((n_eq @ eigen__0) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP124])])).
103.34/102.72	thf(sP125,plain,sP125 <=> (![X1:$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:$i]:((in @ X4) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => (((l_or @ ((lessf @ X2) @ X3)) @ ((n_eq @ X2) @ X3)) => ((l_or @ ((lessf @ X1) @ X3)) @ ((n_eq @ X1) @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP125])])).
103.34/102.72	thf(sP126,plain,sP126 <=> (sP104 => sP96),introduced(definition,[new_symbols(definition,[sP126])])).
103.34/102.72	thf(sP127,plain,sP127 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)) => (d_not @ ((moref @ eigen__2) @ X1)))))),introduced(definition,[new_symbols(definition,[sP127])])).
103.34/102.72	thf(sP128,plain,sP128 <=> (((l_or @ sP51) @ ((n_eq @ eigen__1) @ eigen__2)) => sP72),introduced(definition,[new_symbols(definition,[sP128])])).
103.34/102.72	thf(sP129,plain,sP129 <=> (d_not @ sP118),introduced(definition,[new_symbols(definition,[sP129])])).
103.34/102.72	thf(sP130,plain,sP130 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => ((d_not @ ((moref @ eigen__2) @ X1)) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP130])])).
103.34/102.72	thf(sP131,plain,sP131 <=> (sP118 = sP55),introduced(definition,[new_symbols(definition,[sP131])])).
103.34/102.72	thf(sP132,plain,sP132 <=> (sP104 => sP70),introduced(definition,[new_symbols(definition,[sP132])])).
103.34/102.72	thf(sP133,plain,sP133 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1)) => (d_not @ ((moref @ eigen__2) @ X1))))),introduced(definition,[new_symbols(definition,[sP133])])).
103.34/102.72	thf(sP134,plain,sP134 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP8 => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => ((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)))))),introduced(definition,[new_symbols(definition,[sP134])])).
103.34/102.72	thf(sP135,plain,sP135 <=> (sP81 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP124 => (((n_eq @ eigen__0) @ X1) => (((n_eq @ eigen__0) @ X2) => ((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP135])])).
103.34/102.72	thf(sP136,plain,sP136 <=> ((lessf @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP136])])).
103.34/102.72	thf(sP137,plain,sP137 <=> (sP8 => sP43),introduced(definition,[new_symbols(definition,[sP137])])).
103.34/102.72	thf(sP138,plain,sP138 <=> (sP104 => sP134),introduced(definition,[new_symbols(definition,[sP138])])).
103.34/102.72	thf(sP139,plain,sP139 <=> (((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))) => (sP8 => sP77)),introduced(definition,[new_symbols(definition,[sP139])])).
103.34/102.72	thf(sP140,plain,sP140 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP8 => (((lessf @ eigen__1) @ X1) => ((lessf @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP140])])).
103.34/102.72	thf(sP141,plain,sP141 <=> (sP104 => sP107),introduced(definition,[new_symbols(definition,[sP141])])).
103.34/102.72	thf(sP142,plain,sP142 <=> ((is_of @ eigen__2) @ (^[X1:$i]:((in @ X1) @ (pair1type @ nat)))),introduced(definition,[new_symbols(definition,[sP142])])).
103.34/102.72	thf(sP143,plain,sP143 <=> ((l_or @ sP51) @ ((n_eq @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP143])])).
103.34/102.72	thf(sP144,plain,sP144 <=> (sP81 => sP116),introduced(definition,[new_symbols(definition,[sP144])])).
103.34/102.72	thf(sP145,plain,sP145 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__1) @ X1)) @ ((n_eq @ eigen__1) @ X1)) => ((moreq @ X1) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP145])])).
103.34/102.72	thf(sP146,plain,sP146 <=> (sP142 => sP123),introduced(definition,[new_symbols(definition,[sP146])])).
103.34/102.72	thf(sP147,plain,sP147 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => ((d_not @ ((moref @ X1) @ X2)) => ((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP147])])).
103.34/102.72	thf(sP148,plain,sP148 <=> (sP81 => sP24),introduced(definition,[new_symbols(definition,[sP148])])).
103.34/102.72	thf(sP149,plain,sP149 <=> (((moref @ eigen__1) @ eigen__1) => sP99),introduced(definition,[new_symbols(definition,[sP149])])).
103.34/102.72	thf(sP150,plain,sP150 <=> (![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 @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => (((n_eq @ X1) @ X3) => (((n_eq @ X2) @ X4) => ((l_or @ ((lessf @ X3) @ X4)) @ ((n_eq @ X3) @ X4))))))))))))),introduced(definition,[new_symbols(definition,[sP150])])).
103.34/102.72	thf(sP151,plain,sP151 <=> (sP41 => sP29),introduced(definition,[new_symbols(definition,[sP151])])).
103.34/102.72	thf(sP152,plain,sP152 <=> (sP104 => (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ X1) => (((moreq @ X1) @ X2) => ((moref @ eigen__1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP152])])).
103.34/102.72	thf(sP153,plain,sP153 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (sP124 => (((n_eq @ eigen__0) @ X1) => (((n_eq @ eigen__0) @ X2) => ((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP153])])).
103.34/102.72	thf(sP154,plain,sP154 <=> (sP81 => sP4),introduced(definition,[new_symbols(definition,[sP154])])).
103.34/102.72	thf(sP155,plain,sP155 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((moref @ eigen__1) @ X1) => (((moreq @ X1) @ X2) => ((moref @ eigen__1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP155])])).
103.34/102.72	thf(sP156,plain,sP156 <=> (sP142 => sP137),introduced(definition,[new_symbols(definition,[sP156])])).
103.34/102.72	thf(sP157,plain,sP157 <=> (sP8 => sP77),introduced(definition,[new_symbols(definition,[sP157])])).
103.34/102.72	thf(sP158,plain,sP158 <=> ((l_or @ ((lessf @ eigen__2) @ eigen__2)) @ ((n_eq @ eigen__2) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP158])])).
103.34/102.72	thf(sP159,plain,sP159 <=> ((moref @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP159])])).
103.34/102.72	thf(sP160,plain,sP160 <=> ((n_eq @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP160])])).
103.34/102.72	thf(sP161,plain,sP161 <=> (sP142 => sP120),introduced(definition,[new_symbols(definition,[sP161])])).
103.34/102.72	thf(sP162,plain,sP162 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (![X2:$i]:(((is_of @ X2) @ (^[X3:$i]:((in @ X3) @ (pair1type @ nat)))) => (((l_or @ ((lessf @ eigen__0) @ X1)) @ ((n_eq @ eigen__0) @ X1)) => (((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)) => ((l_or @ ((lessf @ eigen__0) @ X2)) @ ((n_eq @ eigen__0) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP162])])).
103.34/102.72	thf(sP163,plain,sP163 <=> (sP159 = sP55),introduced(definition,[new_symbols(definition,[sP163])])).
103.34/102.72	thf(sP164,plain,sP164 <=> (d_not @ sP5),introduced(definition,[new_symbols(definition,[sP164])])).
103.34/102.72	thf(sP165,plain,sP165 <=> ((moref @ eigen__2) @ eigen__1),introduced(definition,[new_symbols(definition,[sP165])])).
103.34/102.72	thf(sP166,plain,sP166 <=> ((moref @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP166])])).
103.34/102.72	thf(sP167,plain,sP167 <=> (sP142 => sP110),introduced(definition,[new_symbols(definition,[sP167])])).
103.34/102.72	thf(sP168,plain,sP168 <=> (sP93 => sP118),introduced(definition,[new_symbols(definition,[sP168])])).
103.34/102.72	thf(sP169,plain,sP169 <=> (![X1:$i]:(((is_of @ X1) @ (^[X2:$i]:((in @ X2) @ (pair1type @ nat)))) => (sP56 => (sP160 => (((n_eq @ eigen__1) @ X1) => ((l_or @ ((lessf @ eigen__2) @ X1)) @ ((n_eq @ eigen__2) @ X1))))))),introduced(definition,[new_symbols(definition,[sP169])])).
103.34/102.72	thf(def_all_of,definition,(all_of = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((is_of @ X3) @ X1) => (X2 @ X3))))))).
103.34/102.72	thf(def_frac,definition,(frac = (pair1type @ nat))).
103.34/102.72	thf(def_lesseq,definition,(lesseq = (^[X1:$i]:(^[X2:$i]:((l_or @ ((lessf @ X1) @ X2)) @ ((n_eq @ X1) @ X2)))))).
103.34/102.72	thf(satz52,conjecture,sP125).
103.34/102.72	thf(h1,negated_conjecture,(~(sP125)),inference(assume_negation,[status(cth)],[satz52])).
103.34/102.72	thf(1,plain,(~(sP120) | sP61),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(2,plain,((~(sP61) | ~(sP104)) | sP53),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(3,plain,((~(sP53) | ~(sP55)) | sP168),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(4,plain,((~(sP168) | ~(sP93)) | sP118),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(5,plain,(~(sP15) | sP148),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(6,plain,((~(sP148) | ~(sP81)) | sP24),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(7,plain,((~(sP24) | ~(sP118)) | sP23),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(8,plain,((~(sP23) | ~(sP44)) | sP67),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(9,plain,(~(sP15) | sP146),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(10,plain,((~(sP146) | ~(sP142)) | sP123),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(11,plain,((~(sP123) | ~(sP118)) | sP66),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(12,plain,((~(sP66) | ~(sP29)) | sP55),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(13,plain,(~(sP4) | sP161),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(14,plain,((~(sP161) | ~(sP142)) | sP120),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(15,plain,(~(sP4) | sP11),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(16,plain,((~(sP11) | ~(sP104)) | sP15),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(17,plain,(~(sP54) | sP141),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(18,plain,((~(sP141) | ~(sP104)) | sP107),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(19,plain,((~(sP107) | ~(sP59)) | sP121),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(20,plain,((~(sP121) | ~(sP93)) | sP166),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(21,plain,(~(sP102) | sP13),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(22,plain,((~(sP13) | ~(sP81)) | sP149),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(23,plain,((~(sP149) | ~(sP166)) | sP99),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(24,plain,((~(sP99) | ~(sP44)) | sP5),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(25,plain,(~(sP155) | sP64),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(26,plain,((~(sP64) | ~(sP142)) | sP54),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(27,plain,(~(sP155) | sP20),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(28,plain,((~(sP20) | ~(sP104)) | sP102),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(29,plain,(~(sP110) | sP76),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(30,plain,((~(sP76) | ~(sP104)) | sP92),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(31,plain,((~(sP92) | ~(sP159)) | sP33),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(32,plain,((~(sP33) | ~(sP93)) | sP165),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(33,plain,(~(sP26) | sP167),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(34,plain,((~(sP167) | ~(sP142)) | sP110),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(35,plain,(~(sP42) | sP98),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(36,plain,((~(sP98) | ~(sP142)) | sP26),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(37,plain,(~(sP42) | sP152),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(38,plain,((~(sP152) | ~(sP104)) | sP155),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(39,plain,(~(sP42) | sP154),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(40,plain,((~(sP154) | ~(sP81)) | sP4),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(41,plain,(~(sP32) | sP75),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(42,plain,((~(sP75) | ~(sP104)) | sP151),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(43,plain,((~(sP151) | ~(sP41)) | sP29),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(44,plain,(~(sP116) | sP115),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(45,plain,((~(sP115) | ~(sP104)) | sP34),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(46,plain,((~(sP34) | ~(sP8)) | sP44),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(47,plain,(~(sP145) | sP62),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(48,plain,((~(sP62) | ~(sP142)) | sP87),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(49,plain,((~(sP87) | ~(sP143)) | sP93),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(50,plain,(~(sP113) | sP106),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(51,plain,((~(sP106) | ~(sP142)) | sP32),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(52,plain,(~(sP113) | sP112),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(53,plain,((~(sP112) | ~(sP104)) | sP145),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(54,plain,(~(sP113) | sP144),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(55,plain,((~(sP144) | ~(sP81)) | sP116),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(56,plain,((sP39 | ~(sP67)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(57,plain,((~(sP14) | sP164) | ~(sP39)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(58,plain,((sP57 | ~(sP59)) | ~(sP166)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(59,plain,((~(sP72) | sP97) | ~(sP57)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(60,plain,((sP46 | sP55) | sP59),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(61,plain,((sP36 | ~(sP59)) | ~(sP67)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(62,plain,((~(sP72) | sP14) | ~(sP36)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(63,plain,((sP47 | ~(sP59)) | ~(sP165)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(64,plain,((~(sP72) | sP28) | ~(sP47)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(65,plain,((sP163 | sP159) | sP55),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(66,plain,((~(sP19) | sP50) | ~(sP163)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(67,plain,((sP131 | ~(sP118)) | ~(sP55)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(68,plain,((sP131 | sP118) | sP55),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(69,plain,((~(sP129) | sP50) | ~(sP131)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(70,plain,((~(sP58) | ~(sP46)) | sP119),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(71,plain,(~(sP10) | sP58),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(72,plain,(~(sP108) | sP10),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(73,plain,((~(sP72) | sP50) | ~(sP119)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(74,plain,(~(sP130) | sP109),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(75,plain,((~(sP109) | ~(sP104)) | sP117),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(76,plain,((~(sP117) | ~(sP28)) | sP41),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(77,plain,(~(sP80) | sP7),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(78,plain,((~(sP7) | ~(sP104)) | sP74),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(79,plain,((~(sP74) | ~(sP97)) | sP56),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(80,plain,(~(sP80) | sP122),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(81,plain,((~(sP122) | ~(sP81)) | sP6),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(82,plain,((~(sP6) | ~(sP164)) | sP100),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(83,plain,(~(sP103) | sP89),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(84,plain,((~(sP89) | ~(sP142)) | sP18),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(85,plain,((~(sP18) | ~(sP50)) | sP79),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(86,plain,(~(sP103) | sP38),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(87,plain,((~(sP38) | ~(sP81)) | sP105),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(88,plain,((~(sP105) | ~(sP14)) | sP124),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(89,plain,(~(sP147) | sP17),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(90,plain,((~(sP17) | ~(sP142)) | sP130),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(91,plain,(~(sP147) | sP31),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(92,plain,((~(sP31) | ~(sP104)) | sP80),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(93,plain,(~(sP147) | sP52),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(94,plain,((~(sP52) | ~(sP81)) | sP103),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(95,plain,(~(sP90) | sP30),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(96,plain,((~(sP30) | ~(sP142)) | sP128),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(97,plain,((~(sP128) | ~(sP143)) | sP72),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(98,plain,(~(sP40) | sP114),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(99,plain,((~(sP114) | ~(sP104)) | sP71),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(100,plain,((~(sP71) | ~(sP8)) | sP129),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(101,plain,(~(sP133) | sP83),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(102,plain,((~(sP83) | ~(sP142)) | sP63),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(103,plain,((~(sP63) | ~(sP158)) | sP19),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(104,plain,(~(sP3) | sP127),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(105,plain,((~(sP127) | ~(sP142)) | sP133),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(106,plain,(~(sP3) | sP37),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(107,plain,((~(sP37) | ~(sP104)) | sP90),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(108,plain,(~(sP3) | sP21),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(109,plain,((~(sP21) | ~(sP81)) | sP40),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(110,plain,(~(sP140) | sP156),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(111,plain,((~(sP156) | ~(sP142)) | sP137),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(112,plain,((~(sP137) | ~(sP8)) | sP43),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(113,plain,((~(sP43) | ~(sP51)) | sP136),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(114,plain,(~(sP49) | sP35),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(115,plain,((~(sP35) | ~(sP104)) | sP140),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(116,plain,(~(sP25) | sP69),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(117,plain,((~(sP69) | ~(sP142)) | sP88),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(118,plain,((~(sP88) | ~(sP100)) | sP27),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(119,plain,((~(sP27) | ~(sP136)) | sP51),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(120,plain,(~(sP70) | sP48),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(121,plain,((~(sP48) | ~(sP81)) | sP25),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(122,plain,(~(sP73) | sP132),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(123,plain,((~(sP132) | ~(sP104)) | sP70),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(124,plain,(~(sP73) | sP94),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(125,plain,((~(sP94) | ~(sP81)) | sP49),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(126,plain,(~(sP169) | sP86),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(127,plain,((~(sP86) | ~(sP142)) | sP91),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(128,plain,((~(sP91) | ~(sP56)) | sP45),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(129,plain,((~(sP45) | ~(sP160)) | sP85),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(130,plain,(~(sP96) | sP1),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(131,plain,((~(sP1) | ~(sP142)) | sP169),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(132,plain,(~(sP9) | sP22),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(133,plain,((~(sP22) | ~(sP142)) | sP84),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(134,plain,((~(sP84) | ~(sP124)) | sP78),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(135,plain,((~(sP78) | ~(sP101)) | sP82),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(136,plain,(~(sP153) | sP2),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(137,plain,((~(sP2) | ~(sP142)) | sP9),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(138,plain,(~(sP12) | sP135),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(139,plain,((~(sP135) | ~(sP81)) | sP153),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(140,plain,(~(sP65) | sP126),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(141,plain,((~(sP126) | ~(sP104)) | sP96),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(142,plain,((~(sP82) | ~(sP101)) | sP158),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(143,plain,((~(sP85) | ~(sP160)) | sP158),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(144,plain,(~(sP150) | sP111),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(145,plain,((~(sP111) | ~(sP104)) | sP65),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(146,plain,(~(sP150) | sP60),inference(all_rule,[status(thm)],[])).
103.34/102.72	thf(147,plain,((~(sP60) | ~(sP81)) | sP12),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(148,plain,((sP95 | ~(sP51)) | ~(sP136)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(149,plain,((sP95 | sP51) | sP136),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(150,plain,((sP68 | sP160) | sP101),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(151,plain,sP108,inference(eq_sym,[status(thm)],[])).
103.34/102.72	thf(152,plain,(((~(sP143) | sP79) | ~(sP95)) | ~(sP68)),inference(mating_rule,[status(thm)],[])).
103.34/102.72	thf(153,plain,(sP77 | ~(sP79)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(154,plain,(sP77 | sP143),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(155,plain,(sP157 | ~(sP77)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(156,plain,(sP157 | sP8),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(157,plain,(sP139 | ~(sP157)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(158,plain,(sP139 | sP142),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(159,plain,(sP134 | ~(sP139)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
103.34/102.72	thf(160,plain,(sP138 | ~(sP134)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(161,plain,(sP138 | sP104),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(162,plain,(sP162 | ~(sP138)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
103.34/102.72	thf(163,plain,(sP16 | ~(sP162)),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(164,plain,(sP16 | sP81),inference(prop_rule,[status(thm)],[])).
103.34/102.72	thf(165,plain,(sP125 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
103.34/102.72	thf(satz51d,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:$i]:(((moref @ X1) @ X2) => (((moreq @ X2) @ X3) => ((moref @ X1) @ X3)))))))))).
103.34/102.72	thf(166,plain,sP42,inference(preprocess,[status(thm)],[satz51d]).
103.34/102.72	thf(satz51a,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((all_of @ (^[X3:$i]:((in @ X3) @ frac))) @ (^[X3:$i]:(((lesseq @ X1) @ X2) => (((lessf @ X2) @ X3) => ((lessf @ X1) @ X3)))))))))).
103.34/102.72	thf(167,plain,sP73,inference(preprocess,[status(thm)],[satz51a]).
103.34/102.72	thf(satz41d,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((lesseq @ X1) @ X2) => (d_not @ ((moref @ X1) @ X2)))))))).
103.34/102.72	thf(168,plain,sP3,inference(preprocess,[status(thm)],[satz41d]).
103.34/102.72	thf(satz47,axiom,((all_of @ (^[X1:$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:$i]:(((lesseq @ X1) @ X2) => (((n_eq @ X1) @ X3) => (((n_eq @ X2) @ X4) => ((lesseq @ X3) @ X4))))))))))))).
103.34/102.72	thf(169,plain,sP150,inference(preprocess,[status(thm)],[satz47]).
103.34/102.72	thf(satz41e,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:((d_not @ ((moref @ X1) @ X2)) => ((lesseq @ X1) @ X2))))))).
103.34/102.72	thf(170,plain,sP147,inference(preprocess,[status(thm)],[satz41e]).
103.34/102.72	thf(satz49,axiom,((all_of @ (^[X1:$i]:((in @ X1) @ frac))) @ (^[X1:$i]:((all_of @ (^[X2:$i]:((in @ X2) @ frac))) @ (^[X2:$i]:(((lesseq @ X1) @ X2) => ((moreq @ X2) @ X1))))))).
103.34/102.72	thf(171,plain,sP113,inference(preprocess,[status(thm)],[satz49]).
103.34/102.72	thf(172,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,h1])).
103.34/102.72	thf(173,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[172,h0])).
103.34/102.72	thf(0,theorem,sP125,inference(contra,[status(thm),contra(discharge,[h1])],[172,h1])).
103.34/102.72	% SZS output end Proof
103.34/102.72	EOF