%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO068^4.020 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n026.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 03:24:50 PM UTC 2025 % Result : Theorem 4.60s 4.79s % Output : Proof 4.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO068^4.020 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n026.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 : Thu Oct 9 01:09:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.60/4.79 % SZS status Theorem % 4.60/4.79 % Mode: mode506 % 4.60/4.79 % Inferences: 19089 % 4.60/4.79 % SZS output start Proof % 4.60/4.79 thf(ty_p6, type, p6 : ($i>$o)). % 4.60/4.79 thf(ty_p12, type, p12 : ($i>$o)). % 4.60/4.79 thf(ty_p13, type, p13 : ($i>$o)). % 4.60/4.79 thf(ty_p14, type, p14 : ($i>$o)). % 4.60/4.79 thf(ty_eigen__0, type, eigen__0 : $i). % 4.60/4.79 thf(ty_p3, type, p3 : ($i>$o)). % 4.60/4.79 thf(ty_eigen__21, type, eigen__21 : $i). % 4.60/4.79 thf(ty_p10, type, p10 : ($i>$o)). % 4.60/4.79 thf(ty_p16, type, p16 : ($i>$o)). % 4.60/4.79 thf(ty_p4, type, p4 : ($i>$o)). % 4.60/4.79 thf(ty_p2, type, p2 : ($i>$o)). % 4.60/4.79 thf(ty_irel, type, irel : ($i>$i>$o)). % 4.60/4.79 thf(ty_p8, type, p8 : ($i>$o)). % 4.60/4.79 thf(ty_p17, type, p17 : ($i>$o)). % 4.60/4.79 thf(ty_p15, type, p15 : ($i>$o)). % 4.60/4.79 thf(ty_p11, type, p11 : ($i>$o)). % 4.60/4.79 thf(ty_p20, type, p20 : ($i>$o)). % 4.60/4.79 thf(ty_p7, type, p7 : ($i>$o)). % 4.60/4.79 thf(ty_p18, type, p18 : ($i>$o)). % 4.60/4.79 thf(ty_p19, type, p19 : ($i>$o)). % 4.60/4.79 thf(ty_p0, type, p0 : ($i>$o)). % 4.60/4.79 thf(ty_p5, type, p5 : ($i>$o)). % 4.60/4.79 thf(ty_p9, type, p9 : ($i>$o)). % 4.60/4.79 thf(ty_p1, type, p1 : ($i>$o)). % 4.60/4.79 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 4.60/4.79 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 4.60/4.79 thf(eigendef_eigen__21, definition, eigen__21 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p20 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__21])])). % 4.60/4.79 thf(sP1,plain,sP1 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p16 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p15 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 4.60/4.79 thf(sP2,plain,sP2 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP2])])). % 4.60/4.79 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 4.60/4.79 thf(sP4,plain,sP4 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p14 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 4.60/4.79 thf(sP5,plain,sP5 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 4.60/4.79 thf(sP6,plain,sP6 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 4.60/4.79 thf(sP7,plain,sP7 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 4.60/4.79 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 4.60/4.79 thf(sP9,plain,sP9 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 4.60/4.79 thf(sP10,plain,sP10 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 4.60/4.79 thf(sP11,plain,sP11 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 4.60/4.79 thf(sP12,plain,sP12 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))))),introduced(definition,[new_symbols(definition,[sP12])])). % 4.60/4.79 thf(sP13,plain,sP13 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))))),introduced(definition,[new_symbols(definition,[sP13])])). % 4.60/4.79 thf(sP14,plain,sP14 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p20 @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 4.60/4.79 thf(sP15,plain,sP15 <=> (((irel @ eigen__0) @ eigen__21) => (p20 @ eigen__21)),introduced(definition,[new_symbols(definition,[sP15])])). % 4.60/4.79 thf(sP16,plain,sP16 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))),introduced(definition,[new_symbols(definition,[sP16])])). % 4.60/4.79 thf(sP17,plain,sP17 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))))),introduced(definition,[new_symbols(definition,[sP17])])). % 4.60/4.79 thf(sP18,plain,sP18 <=> (sP14 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 4.60/4.79 thf(sP19,plain,sP19 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))) => sP16)),introduced(definition,[new_symbols(definition,[sP19])])). % 4.60/4.79 thf(sP20,plain,sP20 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1)))),introduced(definition,[new_symbols(definition,[sP20])])). % 4.60/4.79 thf(sP21,plain,sP21 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP21])])). % 4.60/4.79 thf(sP22,plain,sP22 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))),introduced(definition,[new_symbols(definition,[sP22])])). % 4.60/4.79 thf(sP23,plain,sP23 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 4.60/4.79 thf(sP24,plain,sP24 <=> (((irel @ eigen__0) @ eigen__0) => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))))),introduced(definition,[new_symbols(definition,[sP24])])). % 4.60/4.79 thf(sP25,plain,sP25 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 4.60/4.79 thf(sP26,plain,sP26 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP26])])). % 4.60/4.79 thf(sP27,plain,sP27 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 4.60/4.79 thf(sP28,plain,sP28 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 4.60/4.79 thf(sP29,plain,sP29 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2)))))),introduced(definition,[new_symbols(definition,[sP29])])). % 4.60/4.79 thf(sP30,plain,sP30 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p18 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p17 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 4.60/4.79 thf(sP31,plain,sP31 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP31])])). % 4.60/4.79 thf(sP32,plain,sP32 <=> (sP31 => sP4),introduced(definition,[new_symbols(definition,[sP32])])). % 4.60/4.79 thf(sP33,plain,sP33 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))))),introduced(definition,[new_symbols(definition,[sP33])])). % 4.60/4.79 thf(sP34,plain,sP34 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p18 @ X1))))),introduced(definition,[new_symbols(definition,[sP34])])). % 4.60/4.79 thf(sP35,plain,sP35 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => sP6),introduced(definition,[new_symbols(definition,[sP35])])). % 4.60/4.79 thf(sP36,plain,sP36 <=> (sP31 => (sP26 => sP21)),introduced(definition,[new_symbols(definition,[sP36])])). % 4.60/4.79 thf(sP37,plain,sP37 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))))),introduced(definition,[new_symbols(definition,[sP37])])). % 4.60/4.79 thf(sP38,plain,sP38 <=> (sP26 => sP21),introduced(definition,[new_symbols(definition,[sP38])])). % 4.60/4.79 thf(sP39,plain,sP39 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2)))))),introduced(definition,[new_symbols(definition,[sP39])])). % 4.60/4.79 thf(sP40,plain,sP40 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP40])])). % 4.60/4.79 thf(sP41,plain,sP41 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p14 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))))))),introduced(definition,[new_symbols(definition,[sP41])])). % 4.60/4.79 thf(sP42,plain,sP42 <=> (p20 @ eigen__21),introduced(definition,[new_symbols(definition,[sP42])])). % 4.60/4.79 thf(sP43,plain,sP43 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p11 @ X1))),introduced(definition,[new_symbols(definition,[sP43])])). % 4.60/4.79 thf(sP44,plain,sP44 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1)))),introduced(definition,[new_symbols(definition,[sP44])])). % 4.60/4.79 thf(sP45,plain,sP45 <=> (sP31 => sP3),introduced(definition,[new_symbols(definition,[sP45])])). % 4.60/4.79 thf(sP46,plain,sP46 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2))))))),introduced(definition,[new_symbols(definition,[sP46])])). % 4.60/4.79 thf(sP47,plain,sP47 <=> (sP31 => (sP14 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))))),introduced(definition,[new_symbols(definition,[sP47])])). % 4.60/4.79 thf(sP48,plain,sP48 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2)))))),introduced(definition,[new_symbols(definition,[sP48])])). % 4.60/4.79 thf(sP49,plain,sP49 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p17 @ X1))),introduced(definition,[new_symbols(definition,[sP49])])). % 4.60/4.79 thf(sP50,plain,sP50 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p18 @ X1))) => sP49),introduced(definition,[new_symbols(definition,[sP50])])). % 4.60/4.79 thf(sP51,plain,sP51 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p18 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2)))))),introduced(definition,[new_symbols(definition,[sP51])])). % 4.60/4.79 thf(sP52,plain,sP52 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p2 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP52])])). % 4.60/4.79 thf(sP53,plain,sP53 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))))))),introduced(definition,[new_symbols(definition,[sP53])])). % 4.60/4.79 thf(sP54,plain,sP54 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))) => sP9),introduced(definition,[new_symbols(definition,[sP54])])). % 4.60/4.79 thf(sP55,plain,sP55 <=> (sP14 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1)))),introduced(definition,[new_symbols(definition,[sP55])])). % 4.60/4.79 thf(sP56,plain,sP56 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1)))),introduced(definition,[new_symbols(definition,[sP56])])). % 4.60/4.79 thf(sP57,plain,sP57 <=> (sP43 => sP48),introduced(definition,[new_symbols(definition,[sP57])])). % 4.60/4.79 thf(sP58,plain,sP58 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p12 @ X1))),introduced(definition,[new_symbols(definition,[sP58])])). % 4.60/4.79 thf(sP59,plain,sP59 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2)))))),introduced(definition,[new_symbols(definition,[sP59])])). % 4.60/4.79 thf(sP60,plain,sP60 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p13 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p12 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP60])])). % 4.60/4.79 thf(sP61,plain,sP61 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1)))),introduced(definition,[new_symbols(definition,[sP61])])). % 4.60/4.79 thf(sP62,plain,sP62 <=> (sP31 => (p0 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP62])])). % 4.60/4.79 thf(sP63,plain,sP63 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p15 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p15 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p14 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 4.60/4.79 thf(sP64,plain,sP64 <=> (sP31 => sP50),introduced(definition,[new_symbols(definition,[sP64])])). % 4.60/4.79 thf(sP65,plain,sP65 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p14 @ X1))),introduced(definition,[new_symbols(definition,[sP65])])). % 4.60/4.79 thf(sP66,plain,sP66 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p18 @ X1)))),introduced(definition,[new_symbols(definition,[sP66])])). % 4.60/4.79 thf(sP67,plain,sP67 <=> (sP22 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))))))),introduced(definition,[new_symbols(definition,[sP67])])). % 4.60/4.79 thf(sP68,plain,sP68 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))))),introduced(definition,[new_symbols(definition,[sP68])])). % 4.60/4.79 thf(sP69,plain,sP69 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p9 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p8 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP69])])). % 4.60/4.79 thf(sP70,plain,sP70 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))) => sP29),introduced(definition,[new_symbols(definition,[sP70])])). % 4.60/4.79 thf(sP71,plain,sP71 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))))),introduced(definition,[new_symbols(definition,[sP71])])). % 4.60/4.79 thf(sP72,plain,sP72 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP72])])). % 4.60/4.79 thf(sP73,plain,sP73 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p7 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP73])])). % 4.60/4.79 thf(sP74,plain,sP74 <=> (sP22 => sP16),introduced(definition,[new_symbols(definition,[sP74])])). % 4.60/4.79 thf(sP75,plain,sP75 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))),introduced(definition,[new_symbols(definition,[sP75])])). % 4.60/4.79 thf(sP76,plain,sP76 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2)))))),introduced(definition,[new_symbols(definition,[sP76])])). % 4.60/4.79 thf(sP77,plain,sP77 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))),introduced(definition,[new_symbols(definition,[sP77])])). % 4.60/4.79 thf(sP78,plain,sP78 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))) => sP58),introduced(definition,[new_symbols(definition,[sP78])])). % 4.60/4.79 thf(sP79,plain,sP79 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2))))))),introduced(definition,[new_symbols(definition,[sP79])])). % 4.60/4.80 thf(sP80,plain,sP80 <=> (sP31 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))) => sP65)),introduced(definition,[new_symbols(definition,[sP80])])). % 4.60/4.80 thf(sP81,plain,sP81 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP81])])). % 4.60/4.80 thf(sP82,plain,sP82 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p17 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p16 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP82])])). % 4.60/4.80 thf(sP83,plain,sP83 <=> (sP16 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1)))),introduced(definition,[new_symbols(definition,[sP83])])). % 4.60/4.80 thf(sP84,plain,sP84 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))),introduced(definition,[new_symbols(definition,[sP84])])). % 4.60/4.80 thf(sP85,plain,sP85 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p12 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p11 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP85])])). % 4.60/4.80 thf(sP86,plain,sP86 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p20 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p19 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP86])])). % 4.60/4.80 thf(sP87,plain,sP87 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1)))),introduced(definition,[new_symbols(definition,[sP87])])). % 4.60/4.80 thf(sP88,plain,sP88 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p19 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p18 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP88])])). % 4.60/4.80 thf(sP89,plain,sP89 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))),introduced(definition,[new_symbols(definition,[sP89])])). % 4.60/4.80 thf(sP90,plain,sP90 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP90])])). % 4.60/4.80 thf(sP91,plain,sP91 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))),introduced(definition,[new_symbols(definition,[sP91])])). % 4.60/4.80 thf(sP92,plain,sP92 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2)))))),introduced(definition,[new_symbols(definition,[sP92])])). % 4.60/4.80 thf(sP93,plain,sP93 <=> (sP58 => sP43),introduced(definition,[new_symbols(definition,[sP93])])). % 4.60/4.80 thf(sP94,plain,sP94 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p17 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p16 @ X2)))))),introduced(definition,[new_symbols(definition,[sP94])])). % 4.60/4.80 thf(sP95,plain,sP95 <=> (sP89 => sP26),introduced(definition,[new_symbols(definition,[sP95])])). % 4.60/4.80 thf(sP96,plain,sP96 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p13 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p12 @ X2)))))),introduced(definition,[new_symbols(definition,[sP96])])). % 4.60/4.80 thf(sP97,plain,sP97 <=> (sP26 => sP81),introduced(definition,[new_symbols(definition,[sP97])])). % 4.60/4.80 thf(sP98,plain,sP98 <=> (sP84 => sP39),introduced(definition,[new_symbols(definition,[sP98])])). % 4.60/4.80 thf(sP99,plain,sP99 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2)))))),introduced(definition,[new_symbols(definition,[sP99])])). % 4.60/4.80 thf(sP100,plain,sP100 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP100])])). % 4.60/4.80 thf(sP101,plain,sP101 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p20 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p19 @ X2)))))),introduced(definition,[new_symbols(definition,[sP101])])). % 4.60/4.80 thf(sP102,plain,sP102 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))),introduced(definition,[new_symbols(definition,[sP102])])). % 4.60/4.80 thf(sP103,plain,sP103 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p8 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p7 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP103])])). % 4.60/4.80 thf(sP104,plain,sP104 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p18 @ X1))),introduced(definition,[new_symbols(definition,[sP104])])). % 4.60/4.80 thf(sP105,plain,sP105 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p13 @ X1))),introduced(definition,[new_symbols(definition,[sP105])])). % 4.60/4.80 thf(sP106,plain,sP106 <=> (sP31 => sP95),introduced(definition,[new_symbols(definition,[sP106])])). % 4.60/4.80 thf(sP107,plain,sP107 <=> (sP58 => sP25),introduced(definition,[new_symbols(definition,[sP107])])). % 4.60/4.80 thf(sP108,plain,sP108 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))),introduced(definition,[new_symbols(definition,[sP108])])). % 4.60/4.80 thf(sP109,plain,sP109 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p16 @ X1))),introduced(definition,[new_symbols(definition,[sP109])])). % 4.60/4.80 thf(sP110,plain,sP110 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p11 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p11 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p10 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP110])])). % 4.60/4.80 thf(sP111,plain,sP111 <=> (sP91 => sP89),introduced(definition,[new_symbols(definition,[sP111])])). % 4.60/4.80 thf(sP112,plain,sP112 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p10 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p9 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP112])])). % 4.60/4.80 thf(sP113,plain,sP113 <=> (sP31 => sP56),introduced(definition,[new_symbols(definition,[sP113])])). % 4.60/4.80 thf(sP114,plain,sP114 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p19 @ X1))),introduced(definition,[new_symbols(definition,[sP114])])). % 4.60/4.80 thf(sP115,plain,sP115 <=> (sP102 => sP22),introduced(definition,[new_symbols(definition,[sP115])])). % 4.60/4.80 thf(sP116,plain,sP116 <=> (sP75 => sP102),introduced(definition,[new_symbols(definition,[sP116])])). % 4.60/4.80 thf(sP117,plain,sP117 <=> (sP31 => sP115),introduced(definition,[new_symbols(definition,[sP117])])). % 4.60/4.80 thf(sP118,plain,sP118 <=> (sP104 => sP51),introduced(definition,[new_symbols(definition,[sP118])])). % 4.60/4.80 thf(sP119,plain,sP119 <=> ((!!) @ p20),introduced(definition,[new_symbols(definition,[sP119])])). % 4.60/4.80 thf(sP120,plain,sP120 <=> (sP108 => sP11),introduced(definition,[new_symbols(definition,[sP120])])). % 4.60/4.80 thf(sP121,plain,sP121 <=> (sP102 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))))))),introduced(definition,[new_symbols(definition,[sP121])])). % 4.60/4.80 thf(sP122,plain,sP122 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP122])])). % 4.60/4.80 thf(sP123,plain,sP123 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2)))))),introduced(definition,[new_symbols(definition,[sP123])])). % 4.60/4.80 thf(sP124,plain,sP124 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))) => sP65),introduced(definition,[new_symbols(definition,[sP124])])). % 4.60/4.80 thf(sP125,plain,sP125 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP125])])). % 4.60/4.80 thf(sP126,plain,sP126 <=> (sP16 => sP99),introduced(definition,[new_symbols(definition,[sP126])])). % 4.60/4.80 thf(sP127,plain,sP127 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2)))))),introduced(definition,[new_symbols(definition,[sP127])])). % 4.60/4.80 thf(sP128,plain,sP128 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p14 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p14 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p13 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP128])])). % 4.60/4.80 thf(sP129,plain,sP129 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p15 @ X1))),introduced(definition,[new_symbols(definition,[sP129])])). % 4.60/4.80 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 4.60/4.80 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 4.60/4.80 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 4.60/4.80 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 4.60/4.80 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 4.60/4.80 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 4.60/4.80 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 4.60/4.80 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 4.60/4.80 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 4.60/4.80 thf(def_iand,definition,(iand = mand)). % 4.60/4.80 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.60/4.80 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.60/4.80 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 4.60/4.80 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 4.60/4.80 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 4.60/4.80 thf(def_ivalid,definition,(ivalid = (!!))). % 4.60/4.80 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 4.60/4.80 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 4.60/4.80 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 4.60/4.80 thf(con,conjecture,sP90). % 4.60/4.80 thf(h1,negated_conjecture,(~(sP90)),inference(assume_negation,[status(cth)],[con])). % 4.60/4.80 thf(1,plain,(~(sP119) | sP42),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(2,plain,(sP15 | ~(sP42)),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(3,plain,(sP14 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__21])). % 4.60/4.80 thf(4,plain,(~(sP21) | sP62),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(5,plain,((~(sP62) | ~(sP31)) | sP122),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(6,plain,((~(sP18) | ~(sP14)) | sP101),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(7,plain,(~(sP101) | sP47),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(8,plain,((~(sP47) | ~(sP31)) | sP55),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(9,plain,((~(sP55) | ~(sP14)) | sP114),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(10,plain,((~(sP70) | ~(sP114)) | sP29),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(11,plain,(~(sP29) | sP34),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(12,plain,((~(sP34) | ~(sP31)) | sP66),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(13,plain,((~(sP66) | ~(sP114)) | sP104),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(14,plain,((~(sP118) | ~(sP104)) | sP51),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(15,plain,(~(sP51) | sP64),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(16,plain,((~(sP64) | ~(sP31)) | sP50),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(17,plain,((~(sP50) | ~(sP104)) | sP49),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(18,plain,((~(sP46) | ~(sP49)) | sP94),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(19,plain,(~(sP94) | sP33),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(20,plain,((~(sP33) | ~(sP31)) | sP44),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(21,plain,((~(sP44) | ~(sP49)) | sP109),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(22,plain,((~(sP54) | ~(sP109)) | sP9),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(23,plain,(~(sP9) | sP71),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(24,plain,((~(sP71) | ~(sP31)) | sP87),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(25,plain,((~(sP87) | ~(sP109)) | sP129),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(26,plain,((~(sP53) | ~(sP129)) | sP59),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(27,plain,(~(sP59) | sP80),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(28,plain,((~(sP80) | ~(sP31)) | sP124),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(29,plain,((~(sP124) | ~(sP129)) | sP65),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(30,plain,((~(sP41) | ~(sP65)) | sP92),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(31,plain,(~(sP92) | sP32),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(32,plain,((~(sP32) | ~(sP31)) | sP4),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(33,plain,((~(sP4) | ~(sP65)) | sP105),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(34,plain,((~(sP79) | ~(sP105)) | sP96),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(35,plain,(~(sP96) | sP37),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(36,plain,((~(sP37) | ~(sP31)) | sP78),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(37,plain,((~(sP78) | ~(sP105)) | sP58),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(38,plain,((~(sP107) | ~(sP58)) | sP25),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(39,plain,(~(sP25) | sP17),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(40,plain,((~(sP17) | ~(sP31)) | sP93),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(41,plain,((~(sP93) | ~(sP58)) | sP43),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(42,plain,((~(sP57) | ~(sP43)) | sP48),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(43,plain,(~(sP48) | sP12),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(44,plain,((~(sP12) | ~(sP31)) | sP20),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(45,plain,((~(sP20) | ~(sP43)) | sP84),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(46,plain,((~(sP98) | ~(sP84)) | sP39),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(47,plain,(~(sP39) | sP113),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(48,plain,((~(sP113) | ~(sP31)) | sP56),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(49,plain,((~(sP56) | ~(sP84)) | sP75),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(50,plain,((~(sP28) | ~(sP75)) | sP127),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(51,plain,(~(sP127) | sP68),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(52,plain,((~(sP68) | ~(sP31)) | sP116),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(53,plain,((~(sP116) | ~(sP75)) | sP102),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(54,plain,((~(sP121) | ~(sP102)) | sP123),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(55,plain,(~(sP123) | sP117),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(56,plain,((~(sP117) | ~(sP31)) | sP115),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(57,plain,((~(sP115) | ~(sP102)) | sP22),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(58,plain,((~(sP67) | ~(sP22)) | sP76),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(59,plain,(~(sP76) | sP19),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(60,plain,((~(sP19) | ~(sP31)) | sP74),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(61,plain,((~(sP74) | ~(sP22)) | sP16),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(62,plain,((~(sP126) | ~(sP16)) | sP99),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(63,plain,(~(sP99) | sP13),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(64,plain,((~(sP13) | ~(sP31)) | sP83),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(65,plain,((~(sP83) | ~(sP16)) | sP108),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(66,plain,((~(sP120) | ~(sP108)) | sP11),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(67,plain,(~(sP11) | sP24),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(68,plain,((~(sP24) | ~(sP31)) | sP61),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(69,plain,((~(sP61) | ~(sP108)) | sP77),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(70,plain,((~(sP35) | ~(sP77)) | sP6),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(71,plain,(~(sP6) | sP45),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(72,plain,((~(sP45) | ~(sP31)) | sP3),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(73,plain,((~(sP3) | ~(sP77)) | sP91),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(74,plain,((~(sP27) | ~(sP91)) | sP40),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(75,plain,(~(sP40) | sP7),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(76,plain,((~(sP7) | ~(sP31)) | sP111),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(77,plain,((~(sP111) | ~(sP91)) | sP89),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(78,plain,((~(sP8) | ~(sP89)) | sP125),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(79,plain,(~(sP125) | sP106),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(80,plain,((~(sP106) | ~(sP31)) | sP95),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(81,plain,((~(sP95) | ~(sP89)) | sP26),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(82,plain,((~(sP97) | ~(sP26)) | sP81),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(83,plain,(~(sP81) | sP36),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(84,plain,((~(sP36) | ~(sP31)) | sP38),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(85,plain,((~(sP38) | ~(sP26)) | sP21),inference(prop_rule,[status(thm)],[])). % 4.60/4.80 thf(86,plain,(~(sP2) | sP31),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(87,plain,(~(sP86) | sP18),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(88,plain,(~(sP88) | sP70),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(89,plain,(~(sP30) | sP118),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(90,plain,(~(sP82) | sP46),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(91,plain,(~(sP1) | sP54),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(92,plain,(~(sP63) | sP53),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(93,plain,(~(sP128) | sP41),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(94,plain,(~(sP60) | sP79),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(95,plain,(~(sP85) | sP107),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(96,plain,(~(sP110) | sP57),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(97,plain,(~(sP112) | sP98),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(98,plain,(~(sP69) | sP28),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(99,plain,(~(sP103) | sP121),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(100,plain,(~(sP73) | sP67),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(101,plain,(~(sP10) | sP126),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(102,plain,(~(sP72) | sP120),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(103,plain,(~(sP100) | sP35),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(104,plain,(~(sP5) | sP27),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(105,plain,(~(sP52) | sP8),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(106,plain,(~(sP23) | sP97),inference(all_rule,[status(thm)],[])). % 4.60/4.80 thf(107,plain,(sP90 | ~(sP122)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 4.60/4.80 thf(axiom21,axiom,(ivalid @ ((iimplies @ (iatom @ p20)) @ ((iimplies @ (iatom @ p20)) @ (iatom @ p19))))). % 4.60/4.80 thf(108,plain,sP86,inference(preprocess,[status(thm)],[axiom21]). % 4.60/4.80 thf(axiom20,axiom,(ivalid @ ((iimplies @ (iatom @ p19)) @ ((iimplies @ (iatom @ p19)) @ (iatom @ p18))))). % 4.60/4.80 thf(109,plain,sP88,inference(preprocess,[status(thm)],[axiom20]). % 4.60/4.80 thf(axiom19,axiom,(ivalid @ ((iimplies @ (iatom @ p18)) @ ((iimplies @ (iatom @ p18)) @ (iatom @ p17))))). % 4.60/4.80 thf(110,plain,sP30,inference(preprocess,[status(thm)],[axiom19]). % 4.60/4.80 thf(axiom18,axiom,(ivalid @ ((iimplies @ (iatom @ p17)) @ ((iimplies @ (iatom @ p17)) @ (iatom @ p16))))). % 4.60/4.80 thf(111,plain,sP82,inference(preprocess,[status(thm)],[axiom18]). % 4.60/4.80 thf(axiom17,axiom,(ivalid @ ((iimplies @ (iatom @ p16)) @ ((iimplies @ (iatom @ p16)) @ (iatom @ p15))))). % 4.60/4.80 thf(112,plain,sP1,inference(preprocess,[status(thm)],[axiom17]). % 4.60/4.80 thf(axiom16,axiom,(ivalid @ ((iimplies @ (iatom @ p15)) @ ((iimplies @ (iatom @ p15)) @ (iatom @ p14))))). % 4.60/4.80 thf(113,plain,sP63,inference(preprocess,[status(thm)],[axiom16]). % 4.60/4.80 thf(axiom15,axiom,(ivalid @ ((iimplies @ (iatom @ p14)) @ ((iimplies @ (iatom @ p14)) @ (iatom @ p13))))). % 4.60/4.80 thf(114,plain,sP128,inference(preprocess,[status(thm)],[axiom15]). % 4.60/4.80 thf(axiom14,axiom,(ivalid @ ((iimplies @ (iatom @ p13)) @ ((iimplies @ (iatom @ p13)) @ (iatom @ p12))))). % 4.60/4.80 thf(115,plain,sP60,inference(preprocess,[status(thm)],[axiom14]). % 4.60/4.80 thf(axiom13,axiom,(ivalid @ ((iimplies @ (iatom @ p12)) @ ((iimplies @ (iatom @ p12)) @ (iatom @ p11))))). % 4.60/4.80 thf(116,plain,sP85,inference(preprocess,[status(thm)],[axiom13]). % 4.60/4.80 thf(axiom12,axiom,(ivalid @ ((iimplies @ (iatom @ p11)) @ ((iimplies @ (iatom @ p11)) @ (iatom @ p10))))). % 4.60/4.80 thf(117,plain,sP110,inference(preprocess,[status(thm)],[axiom12]). % 4.60/4.80 thf(axiom11,axiom,(ivalid @ ((iimplies @ (iatom @ p10)) @ ((iimplies @ (iatom @ p10)) @ (iatom @ p9))))). % 4.60/4.80 thf(118,plain,sP112,inference(preprocess,[status(thm)],[axiom11]). % 4.60/4.80 thf(axiom10,axiom,(ivalid @ ((iimplies @ (iatom @ p9)) @ ((iimplies @ (iatom @ p9)) @ (iatom @ p8))))). % 4.60/4.80 thf(119,plain,sP69,inference(preprocess,[status(thm)],[axiom10]). % 4.60/4.80 thf(axiom9,axiom,(ivalid @ ((iimplies @ (iatom @ p8)) @ ((iimplies @ (iatom @ p8)) @ (iatom @ p7))))). % 4.60/4.80 thf(120,plain,sP103,inference(preprocess,[status(thm)],[axiom9]). % 4.60/4.80 thf(axiom8,axiom,(ivalid @ ((iimplies @ (iatom @ p7)) @ ((iimplies @ (iatom @ p7)) @ (iatom @ p6))))). % 4.60/4.80 thf(121,plain,sP73,inference(preprocess,[status(thm)],[axiom8]). % 4.60/4.80 thf(axiom7,axiom,(ivalid @ ((iimplies @ (iatom @ p6)) @ ((iimplies @ (iatom @ p6)) @ (iatom @ p5))))). % 4.60/4.80 thf(122,plain,sP10,inference(preprocess,[status(thm)],[axiom7]). % 4.60/4.80 thf(axiom6,axiom,(ivalid @ ((iimplies @ (iatom @ p5)) @ ((iimplies @ (iatom @ p5)) @ (iatom @ p4))))). % 4.60/4.80 thf(123,plain,sP72,inference(preprocess,[status(thm)],[axiom6]). % 4.60/4.80 thf(axiom5,axiom,(ivalid @ ((iimplies @ (iatom @ p4)) @ ((iimplies @ (iatom @ p4)) @ (iatom @ p3))))). % 4.60/4.80 thf(124,plain,sP100,inference(preprocess,[status(thm)],[axiom5]). % 4.60/4.80 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ p3)) @ ((iimplies @ (iatom @ p3)) @ (iatom @ p2))))). % 4.60/4.80 thf(125,plain,sP5,inference(preprocess,[status(thm)],[axiom4]). % 4.60/4.80 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ p2)) @ ((iimplies @ (iatom @ p2)) @ (iatom @ p1))))). % 4.60/4.80 thf(126,plain,sP52,inference(preprocess,[status(thm)],[axiom3]). % 4.60/4.80 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))). % 4.60/4.80 thf(127,plain,sP23,inference(preprocess,[status(thm)],[axiom2]). % 4.60/4.80 thf(axiom1,axiom,(ivalid @ (iatom @ p20))). % 4.60/4.80 thf(128,plain,sP119,inference(preprocess,[status(thm)],[axiom1]). % 4.60/4.80 thf(refl_axiom,axiom,sP2). % 4.60/4.80 thf(129,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,refl_axiom,h1])). % 4.60/4.80 thf(130,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[129,h0])). % 4.60/4.80 thf(0,theorem,sP90,inference(contra,[status(thm),contra(discharge,[h1])],[129,h1])). % 4.60/4.80 % SZS output end Proof %------------------------------------------------------------------------------