%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO068^4.010 : 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 : n001.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 1.11s 1.38s % Output : Proof 1.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO068^4.010 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n001.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 9 01:34:08 EDT 2025 % 0.14/0.34 % CPUTime : % 1.11/1.38 % SZS status Theorem % 1.11/1.38 % Mode: mode506 % 1.11/1.38 % Inferences: 19771 % 1.11/1.38 % SZS output start Proof % 1.11/1.38 thf(ty_p6, type, p6 : ($i>$o)). % 1.11/1.38 thf(ty_eigen__0, type, eigen__0 : $i). % 1.11/1.38 thf(ty_p3, type, p3 : ($i>$o)). % 1.11/1.38 thf(ty_p10, type, p10 : ($i>$o)). % 1.11/1.38 thf(ty_p4, type, p4 : ($i>$o)). % 1.11/1.38 thf(ty_p2, type, p2 : ($i>$o)). % 1.11/1.38 thf(ty_eigen__11, type, eigen__11 : $i). % 1.11/1.38 thf(ty_irel, type, irel : ($i>$i>$o)). % 1.11/1.38 thf(ty_p8, type, p8 : ($i>$o)). % 1.11/1.38 thf(ty_p7, type, p7 : ($i>$o)). % 1.11/1.38 thf(ty_p0, type, p0 : ($i>$o)). % 1.11/1.38 thf(ty_p5, type, p5 : ($i>$o)). % 1.11/1.38 thf(ty_p9, type, p9 : ($i>$o)). % 1.11/1.38 thf(ty_p1, type, p1 : ($i>$o)). % 1.11/1.38 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.11/1.38 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (p10 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 1.11/1.38 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((p0 @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.11/1.38 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 1.11/1.38 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p1 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.11/1.38 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.11/1.38 thf(sP4,plain,sP4 <=> (![X1:$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,[sP4])])). % 1.11/1.38 thf(sP5,plain,sP5 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2)))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.11/1.38 thf(sP6,plain,sP6 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.11/1.38 thf(sP7,plain,sP7 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p5 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.11/1.38 thf(sP8,plain,sP8 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p0 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.11/1.38 thf(sP9,plain,sP9 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])). % 1.11/1.38 thf(sP10,plain,sP10 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.11/1.38 thf(sP11,plain,sP11 <=> ((![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,[sP11])])). % 1.11/1.38 thf(sP12,plain,sP12 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.11/1.38 thf(sP13,plain,sP13 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p1 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p0 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.11/1.38 thf(sP14,plain,sP14 <=> (sP2 => sP8),introduced(definition,[new_symbols(definition,[sP14])])). % 1.11/1.38 thf(sP15,plain,sP15 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p2 @ X1))),introduced(definition,[new_symbols(definition,[sP15])])). % 1.11/1.38 thf(sP16,plain,sP16 <=> (sP9 => sP12),introduced(definition,[new_symbols(definition,[sP16])])). % 1.11/1.38 thf(sP17,plain,sP17 <=> (sP9 => sP10),introduced(definition,[new_symbols(definition,[sP17])])). % 1.11/1.38 thf(sP18,plain,sP18 <=> (sP9 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => sP15)),introduced(definition,[new_symbols(definition,[sP18])])). % 1.11/1.38 thf(sP19,plain,sP19 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 1.11/1.38 thf(sP20,plain,sP20 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p8 @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 1.11/1.38 thf(sP21,plain,sP21 <=> (sP15 => sP2),introduced(definition,[new_symbols(definition,[sP21])])). % 1.11/1.38 thf(sP22,plain,sP22 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p9 @ X1))),introduced(definition,[new_symbols(definition,[sP22])])). % 1.11/1.38 thf(sP23,plain,sP23 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 1.11/1.38 thf(sP24,plain,sP24 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 1.11/1.38 thf(sP25,plain,sP25 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 1.11/1.38 thf(sP26,plain,sP26 <=> (sP9 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))))),introduced(definition,[new_symbols(definition,[sP26])])). % 1.11/1.38 thf(sP27,plain,sP27 <=> ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 1.11/1.38 thf(sP28,plain,sP28 <=> (![X1:$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,[sP28])])). % 1.11/1.38 thf(sP29,plain,sP29 <=> (p10 @ eigen__11),introduced(definition,[new_symbols(definition,[sP29])])). % 1.11/1.38 thf(sP30,plain,sP30 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p5 @ X1))),introduced(definition,[new_symbols(definition,[sP30])])). % 1.11/1.38 thf(sP31,plain,sP31 <=> (sP30 => (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1)))),introduced(definition,[new_symbols(definition,[sP31])])). % 1.11/1.38 thf(sP32,plain,sP32 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p4 @ X1))),introduced(definition,[new_symbols(definition,[sP32])])). % 1.11/1.38 thf(sP33,plain,sP33 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p7 @ X1))),introduced(definition,[new_symbols(definition,[sP33])])). % 1.11/1.38 thf(sP34,plain,sP34 <=> (sP20 => sP23),introduced(definition,[new_symbols(definition,[sP34])])). % 1.11/1.38 thf(sP35,plain,sP35 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p3 @ X1))),introduced(definition,[new_symbols(definition,[sP35])])). % 1.11/1.38 thf(sP36,plain,sP36 <=> (![X1:$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,[sP36])])). % 1.11/1.38 thf(sP37,plain,sP37 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p6 @ X1))),introduced(definition,[new_symbols(definition,[sP37])])). % 1.11/1.38 thf(sP38,plain,sP38 <=> (![X1:$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,[sP38])])). % 1.11/1.38 thf(sP39,plain,sP39 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p7 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p6 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP39])])). % 1.11/1.38 thf(sP40,plain,sP40 <=> (sP15 => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP40])])). % 1.11/1.38 thf(sP41,plain,sP41 <=> (sP9 => (sP32 => sP35)),introduced(definition,[new_symbols(definition,[sP41])])). % 1.11/1.38 thf(sP42,plain,sP42 <=> (sP33 => sP37),introduced(definition,[new_symbols(definition,[sP42])])). % 1.11/1.38 thf(sP43,plain,sP43 <=> (sP22 => sP20),introduced(definition,[new_symbols(definition,[sP43])])). % 1.11/1.38 thf(sP44,plain,sP44 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p7 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p6 @ X2)))))),introduced(definition,[new_symbols(definition,[sP44])])). % 1.11/1.38 thf(sP45,plain,sP45 <=> (sP9 => sP43),introduced(definition,[new_symbols(definition,[sP45])])). % 1.11/1.38 thf(sP46,plain,sP46 <=> ((!!) @ p0),introduced(definition,[new_symbols(definition,[sP46])])). % 1.11/1.38 thf(sP47,plain,sP47 <=> (sP9 => ((![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))) => sP22)),introduced(definition,[new_symbols(definition,[sP47])])). % 1.11/1.38 thf(sP48,plain,sP48 <=> (sP9 => (p0 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP48])])). % 1.11/1.38 thf(sP49,plain,sP49 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p8 @ X2)))))),introduced(definition,[new_symbols(definition,[sP49])])). % 1.11/1.38 thf(sP50,plain,sP50 <=> (sP9 => sP14),introduced(definition,[new_symbols(definition,[sP50])])). % 1.11/1.38 thf(sP51,plain,sP51 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p3 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP51])])). % 1.11/1.38 thf(sP52,plain,sP52 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p4 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP52])])). % 1.11/1.38 thf(sP53,plain,sP53 <=> (sP9 => sP42),introduced(definition,[new_symbols(definition,[sP53])])). % 1.11/1.38 thf(sP54,plain,sP54 <=> (![X1:$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,[sP54])])). % 1.11/1.38 thf(sP55,plain,sP55 <=> (sP33 => sP44),introduced(definition,[new_symbols(definition,[sP55])])). % 1.11/1.38 thf(sP56,plain,sP56 <=> (sP32 => sP35),introduced(definition,[new_symbols(definition,[sP56])])). % 1.11/1.38 thf(sP57,plain,sP57 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (p10 @ X1))),introduced(definition,[new_symbols(definition,[sP57])])). % 1.11/1.38 thf(sP58,plain,sP58 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p9 @ X2)))))),introduced(definition,[new_symbols(definition,[sP58])])). % 1.11/1.38 thf(sP59,plain,sP59 <=> (p0 @ eigen__0),introduced(definition,[new_symbols(definition,[sP59])])). % 1.11/1.38 thf(sP60,plain,sP60 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (p10 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((![X3:$i]:(((irel @ X2) @ X3) => (p10 @ X3))) => (![X3:$i]:(((irel @ X2) @ X3) => (p9 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP60])])). % 1.11/1.38 thf(sP61,plain,sP61 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p5 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP61])])). % 1.11/1.38 thf(sP62,plain,sP62 <=> (sP37 => sP5),introduced(definition,[new_symbols(definition,[sP62])])). % 1.11/1.38 thf(sP63,plain,sP63 <=> ((!!) @ p10),introduced(definition,[new_symbols(definition,[sP63])])). % 1.11/1.38 thf(sP64,plain,sP64 <=> (sP9 => sP21),introduced(definition,[new_symbols(definition,[sP64])])). % 1.11/1.38 thf(sP65,plain,sP65 <=> (sP35 => sP15),introduced(definition,[new_symbols(definition,[sP65])])). % 1.11/1.38 thf(sP66,plain,sP66 <=> (sP2 => sP6),introduced(definition,[new_symbols(definition,[sP66])])). % 1.11/1.38 thf(sP67,plain,sP67 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((![X2:$i]:(((irel @ X1) @ X2) => (p2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => (p1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP67])])). % 1.11/1.38 thf(sP68,plain,sP68 <=> (sP57 => sP22),introduced(definition,[new_symbols(definition,[sP68])])). % 1.11/1.38 thf(sP69,plain,sP69 <=> (((irel @ eigen__0) @ eigen__11) => sP29),introduced(definition,[new_symbols(definition,[sP69])])). % 1.11/1.38 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.11/1.38 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.11/1.38 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.11/1.38 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 1.11/1.38 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 1.11/1.38 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 1.11/1.38 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 1.11/1.38 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 1.11/1.38 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 1.11/1.38 thf(def_iand,definition,(iand = mand)). % 1.11/1.38 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.11/1.38 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 1.11/1.38 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 1.11/1.38 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 1.11/1.38 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 1.11/1.38 thf(def_ivalid,definition,(ivalid = (!!))). % 1.11/1.38 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 1.11/1.38 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 1.11/1.38 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.11/1.38 thf(con,conjecture,sP46). % 1.11/1.38 thf(h1,negated_conjecture,(~(sP46)),inference(assume_negation,[status(cth)],[con])). % 1.11/1.38 thf(1,plain,(~(sP63) | sP29),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(2,plain,(sP69 | ~(sP29)),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(3,plain,(sP57 | ~(sP69)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). % 1.11/1.38 thf(4,plain,(~(sP8) | sP48),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(5,plain,((~(sP48) | ~(sP9)) | sP59),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(6,plain,((~(sP24) | ~(sP57)) | sP58),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(7,plain,(~(sP58) | sP47),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(8,plain,((~(sP47) | ~(sP9)) | sP68),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(9,plain,((~(sP68) | ~(sP57)) | sP22),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(10,plain,((~(sP11) | ~(sP22)) | sP49),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(11,plain,(~(sP49) | sP45),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(12,plain,((~(sP45) | ~(sP9)) | sP43),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(13,plain,((~(sP43) | ~(sP22)) | sP20),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(14,plain,((~(sP34) | ~(sP20)) | sP23),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(15,plain,(~(sP23) | sP16),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(16,plain,((~(sP16) | ~(sP9)) | sP12),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(17,plain,((~(sP12) | ~(sP20)) | sP33),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(18,plain,((~(sP55) | ~(sP33)) | sP44),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(19,plain,(~(sP44) | sP53),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(20,plain,((~(sP53) | ~(sP9)) | sP42),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(21,plain,((~(sP42) | ~(sP33)) | sP37),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(22,plain,((~(sP62) | ~(sP37)) | sP5),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(23,plain,(~(sP5) | sP17),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(24,plain,((~(sP17) | ~(sP9)) | sP10),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(25,plain,((~(sP10) | ~(sP37)) | sP30),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(26,plain,((~(sP3) | ~(sP30)) | sP61),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(27,plain,(~(sP61) | sP26),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(28,plain,((~(sP26) | ~(sP9)) | sP31),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(29,plain,((~(sP31) | ~(sP30)) | sP32),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(30,plain,((~(sP19) | ~(sP32)) | sP25),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(31,plain,(~(sP25) | sP41),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(32,plain,((~(sP41) | ~(sP9)) | sP56),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(33,plain,((~(sP56) | ~(sP32)) | sP35),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(34,plain,((~(sP27) | ~(sP35)) | sP51),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(35,plain,(~(sP51) | sP18),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(36,plain,((~(sP18) | ~(sP9)) | sP65),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(37,plain,((~(sP65) | ~(sP35)) | sP15),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(38,plain,((~(sP40) | ~(sP15)) | sP67),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(39,plain,(~(sP67) | sP64),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(40,plain,((~(sP64) | ~(sP9)) | sP21),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(41,plain,((~(sP21) | ~(sP15)) | sP2),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(42,plain,((~(sP66) | ~(sP2)) | sP6),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(43,plain,(~(sP6) | sP50),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(44,plain,((~(sP50) | ~(sP9)) | sP14),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(45,plain,((~(sP14) | ~(sP2)) | sP8),inference(prop_rule,[status(thm)],[])). % 1.11/1.38 thf(46,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(47,plain,(~(sP60) | sP24),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(48,plain,(~(sP36) | sP11),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(49,plain,(~(sP54) | sP34),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(50,plain,(~(sP39) | sP55),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(51,plain,(~(sP7) | sP62),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(52,plain,(~(sP38) | sP3),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(53,plain,(~(sP52) | sP19),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(54,plain,(~(sP4) | sP27),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(55,plain,(~(sP28) | sP40),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(56,plain,(~(sP13) | sP66),inference(all_rule,[status(thm)],[])). % 1.11/1.38 thf(57,plain,(sP46 | ~(sP59)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.11/1.38 thf(axiom11,axiom,(ivalid @ ((iimplies @ (iatom @ p10)) @ ((iimplies @ (iatom @ p10)) @ (iatom @ p9))))). % 1.11/1.38 thf(58,plain,sP60,inference(preprocess,[status(thm)],[axiom11]). % 1.11/1.38 thf(axiom10,axiom,(ivalid @ ((iimplies @ (iatom @ p9)) @ ((iimplies @ (iatom @ p9)) @ (iatom @ p8))))). % 1.11/1.38 thf(59,plain,sP36,inference(preprocess,[status(thm)],[axiom10]). % 1.11/1.38 thf(axiom9,axiom,(ivalid @ ((iimplies @ (iatom @ p8)) @ ((iimplies @ (iatom @ p8)) @ (iatom @ p7))))). % 1.11/1.38 thf(60,plain,sP54,inference(preprocess,[status(thm)],[axiom9]). % 1.11/1.38 thf(axiom8,axiom,(ivalid @ ((iimplies @ (iatom @ p7)) @ ((iimplies @ (iatom @ p7)) @ (iatom @ p6))))). % 1.11/1.38 thf(61,plain,sP39,inference(preprocess,[status(thm)],[axiom8]). % 1.11/1.38 thf(axiom7,axiom,(ivalid @ ((iimplies @ (iatom @ p6)) @ ((iimplies @ (iatom @ p6)) @ (iatom @ p5))))). % 1.11/1.38 thf(62,plain,sP7,inference(preprocess,[status(thm)],[axiom7]). % 1.11/1.38 thf(axiom6,axiom,(ivalid @ ((iimplies @ (iatom @ p5)) @ ((iimplies @ (iatom @ p5)) @ (iatom @ p4))))). % 1.11/1.38 thf(63,plain,sP38,inference(preprocess,[status(thm)],[axiom6]). % 1.11/1.38 thf(axiom5,axiom,(ivalid @ ((iimplies @ (iatom @ p4)) @ ((iimplies @ (iatom @ p4)) @ (iatom @ p3))))). % 1.11/1.38 thf(64,plain,sP52,inference(preprocess,[status(thm)],[axiom5]). % 1.11/1.38 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ p3)) @ ((iimplies @ (iatom @ p3)) @ (iatom @ p2))))). % 1.11/1.38 thf(65,plain,sP4,inference(preprocess,[status(thm)],[axiom4]). % 1.11/1.38 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ p2)) @ ((iimplies @ (iatom @ p2)) @ (iatom @ p1))))). % 1.11/1.38 thf(66,plain,sP28,inference(preprocess,[status(thm)],[axiom3]). % 1.11/1.38 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ p1)) @ ((iimplies @ (iatom @ p1)) @ (iatom @ p0))))). % 1.11/1.38 thf(67,plain,sP13,inference(preprocess,[status(thm)],[axiom2]). % 1.11/1.38 thf(axiom1,axiom,(ivalid @ (iatom @ p10))). % 1.11/1.38 thf(68,plain,sP63,inference(preprocess,[status(thm)],[axiom1]). % 1.11/1.38 thf(refl_axiom,axiom,sP1). % 1.11/1.38 thf(69,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,refl_axiom,h1])). % 1.11/1.38 thf(70,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[69,h0])). % 1.11/1.38 thf(0,theorem,sP46,inference(contra,[status(thm),contra(discharge,[h1])],[69,h1])). % 1.11/1.38 % SZS output end Proof %------------------------------------------------------------------------------