%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO064^4.004 : 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 : n017.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 03:24:48 PM UTC 2025 % Result : Theorem 4.59s 4.91s % Output : Proof 4.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO064^4.004 : 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 % 0.13/0.34 % Computer : n017.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 00:28:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.59/4.91 % SZS status Theorem % 4.59/4.91 % Mode: mode506 % 4.59/4.91 % Inferences: 44153 % 4.59/4.91 % SZS output start Proof % 4.59/4.91 thf(ty_a, type, a : ($i>$o)). % 4.59/4.91 thf(ty_eigen__6, type, eigen__6 : $i). % 4.59/4.91 thf(ty_a4, type, a4 : ($i>$o)). % 4.59/4.91 thf(ty_eigen__2, type, eigen__2 : $i). % 4.59/4.91 thf(ty_a3, type, a3 : ($i>$o)). % 4.59/4.91 thf(ty_eigen__7, type, eigen__7 : $i). % 4.59/4.91 thf(ty_a1, type, a1 : ($i>$o)). % 4.59/4.91 thf(ty_eigen__1, type, eigen__1 : $i). % 4.59/4.91 thf(ty_a2, type, a2 : ($i>$o)). % 4.59/4.91 thf(ty_b3, type, b3 : ($i>$o)). % 4.59/4.91 thf(ty_b, type, b : ($i>$o)). % 4.59/4.91 thf(ty_eigen__0, type, eigen__0 : $i). % 4.59/4.91 thf(ty_eigen__4, type, eigen__4 : $i). % 4.59/4.91 thf(ty_b2, type, b2 : ($i>$o)). % 4.59/4.91 thf(ty_eigen__3, type, eigen__3 : $i). % 4.59/4.91 thf(ty_b1, type, b1 : ($i>$o)). % 4.59/4.91 thf(ty_irel, type, irel : ($i>$i>$o)). % 4.59/4.91 thf(ty_eigen__8, type, eigen__8 : $i). % 4.59/4.91 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 4.59/4.91 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b2 @ X2) => (~((a3 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b3 @ X2) => (~((a4 @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 4.59/4.91 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b1 @ X3) => (~((a2 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((b2 @ X4) => (~((a3 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((b3 @ X4) => (~((a4 @ X4)))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 4.59/4.91 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => (~(((b2 @ X1) => (~((a3 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 4.59/4.91 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~(((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b @ X3) => (~((a1 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((b1 @ X4) => (~((a2 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((b2 @ X5) => (~((a3 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => (~(((b3 @ X5) => (~((a4 @ X5)))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 4.59/4.91 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 4.59/4.91 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b1 @ X2) => (~((a2 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b2 @ X3) => (~((a3 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((b3 @ X3) => (~((a4 @ X3))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 4.59/4.91 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => (~(((b3 @ X1) => (~((a4 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 4.59/4.91 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__2) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__7])])). % 4.59/4.91 thf(sP1,plain,sP1 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => (~(((b1 @ X1) => (~((a2 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 4.59/4.91 thf(sP2,plain,sP2 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP2])])). % 4.59/4.91 thf(sP3,plain,sP3 <=> (b2 @ eigen__6),introduced(definition,[new_symbols(definition,[sP3])])). % 4.59/4.91 thf(sP4,plain,sP4 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => (a2 @ X1))),introduced(definition,[new_symbols(definition,[sP4])])). % 4.59/4.91 thf(sP5,plain,sP5 <=> ((b3 @ eigen__4) => (~((a4 @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP5])])). % 4.59/4.91 thf(sP6,plain,sP6 <=> (![X1:$i]:((~((((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP6])])). % 4.59/4.91 thf(sP7,plain,sP7 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (b1 @ X4))))) => (![X4:$i]:(((irel @ X3) @ X4) => (a1 @ X4)))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (b1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 4.59/4.91 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__0) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP8])])). % 4.59/4.91 thf(sP9,plain,sP9 <=> ((~((((irel @ eigen__1) @ eigen__2) => (~(((irel @ eigen__2) @ eigen__7)))))) => ((irel @ eigen__1) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP9])])). % 4.59/4.91 thf(sP10,plain,sP10 <=> (((irel @ eigen__2) @ eigen__6) => sP3),introduced(definition,[new_symbols(definition,[sP10])])). % 4.59/4.91 thf(sP11,plain,sP11 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 4.59/4.91 thf(sP12,plain,sP12 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 4.59/4.91 thf(sP13,plain,sP13 <=> ((irel @ eigen__2) @ eigen__6),introduced(definition,[new_symbols(definition,[sP13])])). % 4.59/4.91 thf(sP14,plain,sP14 <=> (((irel @ eigen__0) @ eigen__1) => ((~(sP11)) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))))),introduced(definition,[new_symbols(definition,[sP14])])). % 4.59/4.91 thf(sP15,plain,sP15 <=> (a1 @ eigen__8),introduced(definition,[new_symbols(definition,[sP15])])). % 4.59/4.91 thf(sP16,plain,sP16 <=> (((irel @ eigen__2) @ eigen__7) => (a2 @ eigen__7)),introduced(definition,[new_symbols(definition,[sP16])])). % 4.59/4.91 thf(sP17,plain,sP17 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (b2 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (b3 @ X4))))) => (![X4:$i]:(((irel @ X3) @ X4) => (a3 @ X4)))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (b3 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 4.59/4.91 thf(sP18,plain,sP18 <=> (sP3 => (~((a3 @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP18])])). % 4.59/4.91 thf(sP19,plain,sP19 <=> ((~((![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b2 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a2 @ X2)))))))) => (![X1:$i]:(((irel @ eigen__2) @ X1) => (b2 @ X1)))),introduced(definition,[new_symbols(definition,[sP19])])). % 4.59/4.91 thf(sP20,plain,sP20 <=> ((irel @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP20])])). % 4.59/4.91 thf(sP21,plain,sP21 <=> (a2 @ eigen__7),introduced(definition,[new_symbols(definition,[sP21])])). % 4.59/4.91 thf(sP22,plain,sP22 <=> (((irel @ eigen__2) @ eigen__3) => ((~((![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((b2 @ X1) => (~((a3 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((b3 @ X1) => (~((a4 @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 4.59/4.91 thf(sP23,plain,sP23 <=> (((irel @ eigen__0) @ eigen__0) => ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))))) => sP12)),introduced(definition,[new_symbols(definition,[sP23])])). % 4.59/4.91 thf(sP24,plain,sP24 <=> ((~((![X1:$i]:(((irel @ eigen__3) @ X1) => (b3 @ X1))))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => (a3 @ X1)))),introduced(definition,[new_symbols(definition,[sP24])])). % 4.59/4.91 thf(sP25,plain,sP25 <=> (((irel @ eigen__0) @ eigen__8) => (b @ eigen__8)),introduced(definition,[new_symbols(definition,[sP25])])). % 4.59/4.91 thf(sP26,plain,sP26 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b2 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a2 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP26])])). % 4.59/4.91 thf(sP27,plain,sP27 <=> ((irel @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP27])])). % 4.59/4.91 thf(sP28,plain,sP28 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b1 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a1 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP28])])). % 4.59/4.91 thf(sP29,plain,sP29 <=> (sP20 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP29])])). % 4.59/4.91 thf(sP30,plain,sP30 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))))) => sP12),introduced(definition,[new_symbols(definition,[sP30])])). % 4.59/4.91 thf(sP31,plain,sP31 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (a3 @ X1))),introduced(definition,[new_symbols(definition,[sP31])])). % 4.59/4.91 thf(sP32,plain,sP32 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b3 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP32])])). % 4.59/4.91 thf(sP33,plain,sP33 <=> (![X1:$i]:((![X2:$i]:(((irel @ X1) @ X2) => (b1 @ X2))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (b2 @ X4))))) => (![X4:$i]:(((irel @ X3) @ X4) => (a2 @ X4)))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (b2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP33])])). % 4.59/4.91 thf(sP34,plain,sP34 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => (b2 @ X1))),introduced(definition,[new_symbols(definition,[sP34])])). % 4.59/4.91 thf(sP35,plain,sP35 <=> (((irel @ eigen__1) @ eigen__8) => sP15),introduced(definition,[new_symbols(definition,[sP35])])). % 4.59/4.91 thf(sP36,plain,sP36 <=> (((irel @ eigen__2) @ eigen__3) => (~(((irel @ eigen__3) @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP36])])). % 4.59/4.91 thf(sP37,plain,sP37 <=> (sP34 => (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b3 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a3 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 4.59/4.91 thf(sP38,plain,sP38 <=> (b @ eigen__8),introduced(definition,[new_symbols(definition,[sP38])])). % 4.59/4.91 thf(sP39,plain,sP39 <=> ((irel @ eigen__1) @ eigen__8),introduced(definition,[new_symbols(definition,[sP39])])). % 4.59/4.91 thf(sP40,plain,sP40 <=> ((irel @ eigen__2) @ eigen__7),introduced(definition,[new_symbols(definition,[sP40])])). % 4.59/4.91 thf(sP41,plain,sP41 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a @ X2)))))),introduced(definition,[new_symbols(definition,[sP41])])). % 4.59/4.91 thf(sP42,plain,sP42 <=> (((irel @ eigen__1) @ eigen__2) => ((~(sP1)) => (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b2 @ X2) => (~((a3 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b3 @ X2) => (~((a4 @ X2))))))))))))),introduced(definition,[new_symbols(definition,[sP42])])). % 4.59/4.91 thf(sP43,plain,sP43 <=> ((~(sP1)) => (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b2 @ X2) => (~((a3 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b3 @ X2) => (~((a4 @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP43])])). % 4.59/4.91 thf(sP44,plain,sP44 <=> ((~(sP34)) => sP4),introduced(definition,[new_symbols(definition,[sP44])])). % 4.59/4.91 thf(sP45,plain,sP45 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (b3 @ X1))),introduced(definition,[new_symbols(definition,[sP45])])). % 4.59/4.91 thf(sP46,plain,sP46 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP46])])). % 4.59/4.91 thf(sP47,plain,sP47 <=> ((irel @ eigen__3) @ eigen__6),introduced(definition,[new_symbols(definition,[sP47])])). % 4.59/4.91 thf(sP48,plain,sP48 <=> ((~(sP12)) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b1 @ X3) => (~((a2 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((b2 @ X4) => (~((a3 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((b3 @ X4) => (~((a4 @ X4)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP48])])). % 4.59/4.91 thf(sP49,plain,sP49 <=> ((irel @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP49])])). % 4.59/4.91 thf(sP50,plain,sP50 <=> (sP46 => (~(sP39))),introduced(definition,[new_symbols(definition,[sP50])])). % 4.59/4.91 thf(sP51,plain,sP51 <=> ((~(sP50)) => ((irel @ eigen__0) @ eigen__8)),introduced(definition,[new_symbols(definition,[sP51])])). % 4.59/4.91 thf(sP52,plain,sP52 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b @ X2) => (~((a1 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b1 @ X3) => (~((a2 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((b2 @ X4) => (~((a3 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((b3 @ X4) => (~((a4 @ X4))))))))))))))))),introduced(definition,[new_symbols(definition,[sP52])])). % 4.59/4.91 thf(sP53,plain,sP53 <=> (![X1:$i]:((~((((irel @ eigen__2) @ eigen__3) => (~(((irel @ eigen__3) @ X1)))))) => ((irel @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP53])])). % 4.59/4.91 thf(sP54,plain,sP54 <=> (sP47 => (a3 @ eigen__6)),introduced(definition,[new_symbols(definition,[sP54])])). % 4.59/4.91 thf(sP55,plain,sP55 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((b3 @ X1) => (~((a4 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP55])])). % 4.59/4.91 thf(sP56,plain,sP56 <=> (sP27 => sP44),introduced(definition,[new_symbols(definition,[sP56])])). % 4.59/4.91 thf(sP57,plain,sP57 <=> ((~(sP32)) => sP45),introduced(definition,[new_symbols(definition,[sP57])])). % 4.59/4.91 thf(sP58,plain,sP58 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (b @ X1))),introduced(definition,[new_symbols(definition,[sP58])])). % 4.59/4.91 thf(sP59,plain,sP59 <=> (sP49 => sP24),introduced(definition,[new_symbols(definition,[sP59])])). % 4.59/4.91 thf(sP60,plain,sP60 <=> (b1 @ eigen__7),introduced(definition,[new_symbols(definition,[sP60])])). % 4.59/4.91 thf(sP61,plain,sP61 <=> ((irel @ eigen__1) @ eigen__7),introduced(definition,[new_symbols(definition,[sP61])])). % 4.59/4.91 thf(sP62,plain,sP62 <=> (((irel @ eigen__1) @ eigen__2) => sP19),introduced(definition,[new_symbols(definition,[sP62])])). % 4.59/4.91 thf(sP63,plain,sP63 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b2 @ X2) => (~((a3 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((b3 @ X2) => (~((a4 @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 4.59/4.91 thf(sP64,plain,sP64 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((b1 @ X2) => (~((a2 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b2 @ X3) => (~((a3 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((b3 @ X3) => (~((a4 @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP64])])). % 4.59/4.91 thf(sP65,plain,sP65 <=> ((~((![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((b2 @ X1) => (~((a3 @ X1)))))))))) => sP55),introduced(definition,[new_symbols(definition,[sP65])])). % 4.59/4.91 thf(sP66,plain,sP66 <=> (((irel @ eigen__2) @ eigen__3) => sP57),introduced(definition,[new_symbols(definition,[sP66])])). % 4.59/4.91 thf(sP67,plain,sP67 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((irel @ X1) @ X2) => (~(((irel @ X2) @ X3)))))) => ((irel @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP67])])). % 4.59/4.91 thf(sP68,plain,sP68 <=> ((~(sP11)) => (![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1)))),introduced(definition,[new_symbols(definition,[sP68])])). % 4.59/4.91 thf(sP69,plain,sP69 <=> ((irel @ eigen__0) @ eigen__8),introduced(definition,[new_symbols(definition,[sP69])])). % 4.59/4.91 thf(sP70,plain,sP70 <=> (sP61 => sP60),introduced(definition,[new_symbols(definition,[sP70])])). % 4.59/4.91 thf(sP71,plain,sP71 <=> ((irel @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP71])])). % 4.59/4.91 thf(sP72,plain,sP72 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((b @ X3) => (~((a1 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((b1 @ X4) => (~((a2 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((b2 @ X5) => (~((a3 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => (~(((b3 @ X5) => (~((a4 @ X5))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP72])])). % 4.59/4.91 thf(sP73,plain,sP73 <=> (sP39 => (~((sP38 => (~(sP15)))))),introduced(definition,[new_symbols(definition,[sP73])])). % 4.59/4.91 thf(sP74,plain,sP74 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (a1 @ X1))),introduced(definition,[new_symbols(definition,[sP74])])). % 4.59/4.91 thf(sP75,plain,sP75 <=> (((irel @ eigen__1) @ eigen__1) => ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))))) => sP74)),introduced(definition,[new_symbols(definition,[sP75])])). % 4.59/4.91 thf(sP76,plain,sP76 <=> (![X1:$i]:((~((((irel @ eigen__1) @ eigen__2) => (~(((irel @ eigen__2) @ X1)))))) => ((irel @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP76])])). % 4.59/4.91 thf(sP77,plain,sP77 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__1) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP77])])). % 4.59/4.91 thf(sP78,plain,sP78 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b @ X2))))),introduced(definition,[new_symbols(definition,[sP78])])). % 4.59/4.91 thf(sP79,plain,sP79 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__2) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__2) @ X2)))),introduced(definition,[new_symbols(definition,[sP79])])). % 4.59/4.91 thf(sP80,plain,sP80 <=> (sP46 => ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1)))))))))) => sP64)),introduced(definition,[new_symbols(definition,[sP80])])). % 4.59/4.91 thf(sP81,plain,sP81 <=> (a4 @ eigen__4),introduced(definition,[new_symbols(definition,[sP81])])). % 4.59/4.91 thf(sP82,plain,sP82 <=> ((![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))) => sP26),introduced(definition,[new_symbols(definition,[sP82])])). % 4.59/4.91 thf(sP83,plain,sP83 <=> (sP40 => (~((sP60 => (~(sP21)))))),introduced(definition,[new_symbols(definition,[sP83])])). % 4.59/4.91 thf(sP84,plain,sP84 <=> (sP60 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP84])])). % 4.59/4.91 thf(sP85,plain,sP85 <=> (sP38 => (~(sP15))),introduced(definition,[new_symbols(definition,[sP85])])). % 4.59/4.91 thf(sP86,plain,sP86 <=> (a3 @ eigen__6),introduced(definition,[new_symbols(definition,[sP86])])). % 4.59/4.91 thf(sP87,plain,sP87 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((b @ X1) => (~((a1 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP87])])). % 4.59/4.91 thf(sP88,plain,sP88 <=> ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))))) => sP74),introduced(definition,[new_symbols(definition,[sP88])])). % 4.59/4.91 thf(sP89,plain,sP89 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP89])])). % 4.59/4.91 thf(sP90,plain,sP90 <=> ((irel @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP90])])). % 4.59/4.91 thf(sP91,plain,sP91 <=> (((irel @ eigen__1) @ eigen__2) => (~(sP40))),introduced(definition,[new_symbols(definition,[sP91])])). % 4.59/4.91 thf(sP92,plain,sP92 <=> ((~(sP87)) => sP64),introduced(definition,[new_symbols(definition,[sP92])])). % 4.59/4.91 thf(sP93,plain,sP93 <=> (sP20 => (b3 @ eigen__4)),introduced(definition,[new_symbols(definition,[sP93])])). % 4.59/4.91 thf(sP94,plain,sP94 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (b1 @ X1))),introduced(definition,[new_symbols(definition,[sP94])])). % 4.59/4.91 thf(sP95,plain,sP95 <=> (b3 @ eigen__4),introduced(definition,[new_symbols(definition,[sP95])])). % 4.59/4.91 thf(sP96,plain,sP96 <=> ((~(sP41)) => sP58),introduced(definition,[new_symbols(definition,[sP96])])). % 4.59/4.91 thf(sP97,plain,sP97 <=> (sP47 => (~(sP18))),introduced(definition,[new_symbols(definition,[sP97])])). % 4.59/4.91 thf(sP98,plain,sP98 <=> ((!!) @ a4),introduced(definition,[new_symbols(definition,[sP98])])). % 4.59/4.91 thf(sP99,plain,sP99 <=> (sP58 => sP28),introduced(definition,[new_symbols(definition,[sP99])])). % 4.59/4.91 thf(sP100,plain,sP100 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((b2 @ X1) => (~((a3 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP100])])). % 4.59/4.91 thf(sP101,plain,sP101 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (b2 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (a2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP101])])). % 4.59/4.91 thf(sP102,plain,sP102 <=> ((~(sP36)) => sP13),introduced(definition,[new_symbols(definition,[sP102])])). % 4.59/4.91 thf(sP103,plain,sP103 <=> ((irel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP103])])). % 4.59/4.91 thf(sP104,plain,sP104 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (b3 @ X3))))) => (![X3:$i]:(((irel @ X2) @ X3) => (a3 @ X3)))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (b3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP104])])). % 4.59/4.91 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 4.59/4.91 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 4.59/4.91 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 4.59/4.91 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 4.59/4.91 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 4.59/4.91 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 4.59/4.91 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 4.59/4.91 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 4.59/4.91 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 4.59/4.91 thf(def_iand,definition,(iand = mand)). % 4.59/4.91 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.59/4.91 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.59/4.91 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 4.59/4.91 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 4.59/4.91 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 4.59/4.91 thf(def_ivalid,definition,(ivalid = (!!))). % 4.59/4.91 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 4.59/4.91 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 4.59/4.91 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 4.59/4.91 thf(con,conjecture,sP72). % 4.59/4.91 thf(h1,negated_conjecture,(~(sP72)),inference(assume_negation,[status(cth)],[con])). % 4.59/4.91 thf(1,plain,((~(sP54) | ~(sP47)) | sP86),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(2,plain,(~(sP53) | sP102),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(3,plain,((~(sP102) | sP36) | sP13),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(4,plain,((~(sP36) | ~(sP71)) | ~(sP47)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(5,plain,((~(sP16) | ~(sP40)) | sP21),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(6,plain,(~(sP76) | sP9),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(7,plain,((~(sP9) | sP91) | sP61),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(8,plain,((~(sP91) | ~(sP103)) | ~(sP40)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(9,plain,(~(sP4) | sP16),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(10,plain,(~(sP94) | sP70),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(11,plain,((~(sP70) | ~(sP61)) | sP60),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(12,plain,(~(sP31) | sP54),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(13,plain,(~(sP34) | sP10),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(14,plain,((~(sP10) | ~(sP13)) | sP3),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(15,plain,((~(sP35) | ~(sP39)) | sP15),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(16,plain,(~(sP6) | sP51),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(17,plain,((~(sP51) | sP50) | sP69),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(18,plain,((~(sP50) | ~(sP46)) | ~(sP39)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(19,plain,(~(sP74) | sP35),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(20,plain,(~(sP58) | sP25),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(21,plain,((~(sP25) | ~(sP69)) | sP38),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(22,plain,(~(sP8) | sP6),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(23,plain,(~(sP77) | sP76),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(24,plain,(~(sP79) | sP53),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(25,plain,((~(sP85) | ~(sP38)) | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(26,plain,(sP73 | sP85),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(27,plain,(sP73 | sP39),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(28,plain,((~(sP18) | ~(sP3)) | ~(sP86)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(29,plain,((~(sP84) | ~(sP60)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(30,plain,(sP83 | sP84),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(31,plain,(sP83 | sP40),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(32,plain,(sP97 | sP18),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(33,plain,(sP97 | sP47),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(34,plain,(~(sP41) | sP23),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(35,plain,((~(sP23) | ~(sP89)) | sP30),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(36,plain,(~(sP67) | sP8),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(37,plain,(~(sP2) | sP89),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(38,plain,(~(sP7) | sP99),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(39,plain,((~(sP99) | ~(sP58)) | sP28),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(40,plain,(~(sP28) | sP14),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(41,plain,((~(sP14) | ~(sP46)) | sP68),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(42,plain,(~(sP78) | sP96),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(43,plain,((~(sP96) | sP41) | sP58),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(44,plain,((~(sP30) | sP58) | sP12),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(45,plain,(sP87 | ~(sP73)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 4.59/4.91 thf(46,plain,(~(sP11) | sP75),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(47,plain,((~(sP75) | ~(sP90)) | sP88),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(48,plain,(~(sP67) | sP77),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(49,plain,(~(sP2) | sP90),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(50,plain,(~(sP33) | sP82),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(51,plain,((~(sP82) | ~(sP94)) | sP26),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(52,plain,(~(sP26) | sP62),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(53,plain,((~(sP62) | ~(sP103)) | sP19),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(54,plain,((~(sP88) | sP94) | sP74),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(55,plain,((~(sP68) | sP11) | sP94),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(56,plain,(sP1 | ~(sP83)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])). % 4.59/4.91 thf(57,plain,(~(sP101) | sP56),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(58,plain,((~(sP56) | ~(sP27)) | sP44),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(59,plain,(~(sP67) | sP79),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(60,plain,(~(sP2) | sP27),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(61,plain,(~(sP17) | sP37),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(62,plain,((~(sP37) | ~(sP34)) | sP104),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(63,plain,(~(sP104) | sP66),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(64,plain,((~(sP66) | ~(sP71)) | sP57),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(65,plain,((~(sP44) | sP34) | sP4),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(66,plain,((~(sP19) | sP101) | sP34),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(67,plain,(sP100 | ~(sP97)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 4.59/4.91 thf(68,plain,(~(sP32) | sP59),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(69,plain,((~(sP59) | ~(sP49)) | sP24),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(70,plain,(~(sP2) | sP49),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(71,plain,((~(sP57) | sP32) | sP45),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(72,plain,((~(sP24) | sP45) | sP31),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(73,plain,(~(sP45) | sP93),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(74,plain,((~(sP93) | ~(sP20)) | sP95),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(75,plain,(~(sP98) | sP81),inference(all_rule,[status(thm)],[])). % 4.59/4.91 thf(76,plain,((~(sP5) | ~(sP95)) | ~(sP81)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(77,plain,(sP29 | sP5),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(78,plain,(sP29 | sP20),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(79,plain,(sP55 | ~(sP29)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 4.59/4.91 thf(80,plain,(sP65 | ~(sP55)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(81,plain,(sP65 | ~(sP100)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(82,plain,(sP22 | ~(sP65)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(83,plain,(sP22 | sP71),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(84,plain,(sP63 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 4.59/4.91 thf(85,plain,(sP43 | ~(sP63)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(86,plain,(sP43 | ~(sP1)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(87,plain,(sP42 | ~(sP43)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(88,plain,(sP42 | sP103),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(89,plain,(sP64 | ~(sP42)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 4.59/4.91 thf(90,plain,(sP92 | ~(sP64)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(91,plain,(sP92 | ~(sP87)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(92,plain,(sP80 | ~(sP92)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(93,plain,(sP80 | sP46),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(94,plain,(sP52 | ~(sP80)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 4.59/4.91 thf(95,plain,(sP48 | ~(sP52)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(96,plain,(sP48 | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 4.59/4.91 thf(97,plain,(sP72 | ~(sP48)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 4.59/4.91 thf(axiom5,axiom,(ivalid @ ((ior @ ((ior @ (iatom @ b)) @ (iatom @ a))) @ (iatom @ b)))). % 4.59/4.91 thf(98,plain,sP78,inference(preprocess,[status(thm)],[axiom5]). % 4.59/4.91 thf(axiom4,axiom,(ivalid @ ((iimplies @ (iatom @ b)) @ ((ior @ ((ior @ (iatom @ b1)) @ (iatom @ a1))) @ (iatom @ b1))))). % 4.59/4.91 thf(99,plain,sP7,inference(preprocess,[status(thm)],[axiom4]). % 4.59/4.91 thf(axiom3,axiom,(ivalid @ ((iimplies @ (iatom @ b1)) @ ((ior @ ((ior @ (iatom @ b2)) @ (iatom @ a2))) @ (iatom @ b2))))). % 4.59/4.91 thf(100,plain,sP33,inference(preprocess,[status(thm)],[axiom3]). % 4.59/4.91 thf(axiom2,axiom,(ivalid @ ((iimplies @ (iatom @ b2)) @ ((ior @ ((ior @ (iatom @ b3)) @ (iatom @ a3))) @ (iatom @ b3))))). % 4.59/4.91 thf(101,plain,sP17,inference(preprocess,[status(thm)],[axiom2]). % 4.59/4.91 thf(axiom1,axiom,(ivalid @ (iatom @ a4))). % 4.59/4.91 thf(102,plain,sP98,inference(preprocess,[status(thm)],[axiom1]). % 4.59/4.91 thf(trans_axiom,axiom,sP67). % 4.59/4.91 thf(refl_axiom,axiom,sP2). % 4.59/4.91 thf(103,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,trans_axiom,refl_axiom,h1])). % 4.59/4.91 thf(104,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[103,h0])). % 4.59/4.91 thf(0,theorem,sP72,inference(contra,[status(thm),contra(discharge,[h1])],[103,h1])). % 4.59/4.91 % SZS output end Proof %------------------------------------------------------------------------------