%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO066^4.002 : 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 : n021.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 03:24:49 PM UTC 2025 % Result : Theorem 4.36s 4.64s % Output : Proof 4.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO066^4.002 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n021.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 01:22:53 EDT 2025 % 0.13/0.35 % CPUTime : % 4.36/4.64 % SZS status Theorem % 4.36/4.64 % Mode: mode506 % 4.36/4.64 % Inferences: 42920 % 4.36/4.64 % SZS output start Proof % 4.36/4.64 thf(ty_eigen__2, type, eigen__2 : $i). % 4.36/4.64 thf(ty_eigen__7, type, eigen__7 : $i). % 4.36/4.64 thf(ty_eigen__1, type, eigen__1 : $i). % 4.36/4.64 thf(ty_eigen__0, type, eigen__0 : $i). % 4.36/4.64 thf(ty_eigen__4, type, eigen__4 : $i). % 4.36/4.64 thf(ty_eigen__5, type, eigen__5 : $i). % 4.36/4.64 thf(ty_eigen__11, type, eigen__11 : $i). % 4.36/4.64 thf(ty_eigen__3, type, eigen__3 : $i). % 4.36/4.64 thf(ty_irel, type, irel : ($i>$i>$o)). % 4.36/4.64 thf(ty_eigen__10, type, eigen__10 : $i). % 4.36/4.64 thf(ty_eigen__8, type, eigen__8 : $i). % 4.36/4.64 thf(ty_eigen__9, type, eigen__9 : $i). % 4.36/4.64 thf(ty_o31, type, o31 : ($i>$o)). % 4.36/4.64 thf(ty_o12, type, o12 : ($i>$o)). % 4.36/4.64 thf(ty_o21, type, o21 : ($i>$o)). % 4.36/4.64 thf(ty_o11, type, o11 : ($i>$o)). % 4.36/4.64 thf(ty_o32, type, o32 : ($i>$o)). % 4.36/4.64 thf(ty_o22, type, o22 : ($i>$o)). % 4.36/4.64 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 4.36/4.64 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (~(((o11 @ X1) => (~((o21 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 4.36/4.64 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o22 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o32 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((o22 @ X3) => (~((o32 @ X3))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 4.36/4.64 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o11 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o21 @ X3) => (~((o31 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o22 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((o12 @ X5) => (~((o32 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => (~(((o22 @ X5) => (~((o32 @ X5))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 4.36/4.64 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~(((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o11 @ X2) => (~((o21 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o11 @ X3) => (~((o31 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o21 @ X4) => (~((o31 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((o12 @ X5) => (~((o22 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => ((~((![X6:$i]:(((irel @ X5) @ X6) => (~(((o12 @ X6) => (~((o32 @ X6)))))))))) => (![X6:$i]:(((irel @ X5) @ X6) => (~(((o22 @ X6) => (~((o32 @ X6))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 4.36/4.64 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => (~(((o11 @ X1) => (~((o31 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 4.36/4.64 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => (~(((o12 @ X1) => (~((o22 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 4.36/4.64 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o21 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o22 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o32 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((o22 @ X4) => (~((o32 @ X4)))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 4.36/4.64 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o32 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((o22 @ X2) => (~((o32 @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 4.36/4.64 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__2) @ X1) => (~(((o21 @ X1) => (~((o31 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 4.36/4.64 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__4) @ X1) => (~(((o12 @ X1) => (~((o32 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__7])])). % 4.36/4.64 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__4) @ X1) => (~(((o22 @ X1) => (~((o32 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 4.36/4.64 thf(sP1,plain,sP1 <=> (((irel @ eigen__2) @ eigen__3) => ((~((![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((o12 @ X1) => (~((o22 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o32 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((o22 @ X2) => (~((o32 @ X2))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 4.36/4.64 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__4) @ X1) => (~(((o22 @ X1) => (~((o32 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 4.36/4.64 thf(sP3,plain,sP3 <=> (o31 @ eigen__10),introduced(definition,[new_symbols(definition,[sP3])])). % 4.36/4.64 thf(sP4,plain,sP4 <=> ((irel @ eigen__2) @ eigen__8),introduced(definition,[new_symbols(definition,[sP4])])). % 4.36/4.64 thf(sP5,plain,sP5 <=> (![X1:$i]:((~((((irel @ eigen__3) @ eigen__4) => (~(((irel @ eigen__4) @ X1)))))) => ((irel @ eigen__3) @ X1))),introduced(definition,[new_symbols(definition,[sP5])])). % 4.36/4.64 thf(sP6,plain,sP6 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((o11 @ X1) => (~((o21 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o11 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o21 @ X3) => (~((o31 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o22 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((o12 @ X5) => (~((o32 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => (~(((o22 @ X5) => (~((o32 @ X5))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 4.36/4.64 thf(sP7,plain,sP7 <=> ((irel @ eigen__3) @ eigen__8),introduced(definition,[new_symbols(definition,[sP7])])). % 4.36/4.64 thf(sP8,plain,sP8 <=> (((irel @ eigen__0) @ eigen__4) => (~(((irel @ eigen__4) @ eigen__7)))),introduced(definition,[new_symbols(definition,[sP8])])). % 4.36/4.64 thf(sP9,plain,sP9 <=> (o21 @ eigen__11),introduced(definition,[new_symbols(definition,[sP9])])). % 4.36/4.64 thf(sP10,plain,sP10 <=> (((irel @ eigen__2) @ eigen__3) => (~(((irel @ eigen__3) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP10])])). % 4.36/4.64 thf(sP11,plain,sP11 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o21 @ X1))),introduced(definition,[new_symbols(definition,[sP11])])). % 4.36/4.64 thf(sP12,plain,sP12 <=> (((irel @ eigen__0) @ eigen__2) => (~(((irel @ eigen__2) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP12])])). % 4.36/4.64 thf(sP13,plain,sP13 <=> (((irel @ eigen__0) @ eigen__1) => ((~((![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((o11 @ X1) => (~((o31 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o21 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o22 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o32 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((o22 @ X4) => (~((o32 @ X4))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 4.36/4.64 thf(sP14,plain,sP14 <=> ((irel @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP14])])). % 4.36/4.64 thf(sP15,plain,sP15 <=> ((o12 @ eigen__7) => (~((o32 @ eigen__7)))),introduced(definition,[new_symbols(definition,[sP15])])). % 4.36/4.64 thf(sP16,plain,sP16 <=> (((irel @ eigen__0) @ eigen__2) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP16])])). % 4.36/4.64 thf(sP17,plain,sP17 <=> (((irel @ eigen__4) @ eigen__7) => (~(sP15))),introduced(definition,[new_symbols(definition,[sP17])])). % 4.36/4.64 thf(sP18,plain,sP18 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o31 @ X1))),introduced(definition,[new_symbols(definition,[sP18])])). % 4.36/4.64 thf(sP19,plain,sP19 <=> (o22 @ eigen__5),introduced(definition,[new_symbols(definition,[sP19])])). % 4.36/4.64 thf(sP20,plain,sP20 <=> (((irel @ eigen__2) @ eigen__9) => (~(((o21 @ eigen__9) => (~((o31 @ eigen__9))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 4.36/4.64 thf(sP21,plain,sP21 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o32 @ X1))),introduced(definition,[new_symbols(definition,[sP21])])). % 4.36/4.64 thf(sP22,plain,sP22 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (o21 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (o22 @ X2))))),introduced(definition,[new_symbols(definition,[sP22])])). % 4.36/4.64 thf(sP23,plain,sP23 <=> (![X1:$i]:(((irel @ eigen__4) @ X1) => (~(((o12 @ X1) => (~((o32 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 4.36/4.64 thf(sP24,plain,sP24 <=> (((irel @ eigen__0) @ eigen__7) => (o12 @ eigen__7)),introduced(definition,[new_symbols(definition,[sP24])])). % 4.36/4.64 thf(sP25,plain,sP25 <=> (((irel @ eigen__0) @ eigen__9) => (o21 @ eigen__9)),introduced(definition,[new_symbols(definition,[sP25])])). % 4.36/4.64 thf(sP26,plain,sP26 <=> ((irel @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP26])])). % 4.36/4.64 thf(sP27,plain,sP27 <=> (o12 @ eigen__8),introduced(definition,[new_symbols(definition,[sP27])])). % 4.36/4.64 thf(sP28,plain,sP28 <=> (o31 @ eigen__9),introduced(definition,[new_symbols(definition,[sP28])])). % 4.36/4.64 thf(sP29,plain,sP29 <=> ((~((((irel @ eigen__2) @ eigen__3) => (~(sP7))))) => sP4),introduced(definition,[new_symbols(definition,[sP29])])). % 4.36/4.64 thf(sP30,plain,sP30 <=> ((~((![X1:$i]:(((irel @ eigen__0) @ X1) => (o11 @ X1))))) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (o12 @ X1)))),introduced(definition,[new_symbols(definition,[sP30])])). % 4.36/4.64 thf(sP31,plain,sP31 <=> ((~((![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((o12 @ X1) => (~((o22 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o32 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((o22 @ X2) => (~((o32 @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 4.36/4.64 thf(sP32,plain,sP32 <=> (((irel @ eigen__0) @ eigen__5) => (o32 @ eigen__5)),introduced(definition,[new_symbols(definition,[sP32])])). % 4.36/4.64 thf(sP33,plain,sP33 <=> (o12 @ eigen__7),introduced(definition,[new_symbols(definition,[sP33])])). % 4.36/4.64 thf(sP34,plain,sP34 <=> ((~(sP11)) => (![X1:$i]:(((irel @ eigen__0) @ X1) => (o22 @ X1)))),introduced(definition,[new_symbols(definition,[sP34])])). % 4.36/4.64 thf(sP35,plain,sP35 <=> (((irel @ eigen__0) @ eigen__10) => sP3),introduced(definition,[new_symbols(definition,[sP35])])). % 4.36/4.64 thf(sP36,plain,sP36 <=> ((~(sP8)) => ((irel @ eigen__0) @ eigen__7)),introduced(definition,[new_symbols(definition,[sP36])])). % 4.36/4.64 thf(sP37,plain,sP37 <=> (o32 @ eigen__5),introduced(definition,[new_symbols(definition,[sP37])])). % 4.36/4.64 thf(sP38,plain,sP38 <=> (((irel @ eigen__0) @ eigen__9) => sP28),introduced(definition,[new_symbols(definition,[sP38])])). % 4.36/4.64 thf(sP39,plain,sP39 <=> ((irel @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP39])])). % 4.36/4.64 thf(sP40,plain,sP40 <=> ((irel @ eigen__4) @ eigen__7),introduced(definition,[new_symbols(definition,[sP40])])). % 4.36/4.64 thf(sP41,plain,sP41 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__3) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__3) @ X2)))),introduced(definition,[new_symbols(definition,[sP41])])). % 4.36/4.64 thf(sP42,plain,sP42 <=> ((~(sP23)) => sP2),introduced(definition,[new_symbols(definition,[sP42])])). % 4.36/4.64 thf(sP43,plain,sP43 <=> ((irel @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP43])])). % 4.36/4.64 thf(sP44,plain,sP44 <=> ((~((sP43 => (~(((irel @ eigen__2) @ eigen__3)))))) => sP39),introduced(definition,[new_symbols(definition,[sP44])])). % 4.36/4.64 thf(sP45,plain,sP45 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (o31 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (o32 @ X2))))),introduced(definition,[new_symbols(definition,[sP45])])). % 4.36/4.64 thf(sP46,plain,sP46 <=> (![X1:$i]:((~((sP43 => (~(((irel @ eigen__2) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP46])])). % 4.36/4.64 thf(sP47,plain,sP47 <=> ((o11 @ eigen__11) => (~(sP9))),introduced(definition,[new_symbols(definition,[sP47])])). % 4.36/4.64 thf(sP48,plain,sP48 <=> (![X1:$i]:((~((((irel @ eigen__2) @ eigen__3) => (~(((irel @ eigen__3) @ X1)))))) => ((irel @ eigen__2) @ X1))),introduced(definition,[new_symbols(definition,[sP48])])). % 4.36/4.64 thf(sP49,plain,sP49 <=> (![X1:$i]:((~((((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP49])])). % 4.36/4.64 thf(sP50,plain,sP50 <=> ((~((![X1:$i]:(((irel @ eigen__2) @ X1) => (~(((o21 @ X1) => (~((o31 @ X1)))))))))) => (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o22 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o32 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((o22 @ X3) => (~((o32 @ X3))))))))))))))),introduced(definition,[new_symbols(definition,[sP50])])). % 4.36/4.64 thf(sP51,plain,sP51 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__2) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__2) @ X2)))),introduced(definition,[new_symbols(definition,[sP51])])). % 4.36/4.64 thf(sP52,plain,sP52 <=> (o21 @ eigen__9),introduced(definition,[new_symbols(definition,[sP52])])). % 4.36/4.64 thf(sP53,plain,sP53 <=> (((irel @ eigen__0) @ eigen__1) => (~(((irel @ eigen__1) @ eigen__10)))),introduced(definition,[new_symbols(definition,[sP53])])). % 4.36/4.64 thf(sP54,plain,sP54 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o22 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o32 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => (~(((o22 @ X3) => (~((o32 @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP54])])). % 4.36/4.64 thf(sP55,plain,sP55 <=> (sP19 => (~(sP37))),introduced(definition,[new_symbols(definition,[sP55])])). % 4.36/4.64 thf(sP56,plain,sP56 <=> (((irel @ eigen__0) @ eigen__5) => sP19),introduced(definition,[new_symbols(definition,[sP56])])). % 4.36/4.64 thf(sP57,plain,sP57 <=> (((irel @ eigen__3) @ eigen__4) => (~(((irel @ eigen__4) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP57])])). % 4.36/4.64 thf(sP58,plain,sP58 <=> (sP27 => (~((o22 @ eigen__8)))),introduced(definition,[new_symbols(definition,[sP58])])). % 4.36/4.64 thf(sP59,plain,sP59 <=> ((irel @ eigen__0) @ eigen__7),introduced(definition,[new_symbols(definition,[sP59])])). % 4.36/4.64 thf(sP60,plain,sP60 <=> (![X1:$i]:((~((sP39 => (~(((irel @ eigen__3) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP60])])). % 4.36/4.64 thf(sP61,plain,sP61 <=> ((~(sP12)) => sP14),introduced(definition,[new_symbols(definition,[sP61])])). % 4.36/4.64 thf(sP62,plain,sP62 <=> (o32 @ eigen__7),introduced(definition,[new_symbols(definition,[sP62])])). % 4.36/4.64 thf(sP63,plain,sP63 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => (~(((o11 @ X1) => (~((o31 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 4.36/4.64 thf(sP64,plain,sP64 <=> (o11 @ eigen__10),introduced(definition,[new_symbols(definition,[sP64])])). % 4.36/4.64 thf(sP65,plain,sP65 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o11 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o21 @ X3) => (~((o31 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o22 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((o12 @ X5) => (~((o32 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => (~(((o22 @ X5) => (~((o32 @ X5)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP65])])). % 4.36/4.64 thf(sP66,plain,sP66 <=> ((irel @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP66])])). % 4.36/4.64 thf(sP67,plain,sP67 <=> ((irel @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP67])])). % 4.36/4.64 thf(sP68,plain,sP68 <=> ((irel @ eigen__0) @ eigen__10),introduced(definition,[new_symbols(definition,[sP68])])). % 4.36/4.64 thf(sP69,plain,sP69 <=> ((irel @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP69])])). % 4.36/4.64 thf(sP70,plain,sP70 <=> (((irel @ eigen__0) @ eigen__8) => sP27),introduced(definition,[new_symbols(definition,[sP70])])). % 4.36/4.64 thf(sP71,plain,sP71 <=> (sP67 => (~(((irel @ eigen__1) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP71])])). % 4.36/4.64 thf(sP72,plain,sP72 <=> (sP68 => sP64),introduced(definition,[new_symbols(definition,[sP72])])). % 4.36/4.64 thf(sP73,plain,sP73 <=> ((irel @ eigen__0) @ eigen__8),introduced(definition,[new_symbols(definition,[sP73])])). % 4.36/4.64 thf(sP74,plain,sP74 <=> ((irel @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP74])])). % 4.36/4.64 thf(sP75,plain,sP75 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o12 @ X2) => (~((o32 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => (~(((o22 @ X2) => (~((o32 @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP75])])). % 4.36/4.64 thf(sP76,plain,sP76 <=> ((irel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP76])])). % 4.36/4.64 thf(sP77,plain,sP77 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o12 @ X1))),introduced(definition,[new_symbols(definition,[sP77])])). % 4.36/4.64 thf(sP78,plain,sP78 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((irel @ X1) @ X2) => (~(((irel @ X2) @ X3)))))) => ((irel @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP78])])). % 4.36/4.64 thf(sP79,plain,sP79 <=> (![X1:$i]:(![X2:$i]:((~((((irel @ eigen__0) @ X1) => (~(((irel @ X1) @ X2)))))) => ((irel @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP79])])). % 4.36/4.64 thf(sP80,plain,sP80 <=> (sP39 => (~(((irel @ eigen__3) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP80])])). % 4.36/4.64 thf(sP81,plain,sP81 <=> ((irel @ eigen__1) @ eigen__10),introduced(definition,[new_symbols(definition,[sP81])])). % 4.36/4.64 thf(sP82,plain,sP82 <=> (sP64 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP82])])). % 4.36/4.64 thf(sP83,plain,sP83 <=> (![X1:$i]:(((irel @ eigen__3) @ X1) => (~(((o12 @ X1) => (~((o22 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP83])])). % 4.36/4.64 thf(sP84,plain,sP84 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o11 @ X2) => (~((o21 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o11 @ X3) => (~((o31 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o21 @ X4) => (~((o31 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => ((~((![X5:$i]:(((irel @ X4) @ X5) => (~(((o12 @ X5) => (~((o22 @ X5)))))))))) => (![X5:$i]:(((irel @ X4) @ X5) => ((~((![X6:$i]:(((irel @ X5) @ X6) => (~(((o12 @ X6) => (~((o32 @ X6)))))))))) => (![X6:$i]:(((irel @ X5) @ X6) => (~(((o22 @ X6) => (~((o32 @ X6)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP84])])). % 4.36/4.64 thf(sP85,plain,sP85 <=> (((irel @ eigen__0) @ eigen__11) => sP9),introduced(definition,[new_symbols(definition,[sP85])])). % 4.36/4.64 thf(sP86,plain,sP86 <=> ((~(sP80)) => sP66),introduced(definition,[new_symbols(definition,[sP86])])). % 4.36/4.64 thf(sP87,plain,sP87 <=> (![X1:$i]:((~((sP14 => (~(((irel @ eigen__4) @ X1)))))) => ((irel @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP87])])). % 4.36/4.64 thf(sP88,plain,sP88 <=> (sP81 => (~(sP82))),introduced(definition,[new_symbols(definition,[sP88])])). % 4.36/4.64 thf(sP89,plain,sP89 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~(((o11 @ X1) => (~((o21 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP89])])). % 4.36/4.64 thf(sP90,plain,sP90 <=> (sP73 => (o22 @ eigen__8)),introduced(definition,[new_symbols(definition,[sP90])])). % 4.36/4.64 thf(sP91,plain,sP91 <=> (sP43 => (~(sP74))),introduced(definition,[new_symbols(definition,[sP91])])). % 4.36/4.64 thf(sP92,plain,sP92 <=> ((~(sP53)) => sP68),introduced(definition,[new_symbols(definition,[sP92])])). % 4.36/4.64 thf(sP93,plain,sP93 <=> ((~(sP63)) => (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o21 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o22 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o32 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((o22 @ X4) => (~((o32 @ X4)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP93])])). % 4.36/4.64 thf(sP94,plain,sP94 <=> ((irel @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP94])])). % 4.36/4.64 thf(sP95,plain,sP95 <=> ((irel @ eigen__3) @ eigen__5),introduced(definition,[new_symbols(definition,[sP95])])). % 4.36/4.64 thf(sP96,plain,sP96 <=> (((irel @ eigen__0) @ eigen__11) => (~(sP47))),introduced(definition,[new_symbols(definition,[sP96])])). % 4.36/4.64 thf(sP97,plain,sP97 <=> (sP59 => sP62),introduced(definition,[new_symbols(definition,[sP97])])). % 4.36/4.64 thf(sP98,plain,sP98 <=> ((~(sP57)) => sP95),introduced(definition,[new_symbols(definition,[sP98])])). % 4.36/4.64 thf(sP99,plain,sP99 <=> ((~(sP16)) => sP73),introduced(definition,[new_symbols(definition,[sP99])])). % 4.36/4.64 thf(sP100,plain,sP100 <=> ((~((sP43 => (~(((irel @ eigen__2) @ eigen__9)))))) => ((irel @ eigen__0) @ eigen__9)),introduced(definition,[new_symbols(definition,[sP100])])). % 4.36/4.64 thf(sP101,plain,sP101 <=> (sP76 => sP50),introduced(definition,[new_symbols(definition,[sP101])])). % 4.36/4.64 thf(sP102,plain,sP102 <=> ((~(sP71)) => sP43),introduced(definition,[new_symbols(definition,[sP102])])). % 4.36/4.64 thf(sP103,plain,sP103 <=> (![X1:$i]:(((irel @ eigen__1) @ X1) => ((~((![X2:$i]:(((irel @ X1) @ X2) => (~(((o21 @ X2) => (~((o31 @ X2)))))))))) => (![X2:$i]:(((irel @ X1) @ X2) => ((~((![X3:$i]:(((irel @ X2) @ X3) => (~(((o12 @ X3) => (~((o22 @ X3)))))))))) => (![X3:$i]:(((irel @ X2) @ X3) => ((~((![X4:$i]:(((irel @ X3) @ X4) => (~(((o12 @ X4) => (~((o32 @ X4)))))))))) => (![X4:$i]:(((irel @ X3) @ X4) => (~(((o22 @ X4) => (~((o32 @ X4))))))))))))))))),introduced(definition,[new_symbols(definition,[sP103])])). % 4.36/4.64 thf(sP104,plain,sP104 <=> ((irel @ eigen__0) @ eigen__11),introduced(definition,[new_symbols(definition,[sP104])])). % 4.36/4.64 thf(sP105,plain,sP105 <=> (o11 @ eigen__11),introduced(definition,[new_symbols(definition,[sP105])])). % 4.36/4.64 thf(sP106,plain,sP106 <=> (sP94 => (~(sP55))),introduced(definition,[new_symbols(definition,[sP106])])). % 4.36/4.64 thf(sP107,plain,sP107 <=> (sP52 => (~(sP28))),introduced(definition,[new_symbols(definition,[sP107])])). % 4.36/4.64 thf(sP108,plain,sP108 <=> (sP7 => (~(sP58))),introduced(definition,[new_symbols(definition,[sP108])])). % 4.36/4.64 thf(sP109,plain,sP109 <=> ((irel @ eigen__0) @ eigen__9),introduced(definition,[new_symbols(definition,[sP109])])). % 4.36/4.64 thf(sP110,plain,sP110 <=> (o22 @ eigen__8),introduced(definition,[new_symbols(definition,[sP110])])). % 4.36/4.64 thf(sP111,plain,sP111 <=> (![X1:$i]:((~((![X2:$i]:(((irel @ X1) @ X2) => (o11 @ X2))))) => (![X2:$i]:(((irel @ X1) @ X2) => (o12 @ X2))))),introduced(definition,[new_symbols(definition,[sP111])])). % 4.36/4.64 thf(sP112,plain,sP112 <=> ((~(sP18)) => sP21),introduced(definition,[new_symbols(definition,[sP112])])). % 4.36/4.64 thf(sP113,plain,sP113 <=> (sP74 => (~(sP7))),introduced(definition,[new_symbols(definition,[sP113])])). % 4.36/4.64 thf(sP114,plain,sP114 <=> ((irel @ eigen__2) @ eigen__9),introduced(definition,[new_symbols(definition,[sP114])])). % 4.36/4.64 thf(sP115,plain,sP115 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o11 @ X1))),introduced(definition,[new_symbols(definition,[sP115])])). % 4.36/4.64 thf(sP116,plain,sP116 <=> (sP69 => sP42),introduced(definition,[new_symbols(definition,[sP116])])). % 4.36/4.64 thf(sP117,plain,sP117 <=> (sP43 => (~(sP114))),introduced(definition,[new_symbols(definition,[sP117])])). % 4.36/4.64 thf(sP118,plain,sP118 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (o22 @ X1))),introduced(definition,[new_symbols(definition,[sP118])])). % 4.36/4.64 thf(sP119,plain,sP119 <=> (![X1:$i]:(((irel @ eigen__2) @ X1) => (~(((o21 @ X1) => (~((o31 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP119])])). % 4.36/4.64 thf(sP120,plain,sP120 <=> (sP104 => sP105),introduced(definition,[new_symbols(definition,[sP120])])). % 4.36/4.64 thf(sP121,plain,sP121 <=> ((~(sP10)) => sP26),introduced(definition,[new_symbols(definition,[sP121])])). % 4.36/4.64 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 4.36/4.64 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 4.36/4.64 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 4.36/4.64 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 4.36/4.64 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))). % 4.36/4.64 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))). % 4.36/4.64 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))). % 4.36/4.64 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))). % 4.36/4.64 thf(def_ifalse,definition,(ifalse = (inot @ itrue))). % 4.36/4.64 thf(def_iand,definition,(iand = mand)). % 4.36/4.64 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.36/4.64 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))). % 4.36/4.64 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))). % 4.36/4.64 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))). % 4.36/4.64 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))). % 4.36/4.64 thf(def_ivalid,definition,(ivalid = (!!))). % 4.36/4.64 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 4.36/4.64 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 4.36/4.64 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 4.36/4.64 thf(con,conjecture,sP84). % 4.36/4.64 thf(h1,negated_conjecture,(~(sP84)),inference(assume_negation,[status(cth)],[con])). % 4.36/4.64 thf(1,plain,((~(sP97) | ~(sP59)) | sP62),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(2,plain,(~(sP46) | sP99),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(3,plain,((~(sP99) | sP16) | sP73),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(4,plain,((~(sP16) | ~(sP43)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(5,plain,(~(sP118) | sP90),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(6,plain,((~(sP90) | ~(sP73)) | sP110),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(7,plain,((~(sP38) | ~(sP109)) | sP28),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(8,plain,((~(sP35) | ~(sP68)) | sP3),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(9,plain,(~(sP49) | sP92),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(10,plain,((~(sP92) | sP53) | sP68),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(11,plain,((~(sP53) | ~(sP67)) | ~(sP81)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(12,plain,(~(sP18) | sP35),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(13,plain,(~(sP115) | sP72),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(14,plain,((~(sP72) | ~(sP68)) | sP64),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(15,plain,(~(sP46) | sP100),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(16,plain,((~(sP100) | sP117) | sP109),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(17,plain,((~(sP117) | ~(sP43)) | ~(sP114)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(18,plain,(~(sP18) | sP38),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(19,plain,(~(sP11) | sP25),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(20,plain,((~(sP25) | ~(sP109)) | sP52),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(21,plain,(~(sP48) | sP29),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(22,plain,((~(sP29) | sP113) | sP4),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(23,plain,((~(sP113) | ~(sP74)) | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(24,plain,(~(sP77) | sP70),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(25,plain,((~(sP70) | ~(sP73)) | sP27),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(26,plain,(~(sP87) | sP36),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(27,plain,((~(sP36) | sP8) | sP59),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(28,plain,((~(sP8) | ~(sP14)) | ~(sP40)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(29,plain,(~(sP21) | sP97),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(30,plain,(~(sP77) | sP24),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(31,plain,((~(sP24) | ~(sP59)) | sP33),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(32,plain,(~(sP60) | sP86),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(33,plain,((~(sP86) | sP80) | sP66),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(34,plain,((~(sP80) | ~(sP39)) | ~(sP95)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(35,plain,(~(sP41) | sP5),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(36,plain,(~(sP5) | sP98),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(37,plain,((~(sP98) | sP57) | sP95),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(38,plain,((~(sP57) | ~(sP69)) | ~(sP94)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(39,plain,(~(sP46) | sP61),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(40,plain,((~(sP61) | sP12) | sP14),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(41,plain,((~(sP12) | ~(sP43)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(42,plain,(~(sP51) | sP48),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(43,plain,(~(sP48) | sP121),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(44,plain,((~(sP121) | sP10) | sP26),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(45,plain,((~(sP10) | ~(sP74)) | ~(sP69)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(46,plain,(~(sP118) | sP56),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(47,plain,((~(sP56) | ~(sP66)) | sP19),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(48,plain,(~(sP79) | sP87),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(49,plain,(~(sP79) | sP60),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(50,plain,(~(sP79) | sP46),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(51,plain,(~(sP46) | sP44),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(52,plain,((~(sP44) | sP91) | sP39),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(53,plain,((~(sP91) | ~(sP43)) | ~(sP74)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(54,plain,(~(sP79) | sP49),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(55,plain,(~(sP49) | sP102),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(56,plain,((~(sP102) | sP71) | sP43),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(57,plain,((~(sP71) | ~(sP67)) | ~(sP76)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(58,plain,((~(sP85) | ~(sP104)) | sP9),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(59,plain,(~(sP11) | sP85),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(60,plain,(~(sP115) | sP120),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(61,plain,((~(sP120) | ~(sP104)) | sP105),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(62,plain,((~(sP15) | ~(sP33)) | ~(sP62)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(63,plain,(sP17 | sP15),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(64,plain,(sP17 | sP40),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(65,plain,((~(sP58) | ~(sP27)) | ~(sP110)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(66,plain,(sP108 | sP58),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(67,plain,(sP108 | sP7),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(68,plain,((~(sP107) | ~(sP52)) | ~(sP28)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(69,plain,(sP20 | sP107),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(70,plain,(sP20 | sP114),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(71,plain,((~(sP82) | ~(sP64)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(72,plain,(sP88 | sP82),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(73,plain,(sP88 | sP81),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(74,plain,((~(sP47) | ~(sP105)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(75,plain,(sP96 | sP47),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(76,plain,(sP96 | sP104),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(77,plain,(sP89 | ~(sP96)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). % 4.36/4.64 thf(78,plain,(~(sP21) | sP32),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(79,plain,((~(sP32) | ~(sP66)) | sP37),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(80,plain,(~(sP78) | sP79),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(81,plain,(~(sP45) | sP112),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(82,plain,((~(sP112) | sP18) | sP21),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(83,plain,(~(sP22) | sP34),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(84,plain,((~(sP34) | sP11) | sP118),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(85,plain,(~(sP111) | sP30),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(86,plain,((~(sP30) | sP115) | sP77),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(87,plain,(sP63 | ~(sP88)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10])). % 4.36/4.64 thf(88,plain,(sP119 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])). % 4.36/4.64 thf(89,plain,(~(sP78) | sP51),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(90,plain,(sP83 | ~(sP108)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 4.36/4.64 thf(91,plain,(~(sP78) | sP41),inference(all_rule,[status(thm)],[])). % 4.36/4.64 thf(92,plain,(sP23 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])). % 4.36/4.64 thf(93,plain,((~(sP55) | ~(sP19)) | ~(sP37)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(94,plain,(sP106 | sP55),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(95,plain,(sP106 | sP94),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(96,plain,(sP2 | ~(sP106)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 4.36/4.64 thf(97,plain,(sP42 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(98,plain,(sP42 | ~(sP23)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(99,plain,(sP116 | ~(sP42)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(100,plain,(sP116 | sP69),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(101,plain,(sP75 | ~(sP116)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 4.36/4.64 thf(102,plain,(sP31 | ~(sP75)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(103,plain,(sP31 | ~(sP83)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(104,plain,(sP1 | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(105,plain,(sP1 | sP74),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(106,plain,(sP54 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 4.36/4.64 thf(107,plain,(sP50 | ~(sP54)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(108,plain,(sP50 | ~(sP119)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(109,plain,(sP101 | ~(sP50)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(110,plain,(sP101 | sP76),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(111,plain,(sP103 | ~(sP101)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 4.36/4.64 thf(112,plain,(sP93 | ~(sP103)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(113,plain,(sP93 | ~(sP63)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(114,plain,(sP13 | ~(sP93)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(115,plain,(sP13 | sP67),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(116,plain,(sP65 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 4.36/4.64 thf(117,plain,(sP6 | ~(sP65)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(118,plain,(sP6 | ~(sP89)),inference(prop_rule,[status(thm)],[])). % 4.36/4.64 thf(119,plain,(sP84 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 4.36/4.64 thf(axiom3,axiom,(ivalid @ ((ior @ (iatom @ o31)) @ (iatom @ o32)))). % 4.36/4.64 thf(120,plain,sP45,inference(preprocess,[status(thm)],[axiom3]). % 4.36/4.64 thf(axiom2,axiom,(ivalid @ ((ior @ (iatom @ o21)) @ (iatom @ o22)))). % 4.36/4.64 thf(121,plain,sP22,inference(preprocess,[status(thm)],[axiom2]). % 4.36/4.64 thf(axiom1,axiom,(ivalid @ ((ior @ (iatom @ o11)) @ (iatom @ o12)))). % 4.36/4.64 thf(122,plain,sP111,inference(preprocess,[status(thm)],[axiom1]). % 4.36/4.64 thf(trans_axiom,axiom,sP78). % 4.36/4.64 thf(123,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,trans_axiom,h1])). % 4.36/4.64 thf(124,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[123,h0])). % 4.36/4.64 thf(0,theorem,sP84,inference(contra,[status(thm),contra(discharge,[h1])],[123,h1])). % 4.36/4.64 % SZS output end Proof %------------------------------------------------------------------------------