%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO544^1 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n010.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 03:25:59 PM UTC 2025 % Result : Theorem 0.94s 1.18s % Output : Proof 6.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO544^1 : TPTP v9.2.0. Released v5.2.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n010.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 00:28:23 EDT 2025 % 0.13/0.34 % CPUTime : % 0.94/1.18 % SZS status Theorem % 0.94/1.18 % Mode: mode213 % 0.94/1.18 % Inferences: 6541 % 0.94/1.18 % SZS output start Proof % 0.94/1.18 thf(ty_eigen__6, type, eigen__6 : $o). % 0.94/1.18 thf(ty_eigen__2, type, eigen__2 : $i). % 0.94/1.18 thf(ty_eigen__16, type, eigen__16 : $o). % 0.94/1.18 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.94/1.18 thf(ty_eigen__1, type, eigen__1 : $i). % 0.94/1.18 thf(ty_eigen__0, type, eigen__0 : $i). % 0.94/1.18 thf(ty_eigen__4, type, eigen__4 : $o). % 0.94/1.18 thf(ty_eigen__5, type, eigen__5 : $o). % 0.94/1.18 thf(ty_eigen__11, type, eigen__11 : $o). % 0.94/1.18 thf(ty_eigen__3, type, eigen__3 : $i). % 0.94/1.18 thf(ty_f0, type, f0 : ($o>$o)). % 0.94/1.18 thf(ty_eigen__17, type, eigen__17 : $o). % 0.94/1.18 thf(ty_eigen__10, type, eigen__10 : $o). % 0.94/1.18 thf(ty_eigen__8, type, eigen__8 : $o). % 0.94/1.18 thf(ty_eigen__28, type, eigen__28 : $o). % 0.94/1.18 thf(ty_f3, type, f3 : ($o>$o)). % 0.94/1.18 thf(ty_f2, type, f2 : ($o>$o)). % 0.94/1.18 thf(ty_f1, type, f1 : ($o>$o)). % 0.94/1.18 thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.94/1.18 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~(X1))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 0.94/1.18 thf(eigendef_eigen__17, definition, eigen__17 = (eps__0 @ (^[X1:$o]:(~(((f2 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__17])])). % 0.94/1.18 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 0.94/1.18 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 0.94/1.18 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 0.94/1.18 thf(eigendef_eigen__16, definition, eigen__16 = (eps__0 @ (^[X1:$o]:(~(((f2 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__16])])). % 0.94/1.18 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 0.94/1.18 thf(eigendef_eigen__28, definition, eigen__28 = (eps__0 @ (^[X1:$o]:(~(((f3 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__28])])). % 0.94/1.18 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 0.94/1.18 thf(sP1,plain,sP1 <=> ((f3 @ $false) = $false),introduced(definition,[new_symbols(definition,[sP1])])). % 0.94/1.18 thf(sP2,plain,sP2 <=> (f3 @ eigen__28),introduced(definition,[new_symbols(definition,[sP2])])). % 0.94/1.18 thf(sP3,plain,sP3 <=> (f3 @ (~($false))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.94/1.18 thf(sP4,plain,sP4 <=> ((~(((~((((f0 = (^[X1:$o]:$false)) => (~((eigen__0 = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))))) => (~(((f0 = (^[X1:$o]:X1)) => (~((eigen__0 = eigen__2))))))))) => (~(((f0 = (^[X1:$o]:(~($false)))) => (~((eigen__0 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.94/1.18 thf(sP5,plain,sP5 <=> (f0 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.94/1.18 thf(sP6,plain,sP6 <=> ((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 0.94/1.18 thf(sP7,plain,sP7 <=> (f0 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP7])])). % 0.94/1.18 thf(sP8,plain,sP8 <=> ((~($false)) = eigen__16),introduced(definition,[new_symbols(definition,[sP8])])). % 0.94/1.18 thf(sP9,plain,sP9 <=> (![X1:$o]:((f1 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.94/1.18 thf(sP10,plain,sP10 <=> (f1 @ $false),introduced(definition,[new_symbols(definition,[sP10])])). % 0.94/1.18 thf(sP11,plain,sP11 <=> (![X1:$i]:(~(((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.94/1.18 thf(sP12,plain,sP12 <=> (![X1:$o]:((f0 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.94/1.18 thf(sP13,plain,sP13 <=> ((~(((~((((f3 = (^[X1:$o]:$false)) => (~((eigen__3 = eigen__0)))) => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~((eigen__3 = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~((eigen__3 = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~((eigen__3 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.94/1.18 thf(sP14,plain,sP14 <=> ((~($false)) = eigen__28),introduced(definition,[new_symbols(definition,[sP14])])). % 0.94/1.18 thf(sP15,plain,sP15 <=> ((~(((~((((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => (~(((f1 = (^[X1:$o]:(~(X1)))) => (~((eigen__1 = eigen__1))))))))) => (~(((f1 = (^[X1:$o]:X1)) => (~((eigen__1 = eigen__2))))))))) => (~(((f1 = (^[X1:$o]:(~($false)))) => (~((eigen__1 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.94/1.18 thf(sP16,plain,sP16 <=> (![X1:$o]:((f2 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP16])])). % 0.94/1.18 thf(sP17,plain,sP17 <=> ((f1 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.94/1.18 thf(sP18,plain,sP18 <=> (![X1:$o]:((f0 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.94/1.18 thf(sP19,plain,sP19 <=> ($false = eigen__28),introduced(definition,[new_symbols(definition,[sP19])])). % 0.94/1.18 thf(sP20,plain,sP20 <=> ((f2 @ eigen__16) = (~($false))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.94/1.18 thf(sP21,plain,sP21 <=> ((~(((sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~((sP7 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.94/1.18 thf(sP22,plain,sP22 <=> (![X1:$i]:(~(((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.94/1.18 thf(sP23,plain,sP23 <=> (![X1:$o]:((f3 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP23])])). % 0.94/1.18 thf(sP24,plain,sP24 <=> (f2 @ $false),introduced(definition,[new_symbols(definition,[sP24])])). % 0.94/1.18 thf(sP25,plain,sP25 <=> (eigen__6 = $false),introduced(definition,[new_symbols(definition,[sP25])])). % 0.94/1.18 thf(sP26,plain,sP26 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP26])])). % 0.94/1.18 thf(sP27,plain,sP27 <=> (eigen__11 = eigen__10),introduced(definition,[new_symbols(definition,[sP27])])). % 0.94/1.18 thf(sP28,plain,sP28 <=> ((f0 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.94/1.18 thf(sP29,plain,sP29 <=> ((f3 = (^[X1:$o]:(~($false)))) => (~((eigen__3 = eigen__3)))),introduced(definition,[new_symbols(definition,[sP29])])). % 0.94/1.18 thf(sP30,plain,sP30 <=> ((f3 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.94/1.18 thf(sP31,plain,sP31 <=> (sP2 = (~($false))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.94/1.18 thf(sP32,plain,sP32 <=> (f1 @ eigen__8),introduced(definition,[new_symbols(definition,[sP32])])). % 0.94/1.18 thf(sP33,plain,sP33 <=> (f1 @ eigen__10),introduced(definition,[new_symbols(definition,[sP33])])). % 0.94/1.18 thf(sP34,plain,sP34 <=> (![X1:$o]:((f2 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP34])])). % 0.94/1.18 thf(sP35,plain,sP35 <=> (f0 @ eigen__6),introduced(definition,[new_symbols(definition,[sP35])])). % 0.94/1.18 thf(sP36,plain,sP36 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~((eigen__2 = eigen__0)))) => (~(((f2 = (^[X1:$o]:(~(X1)))) => (~((eigen__2 = eigen__1))))))))) => (~(((f2 = (^[X1:$o]:X1)) => (~((eigen__2 = eigen__2))))))))) => (~(((f2 = (^[X1:$o]:(~($false)))) => (~((eigen__2 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 0.94/1.18 thf(sP37,plain,sP37 <=> ((~(((~((sP30 => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 0.94/1.18 thf(sP38,plain,sP38 <=> ((~((sP30 => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP38])])). % 0.94/1.18 thf(sP39,plain,sP39 <=> ((f2 = (^[X1:$o]:X1)) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP39])])). % 0.94/1.18 thf(sP40,plain,sP40 <=> (f1 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP40])])). % 0.94/1.18 thf(sP41,plain,sP41 <=> (f1 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP41])])). % 0.94/1.18 thf(sP42,plain,sP42 <=> ($false = eigen__8),introduced(definition,[new_symbols(definition,[sP42])])). % 0.94/1.18 thf(sP43,plain,sP43 <=> ((f1 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP43])])). % 0.94/1.18 thf(sP44,plain,sP44 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP44])])). % 0.94/1.18 thf(sP45,plain,sP45 <=> (sP7 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP45])])). % 0.94/1.18 thf(sP46,plain,sP46 <=> (f2 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP46])])). % 0.94/1.18 thf(sP47,plain,sP47 <=> (![X1:$o]:((f1 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP47])])). % 0.94/1.18 thf(sP48,plain,sP48 <=> ((sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP48])])). % 0.94/1.18 thf(sP49,plain,sP49 <=> (eigen__5 = eigen__4),introduced(definition,[new_symbols(definition,[sP49])])). % 0.94/1.18 thf(sP50,plain,sP50 <=> (eigen__6 = eigen__4),introduced(definition,[new_symbols(definition,[sP50])])). % 0.94/1.18 thf(sP51,plain,sP51 <=> ((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP51])])). % 0.94/1.18 thf(sP52,plain,sP52 <=> (f2 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP52])])). % 0.94/1.18 thf(sP53,plain,sP53 <=> (![X1:$o]:((f2 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP53])])). % 0.94/1.18 thf(sP54,plain,sP54 <=> (![X1:$o]:((f0 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP54])])). % 0.94/1.18 thf(sP55,plain,sP55 <=> ((f0 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP55])])). % 0.94/1.18 thf(sP56,plain,sP56 <=> ((f0 @ (~($false))) = (~($false))),introduced(definition,[new_symbols(definition,[sP56])])). % 0.94/1.18 thf(sP57,plain,sP57 <=> (sP40 => (~((eigen__1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP57])])). % 0.94/1.18 thf(sP58,plain,sP58 <=> (sP5 => (~(sP26))),introduced(definition,[new_symbols(definition,[sP58])])). % 0.94/1.18 thf(sP59,plain,sP59 <=> (sP52 => (~((eigen__2 = eigen__2)))),introduced(definition,[new_symbols(definition,[sP59])])). % 0.94/1.18 thf(sP60,plain,sP60 <=> eigen__5,introduced(definition,[new_symbols(definition,[sP60])])). % 0.94/1.18 thf(sP61,plain,sP61 <=> (f1 @ (~($false))),introduced(definition,[new_symbols(definition,[sP61])])). % 0.94/1.18 thf(sP62,plain,sP62 <=> eigen__16,introduced(definition,[new_symbols(definition,[sP62])])). % 0.94/1.18 thf(sP63,plain,sP63 <=> ((~($false)) = eigen__17),introduced(definition,[new_symbols(definition,[sP63])])). % 0.94/1.18 thf(sP64,plain,sP64 <=> (f1 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP64])])). % 0.94/1.18 thf(sP65,plain,sP65 <=> (sP27 => (eigen__10 = eigen__11)),introduced(definition,[new_symbols(definition,[sP65])])). % 0.94/1.18 thf(sP66,plain,sP66 <=> (sP10 = $false),introduced(definition,[new_symbols(definition,[sP66])])). % 0.94/1.18 thf(sP67,plain,sP67 <=> eigen__4,introduced(definition,[new_symbols(definition,[sP67])])). % 0.94/1.18 thf(sP68,plain,sP68 <=> ((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP68])])). % 0.94/1.18 thf(sP69,plain,sP69 <=> ((f2 @ (~($false))) = $false),introduced(definition,[new_symbols(definition,[sP69])])). % 0.94/1.18 thf(sP70,plain,sP70 <=> ((~((sP68 => (~((sP40 => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(sP43))),introduced(definition,[new_symbols(definition,[sP70])])). % 0.94/1.18 thf(sP71,plain,sP71 <=> ((f2 @ eigen__17) = eigen__17),introduced(definition,[new_symbols(definition,[sP71])])). % 0.94/1.18 thf(sP72,plain,sP72 <=> ((f2 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP72])])). % 0.94/1.18 thf(sP73,plain,sP73 <=> ((~(sP21)) => (~(sP28))),introduced(definition,[new_symbols(definition,[sP73])])). % 0.94/1.18 thf(sP74,plain,sP74 <=> (sP24 = (~($false))),introduced(definition,[new_symbols(definition,[sP74])])). % 0.94/1.18 thf(sP75,plain,sP75 <=> ((f1 @ eigen__11) = (~(eigen__11))),introduced(definition,[new_symbols(definition,[sP75])])). % 0.94/1.18 thf(sP76,plain,sP76 <=> (sP35 = $false),introduced(definition,[new_symbols(definition,[sP76])])). % 0.94/1.18 thf(sP77,plain,sP77 <=> (![X1:$o]:((f1 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP77])])). % 0.94/1.18 thf(sP78,plain,sP78 <=> (f3 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP78])])). % 0.94/1.18 thf(sP79,plain,sP79 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP72))))) => (~(sP39))))) => (~((sP46 => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP79])])). % 0.94/1.18 thf(sP80,plain,sP80 <=> (sP33 = $false),introduced(definition,[new_symbols(definition,[sP80])])). % 0.94/1.18 thf(sP81,plain,sP81 <=> (![X1:$o]:((f1 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP81])])). % 0.94/1.18 thf(sP82,plain,sP82 <=> (f3 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP82])])). % 0.94/1.18 thf(sP83,plain,sP83 <=> (eigen__11 = eigen__8),introduced(definition,[new_symbols(definition,[sP83])])). % 0.94/1.18 thf(sP84,plain,sP84 <=> (![X1:$o]:((f0 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP84])])). % 0.94/1.18 thf(sP85,plain,sP85 <=> (f3 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP85])])). % 0.94/1.18 thf(sP86,plain,sP86 <=> eigen__17,introduced(definition,[new_symbols(definition,[sP86])])). % 0.94/1.18 thf(sP87,plain,sP87 <=> eigen__6,introduced(definition,[new_symbols(definition,[sP87])])). % 0.94/1.18 thf(sP88,plain,sP88 <=> ((f0 @ sP60) = sP60),introduced(definition,[new_symbols(definition,[sP88])])). % 0.94/1.18 thf(sP89,plain,sP89 <=> ((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP89])])). % 0.94/1.18 thf(sP90,plain,sP90 <=> (eigen__10 = eigen__11),introduced(definition,[new_symbols(definition,[sP90])])). % 0.94/1.18 thf(sP91,plain,sP91 <=> (f0 @ $false),introduced(definition,[new_symbols(definition,[sP91])])). % 0.94/1.18 thf(sP92,plain,sP92 <=> eigen__28,introduced(definition,[new_symbols(definition,[sP92])])). % 0.94/1.18 thf(sP93,plain,sP93 <=> (![X1:$o]:((f3 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP93])])). % 0.94/1.18 thf(sP94,plain,sP94 <=> ((~((((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => (~(sP57))))) => (~((sP64 => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP94])])). % 0.94/1.18 thf(sP95,plain,sP95 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP95])])). % 0.94/1.18 thf(sP96,plain,sP96 <=> (sP32 = (~($false))),introduced(definition,[new_symbols(definition,[sP96])])). % 0.94/1.18 thf(sP97,plain,sP97 <=> (sP30 => (~((sP82 => (~(((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP97])])). % 0.94/1.18 thf(sP98,plain,sP98 <=> ((~(sP70)) => (~(sP17))),introduced(definition,[new_symbols(definition,[sP98])])). % 0.94/1.18 thf(sP99,plain,sP99 <=> (eigen__3 = eigen__3),introduced(definition,[new_symbols(definition,[sP99])])). % 0.94/1.18 thf(sP100,plain,sP100 <=> ((~((sP58 => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))))) => (~((sP7 => (~((eigen__0 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP100])])). % 0.94/1.18 thf(sP101,plain,sP101 <=> (![X1:$i]:(~(((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP101])])). % 0.94/1.18 thf(sP102,plain,sP102 <=> (sP82 => (~(((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP102])])). % 0.94/1.18 thf(sP103,plain,sP103 <=> (f3 @ $false),introduced(definition,[new_symbols(definition,[sP103])])). % 0.94/1.18 thf(sP104,plain,sP104 <=> (f0 @ sP67),introduced(definition,[new_symbols(definition,[sP104])])). % 0.94/1.18 thf(sP105,plain,sP105 <=> (f1 @ eigen__11),introduced(definition,[new_symbols(definition,[sP105])])). % 0.94/1.18 thf(sP106,plain,sP106 <=> (sP58 => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP106])])). % 0.94/1.18 thf(sP107,plain,sP107 <=> (sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP107])])). % 0.94/1.18 thf(sP108,plain,sP108 <=> ((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0),introduced(definition,[new_symbols(definition,[sP108])])). % 0.94/1.18 thf(sP109,plain,sP109 <=> $false,introduced(definition,[new_symbols(definition,[sP109])])). % 0.94/1.18 thf(sP110,plain,sP110 <=> (![X1:$i]:(~(((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP110])])). % 0.94/1.18 thf(sP111,plain,sP111 <=> (![X1:$o]:((f2 @ X1) = (~(sP109)))),introduced(definition,[new_symbols(definition,[sP111])])). % 0.94/1.18 thf(sP112,plain,sP112 <=> ((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~(sP109)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP112])])). % 0.94/1.18 thf(sP113,plain,sP113 <=> (f0 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP113])])). % 0.94/1.18 thf(sP114,plain,sP114 <=> eigen__10,introduced(definition,[new_symbols(definition,[sP114])])). % 0.94/1.18 thf(sP115,plain,sP115 <=> (f0 @ (~(sP109))),introduced(definition,[new_symbols(definition,[sP115])])). % 0.94/1.18 thf(sP116,plain,sP116 <=> (f0 @ sP60),introduced(definition,[new_symbols(definition,[sP116])])). % 0.94/1.18 thf(sP117,plain,sP117 <=> eigen__8,introduced(definition,[new_symbols(definition,[sP117])])). % 0.94/1.18 thf(sP118,plain,sP118 <=> (sP61 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP118])])). % 0.94/1.18 thf(sP119,plain,sP119 <=> (sP40 => (~(sP89))),introduced(definition,[new_symbols(definition,[sP119])])). % 0.94/1.18 thf(sP120,plain,sP120 <=> (((f2 = (^[X1:$o]:sP109)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:sP109)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP72))),introduced(definition,[new_symbols(definition,[sP120])])). % 0.94/1.18 thf(sP121,plain,sP121 <=> (![X1:$o]:((f3 @ X1) = sP109)),introduced(definition,[new_symbols(definition,[sP121])])). % 0.94/1.18 thf(sP122,plain,sP122 <=> (f2 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP122])])). % 0.94/1.18 thf(sP123,plain,sP123 <=> (f3 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP123])])). % 0.94/1.18 thf(sP124,plain,sP124 <=> (f2 = (^[X1:$o]:sP109)),introduced(definition,[new_symbols(definition,[sP124])])). % 0.94/1.18 thf(sP125,plain,sP125 <=> (f2 @ sP86),introduced(definition,[new_symbols(definition,[sP125])])). % 0.94/1.18 thf(sP126,plain,sP126 <=> (sP86 = sP62),introduced(definition,[new_symbols(definition,[sP126])])). % 0.94/1.18 thf(sP127,plain,sP127 <=> (![X1:$o]:((f3 @ X1) = (~(sP109)))),introduced(definition,[new_symbols(definition,[sP127])])). % 0.94/1.18 thf(sP128,plain,sP128 <=> (f2 @ sP62),introduced(definition,[new_symbols(definition,[sP128])])). % 0.94/1.18 thf(sP129,plain,sP129 <=> (sP3 = sP109),introduced(definition,[new_symbols(definition,[sP129])])). % 0.94/1.18 thf(sP130,plain,sP130 <=> (eigen__2 = eigen__2),introduced(definition,[new_symbols(definition,[sP130])])). % 0.94/1.18 thf(sP131,plain,sP131 <=> (sP68 => (~(sP119))),introduced(definition,[new_symbols(definition,[sP131])])). % 0.94/1.18 thf(sP132,plain,sP132 <=> (![X1:$o]:((eigen__11 = X1) => (X1 = eigen__11))),introduced(definition,[new_symbols(definition,[sP132])])). % 0.94/1.18 thf(sP133,plain,sP133 <=> ((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~((sP123 => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__3),introduced(definition,[new_symbols(definition,[sP133])])). % 0.94/1.18 thf(sP134,plain,sP134 <=> (sP78 => (~(sP133))),introduced(definition,[new_symbols(definition,[sP134])])). % 0.94/1.18 thf(sP135,plain,sP135 <=> (f1 = (^[X1:$o]:sP109)),introduced(definition,[new_symbols(definition,[sP135])])). % 0.94/1.18 thf(sP136,plain,sP136 <=> (f2 @ (~(sP109))),introduced(definition,[new_symbols(definition,[sP136])])). % 0.94/1.18 thf(sP137,plain,sP137 <=> eigen__11,introduced(definition,[new_symbols(definition,[sP137])])). % 0.94/1.18 thf(sP138,plain,sP138 <=> ((~(sP120)) => (~(sP39))),introduced(definition,[new_symbols(definition,[sP138])])). % 0.94/1.18 thf(sP139,plain,sP139 <=> (sP114 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP139])])). % 0.94/1.18 thf(sP140,plain,sP140 <=> (sP124 => (~(((eps @ (^[X1:$i]:((~(((~(((sP124 => (~((X1 = eigen__0)))) => (~((sP122 => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP140])])). % 0.94/1.18 thf(sP141,plain,sP141 <=> (f0 = (^[X1:$o]:(~(sP109)))),introduced(definition,[new_symbols(definition,[sP141])])). % 0.94/1.18 thf(sP142,plain,sP142 <=> (sP104 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP142])])). % 0.94/1.18 thf(sP143,plain,sP143 <=> ((~(((sP124 => (~((eigen__2 = eigen__0)))) => (~((sP122 => (~((eigen__2 = eigen__1))))))))) => (~(sP59))),introduced(definition,[new_symbols(definition,[sP143])])). % 0.94/1.18 thf(sP144,plain,sP144 <=> (sP46 => (~(((eps @ (^[X1:$i]:((~(((~(((sP124 => (~((X1 = eigen__0)))) => (~((sP122 => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP144])])). % 0.94/1.18 thf(sP145,plain,sP145 <=> (sP87 = sP60),introduced(definition,[new_symbols(definition,[sP145])])). % 0.94/1.18 thf(sP146,plain,sP146 <=> ((sP135 => (~((eigen__1 = eigen__0)))) => (~(sP57))),introduced(definition,[new_symbols(definition,[sP146])])). % 0.94/1.18 thf(def_case,definition,(case = (^[X1:$o>$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(eps @ (^[X6:$i]:((~(((~((((X1 = (^[X7:$o]:sP109)) => (~((X6 = X2)))) => (~(((X1 = (^[X7:$o]:(~(X7)))) => (~((X6 = X3))))))))) => (~(((X1 = (^[X7:$o]:X7)) => (~((X6 = X4))))))))) => (~(((X1 = (^[X7:$o]:(~(sP109)))) => (~((X6 = X5)))))))))))))))). % 0.94/1.18 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP5 => (~((X5 = X1)))) => (~((sP113 => (~((X5 = X2))))))))) => (~((sP7 => (~((X5 = X3))))))))) => (~((sP141 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP135 => (~((X5 = X1)))) => (~((sP40 => (~((X5 = X2))))))))) => (~((sP64 => (~((X5 = X3))))))))) => (~((sP41 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP124 => (~((X5 = X1)))) => (~((sP122 => (~((X5 = X2))))))))) => (~((sP52 => (~((X5 = X3))))))))) => (~((sP46 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP85 => (~((X5 = X1)))) => (~((sP82 => (~((X5 = X2))))))))) => (~((sP123 => (~((X5 = X3))))))))) => (~((sP78 => (~((X5 = X4))))))))) = X4))))))))))). % 0.94/1.18 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP5 => (~((X5 = X1)))) => (~((sP113 => (~((X5 = X2))))))))) => (~((sP7 => (~((X5 = X3))))))))) => (~((sP141 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP135 => (~((X5 = X1)))) => (~((sP40 => (~((X5 = X2))))))))) => (~((sP64 => (~((X5 = X3))))))))) => (~((sP41 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP124 => (~((X5 = X1)))) => (~((sP122 => (~((X5 = X2))))))))) => (~((sP52 => (~((X5 = X3))))))))) => (~((sP46 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP85 => (~((X5 = X1)))) => (~((sP82 => (~((X5 = X2))))))))) => (~((sP123 => (~((X5 = X3))))))))) => (~((sP78 => (~((X5 = X4))))))))) = X4)))))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.94/1.18 thf(h2,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(~(((~(((~((((eps @ (^[X4:$i]:((~(((~(((sP5 => (~((X4 = eigen__0)))) => (~((sP113 => (~((X4 = X1))))))))) => (~((sP7 => (~((X4 = X2))))))))) => (~((sP141 => (~((X4 = X3))))))))) = eigen__0) => (~(((eps @ (^[X4:$i]:((~(((~(((sP135 => (~((X4 = eigen__0)))) => (~((sP40 => (~((X4 = X1))))))))) => (~((sP64 => (~((X4 = X2))))))))) => (~((sP41 => (~((X4 = X3))))))))) = X1)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP124 => (~((X4 = eigen__0)))) => (~((sP122 => (~((X4 = X1))))))))) => (~((sP52 => (~((X4 = X2))))))))) => (~((sP46 => (~((X4 = X3))))))))) = X2)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP85 => (~((X4 = eigen__0)))) => (~((sP82 => (~((X4 = X1))))))))) => (~((sP123 => (~((X4 = X2))))))))) => (~((sP78 => (~((X4 = X3))))))))) = X3))))))))))),introduced(assumption,[])). % 0.94/1.18 thf(h3,assumption,(~((![X1:$i]:(![X2:$i]:(~(((~(((~((((eps @ (^[X3:$i]:((~(((~(((sP5 => (~((X3 = eigen__0)))) => (~((sP113 => (~((X3 = eigen__1))))))))) => (~((sP7 => (~((X3 = X1))))))))) => (~((sP141 => (~((X3 = X2))))))))) = eigen__0) => (~(((eps @ (^[X3:$i]:((~(((~(((sP135 => (~((X3 = eigen__0)))) => (~((sP40 => (~((X3 = eigen__1))))))))) => (~((sP64 => (~((X3 = X1))))))))) => (~((sP41 => (~((X3 = X2))))))))) = eigen__1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP124 => (~((X3 = eigen__0)))) => (~((sP122 => (~((X3 = eigen__1))))))))) => (~((sP52 => (~((X3 = X1))))))))) => (~((sP46 => (~((X3 = X2))))))))) = X1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP85 => (~((X3 = eigen__0)))) => (~((sP82 => (~((X3 = eigen__1))))))))) => (~((sP123 => (~((X3 = X1))))))))) => (~((sP78 => (~((X3 = X2))))))))) = X2)))))))))),introduced(assumption,[])). % 0.94/1.18 thf(h4,assumption,(~((![X1:$i]:(~(((~(((~((((eps @ (^[X2:$i]:((~(((~(((sP5 => (~((X2 = eigen__0)))) => (~((sP113 => (~((X2 = eigen__1))))))))) => (~((sP7 => (~((X2 = eigen__2))))))))) => (~((sP141 => (~((X2 = X1))))))))) = eigen__0) => (~(((eps @ (^[X2:$i]:((~(((~(((sP135 => (~((X2 = eigen__0)))) => (~((sP40 => (~((X2 = eigen__1))))))))) => (~((sP64 => (~((X2 = eigen__2))))))))) => (~((sP41 => (~((X2 = X1))))))))) = eigen__1)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP124 => (~((X2 = eigen__0)))) => (~((sP122 => (~((X2 = eigen__1))))))))) => (~((sP52 => (~((X2 = eigen__2))))))))) => (~((sP46 => (~((X2 = X1))))))))) = eigen__2)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP85 => (~((X2 = eigen__0)))) => (~((sP82 => (~((X2 = eigen__1))))))))) => (~((sP123 => (~((X2 = eigen__2))))))))) => (~((sP78 => (~((X2 = X1))))))))) = X1))))))))),introduced(assumption,[])). % 0.94/1.18 thf(h5,assumption,((~(((~((sP108 => (~(sP89))))) => (~(sP6))))) => (~(sP133))),introduced(assumption,[])). % 0.94/1.18 thf(h6,assumption,((~((sP108 => (~(sP89))))) => (~(sP6))),introduced(assumption,[])). % 0.94/1.18 thf(h7,assumption,(~(sP133)),introduced(assumption,[])). % 0.94/1.18 thf(h8,assumption,(sP108 => (~(sP89))),introduced(assumption,[])). % 0.94/1.18 thf(h9,assumption,(~(sP6)),introduced(assumption,[])). % 0.94/1.18 thf(h10,assumption,(~(sP108)),introduced(assumption,[])). % 0.94/1.18 thf(h11,assumption,(~(sP89)),introduced(assumption,[])). % 0.94/1.18 thf(h12,assumption,sP91,introduced(assumption,[])). % 0.94/1.18 thf(h13,assumption,sP109,introduced(assumption,[])). % 0.94/1.18 thf(h14,assumption,(~(sP91)),introduced(assumption,[])). % 0.94/1.18 thf(h15,assumption,(~(sP109)),introduced(assumption,[])). % 0.94/1.18 thf(1,plain,$false,inference(tab_false,[status(thm),assumptions([h12,h13,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 0.94/1.18 thf(h16,assumption,sP115,introduced(assumption,[])). % 0.94/1.18 thf(h17,assumption,(~(sP115)),introduced(assumption,[])). % 0.94/1.18 thf(2,plain,$false,inference(tab_false,[status(thm),assumptions([h16,h13,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 0.94/1.18 thf(h18,assumption,sP10,introduced(assumption,[])). % 0.94/1.18 thf(h19,assumption,(~(sP10)),introduced(assumption,[])). % 0.94/1.18 thf(h20,assumption,sP61,introduced(assumption,[])). % 0.94/1.18 thf(h21,assumption,(~(sP61)),introduced(assumption,[])). % 0.94/1.18 thf(3,plain,$false,inference(tab_false,[status(thm),assumptions([h20,h13,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 0.94/1.18 thf(h22,assumption,sP24,introduced(assumption,[])). % 0.94/1.18 thf(h23,assumption,(~(sP24)),introduced(assumption,[])). % 0.94/1.18 thf(4,plain,$false,inference(tab_false,[status(thm),assumptions([h22,h13,h21,h15,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 0.94/1.18 thf(h24,assumption,sP136,introduced(assumption,[])). % 0.94/1.18 thf(h25,assumption,(~(sP136)),introduced(assumption,[])). % 0.94/1.18 thf(h26,assumption,sP103,introduced(assumption,[])). % 0.94/1.18 thf(h27,assumption,(~(sP103)),introduced(assumption,[])). % 0.94/1.18 thf(h28,assumption,sP3,introduced(assumption,[])). % 0.94/1.18 thf(h29,assumption,(~(sP3)),introduced(assumption,[])). % 0.94/1.18 thf(5,plain,((sP25 | sP87) | sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(6,plain,((sP50 | ~(sP87)) | ~(sP67)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(7,plain,((sP145 | ~(sP87)) | ~(sP60)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(8,plain,((sP49 | sP60) | sP67),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(9,plain,((~(sP35) | sP91) | ~(sP25)),inference(mating_rule,[status(thm)],[])). % 0.94/1.18 thf(10,plain,((~(sP35) | sP104) | ~(sP50)),inference(mating_rule,[status(thm)],[])). % 0.94/1.18 thf(11,plain,((~(sP35) | sP116) | ~(sP145)),inference(mating_rule,[status(thm)],[])). % 0.94/1.18 thf(12,plain,((~(sP116) | sP104) | ~(sP49)),inference(mating_rule,[status(thm)],[])). % 0.94/1.18 thf(13,plain,~(sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(14,plain,(~(sP12) | sP55),inference(all_rule,[status(thm)],[])). % 0.94/1.18 thf(15,plain,(~(sP84) | sP56),inference(all_rule,[status(thm)],[])). % 0.94/1.18 thf(16,plain,((~(sP55) | sP91) | sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(17,plain,((~(sP56) | sP115) | sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(18,plain,(~(sP18) | sP55),inference(all_rule,[status(thm)],[])). % 0.94/1.18 thf(19,plain,((sP76 | sP35) | sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(20,plain,(sP54 | ~(sP76)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 0.94/1.18 thf(21,plain,((sP88 | ~(sP116)) | ~(sP60)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(22,plain,((sP88 | sP116) | sP60),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(23,plain,(sP84 | ~(sP88)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 0.94/1.18 thf(24,plain,((sP142 | ~(sP104)) | sP109),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(25,plain,(sP18 | ~(sP142)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 0.94/1.18 thf(26,plain,(~(sP113) | sP12),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(27,plain,(~(sP7) | sP84),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(28,plain,(sP112 | sP113),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(29,plain,(sP107 | sP108),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(30,plain,(~(sP141) | sP18),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(31,plain,(sP45 | sP7),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(32,plain,((~(sP48) | ~(sP107)) | ~(sP112)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(33,plain,(sP28 | sP141),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(34,plain,((~(sP21) | sP48) | ~(sP45)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(35,plain,((~(sP73) | sP21) | ~(sP28)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(36,plain,sP26,inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(37,plain,(sP5 | ~(sP54)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(38,plain,((~(sP58) | ~(sP5)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(39,plain,(sP106 | sP58),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(40,plain,(sP100 | ~(sP106)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(41,plain,(sP4 | ~(sP100)),inference(prop_rule,[status(thm)],[])). % 0.94/1.18 thf(42,plain,(~(sP101) | ~(sP4)),inference(all_rule,[status(thm)],[])). % 5.80/6.04 % SZS status Theorem % 5.80/6.04 % Mode: mode515 % 5.80/6.04 % Inferences: 6541 % 5.80/6.04 % SZS output start Proof % 5.80/6.04 thf(ty_eigen__6, type, eigen__6 : $o). % 5.80/6.04 thf(ty_eigen__2, type, eigen__2 : $i). % 5.80/6.04 thf(ty_eigen__16, type, eigen__16 : $o). % 5.80/6.04 thf(ty_eps, type, eps : (($i>$o)>$i)). % 5.80/6.04 thf(ty_eigen__1, type, eigen__1 : $i). % 5.80/6.04 thf(ty_eigen__0, type, eigen__0 : $i). % 5.80/6.04 thf(ty_eigen__4, type, eigen__4 : $o). % 5.80/6.04 thf(ty_eigen__5, type, eigen__5 : $o). % 5.80/6.04 thf(ty_eigen__11, type, eigen__11 : $o). % 5.80/6.04 thf(ty_eigen__3, type, eigen__3 : $i). % 5.80/6.04 thf(ty_f0, type, f0 : ($o>$o)). % 5.80/6.04 thf(ty_eigen__17, type, eigen__17 : $o). % 5.80/6.04 thf(ty_eigen__10, type, eigen__10 : $o). % 5.80/6.04 thf(ty_eigen__8, type, eigen__8 : $o). % 5.80/6.04 thf(ty_eigen__28, type, eigen__28 : $o). % 5.80/6.04 thf(ty_f3, type, f3 : ($o>$o)). % 5.80/6.04 thf(ty_f2, type, f2 : ($o>$o)). % 5.80/6.04 thf(ty_f1, type, f1 : ($o>$o)). % 5.80/6.04 thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 5.80/6.04 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~(X1))))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 5.80/6.04 thf(eigendef_eigen__17, definition, eigen__17 = (eps__0 @ (^[X1:$o]:(~(((f2 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__17])])). % 5.80/6.04 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 5.80/6.04 thf(eigendef_eigen__10, definition, eigen__10 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 5.80/6.04 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$o]:(~(((f1 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 5.80/6.04 thf(eigendef_eigen__16, definition, eigen__16 = (eps__0 @ (^[X1:$o]:(~(((f2 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__16])])). % 5.80/6.04 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 5.80/6.04 thf(eigendef_eigen__28, definition, eigen__28 = (eps__0 @ (^[X1:$o]:(~(((f3 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__28])])). % 5.80/6.04 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$o]:(~(((f0 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 5.80/6.04 thf(sP1,plain,sP1 <=> ((f3 @ $false) = $false),introduced(definition,[new_symbols(definition,[sP1])])). % 5.80/6.04 thf(sP2,plain,sP2 <=> (f3 @ eigen__28),introduced(definition,[new_symbols(definition,[sP2])])). % 5.80/6.04 thf(sP3,plain,sP3 <=> (f3 @ (~($false))),introduced(definition,[new_symbols(definition,[sP3])])). % 5.80/6.04 thf(sP4,plain,sP4 <=> ((~(((~((((f0 = (^[X1:$o]:$false)) => (~((eigen__0 = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))))) => (~(((f0 = (^[X1:$o]:X1)) => (~((eigen__0 = eigen__2))))))))) => (~(((f0 = (^[X1:$o]:(~($false)))) => (~((eigen__0 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 5.80/6.04 thf(sP5,plain,sP5 <=> (f0 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP5])])). % 5.80/6.04 thf(sP6,plain,sP6 <=> ((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 5.80/6.04 thf(sP7,plain,sP7 <=> (f0 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP7])])). % 5.80/6.04 thf(sP8,plain,sP8 <=> ((~($false)) = eigen__16),introduced(definition,[new_symbols(definition,[sP8])])). % 5.80/6.04 thf(sP9,plain,sP9 <=> (![X1:$o]:((f1 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP9])])). % 5.80/6.04 thf(sP10,plain,sP10 <=> (f1 @ $false),introduced(definition,[new_symbols(definition,[sP10])])). % 5.80/6.04 thf(sP11,plain,sP11 <=> (![X1:$i]:(~(((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 5.80/6.04 thf(sP12,plain,sP12 <=> (![X1:$o]:((f0 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 5.80/6.04 thf(sP13,plain,sP13 <=> ((~(((~((((f3 = (^[X1:$o]:$false)) => (~((eigen__3 = eigen__0)))) => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~((eigen__3 = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~((eigen__3 = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~((eigen__3 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 5.80/6.04 thf(sP14,plain,sP14 <=> ((~($false)) = eigen__28),introduced(definition,[new_symbols(definition,[sP14])])). % 5.80/6.04 thf(sP15,plain,sP15 <=> ((~(((~((((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => (~(((f1 = (^[X1:$o]:(~(X1)))) => (~((eigen__1 = eigen__1))))))))) => (~(((f1 = (^[X1:$o]:X1)) => (~((eigen__1 = eigen__2))))))))) => (~(((f1 = (^[X1:$o]:(~($false)))) => (~((eigen__1 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 5.80/6.04 thf(sP16,plain,sP16 <=> (![X1:$o]:((f2 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP16])])). % 5.80/6.04 thf(sP17,plain,sP17 <=> ((f1 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP17])])). % 5.80/6.04 thf(sP18,plain,sP18 <=> (![X1:$o]:((f0 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP18])])). % 5.80/6.04 thf(sP19,plain,sP19 <=> ($false = eigen__28),introduced(definition,[new_symbols(definition,[sP19])])). % 5.80/6.04 thf(sP20,plain,sP20 <=> ((f2 @ eigen__16) = (~($false))),introduced(definition,[new_symbols(definition,[sP20])])). % 5.80/6.04 thf(sP21,plain,sP21 <=> ((~(((sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~((sP7 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 5.80/6.04 thf(sP22,plain,sP22 <=> (![X1:$i]:(~(((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 5.80/6.04 thf(sP23,plain,sP23 <=> (![X1:$o]:((f3 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP23])])). % 5.80/6.04 thf(sP24,plain,sP24 <=> (f2 @ $false),introduced(definition,[new_symbols(definition,[sP24])])). % 5.80/6.04 thf(sP25,plain,sP25 <=> (eigen__6 = $false),introduced(definition,[new_symbols(definition,[sP25])])). % 5.80/6.04 thf(sP26,plain,sP26 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP26])])). % 5.80/6.04 thf(sP27,plain,sP27 <=> (eigen__11 = eigen__10),introduced(definition,[new_symbols(definition,[sP27])])). % 5.80/6.04 thf(sP28,plain,sP28 <=> ((f0 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP28])])). % 5.80/6.04 thf(sP29,plain,sP29 <=> ((f3 = (^[X1:$o]:(~($false)))) => (~((eigen__3 = eigen__3)))),introduced(definition,[new_symbols(definition,[sP29])])). % 5.80/6.04 thf(sP30,plain,sP30 <=> ((f3 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP30])])). % 5.80/6.04 thf(sP31,plain,sP31 <=> (sP2 = (~($false))),introduced(definition,[new_symbols(definition,[sP31])])). % 5.80/6.04 thf(sP32,plain,sP32 <=> (f1 @ eigen__8),introduced(definition,[new_symbols(definition,[sP32])])). % 5.80/6.04 thf(sP33,plain,sP33 <=> (f1 @ eigen__10),introduced(definition,[new_symbols(definition,[sP33])])). % 5.80/6.04 thf(sP34,plain,sP34 <=> (![X1:$o]:((f2 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP34])])). % 5.80/6.04 thf(sP35,plain,sP35 <=> (f0 @ eigen__6),introduced(definition,[new_symbols(definition,[sP35])])). % 5.80/6.04 thf(sP36,plain,sP36 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~((eigen__2 = eigen__0)))) => (~(((f2 = (^[X1:$o]:(~(X1)))) => (~((eigen__2 = eigen__1))))))))) => (~(((f2 = (^[X1:$o]:X1)) => (~((eigen__2 = eigen__2))))))))) => (~(((f2 = (^[X1:$o]:(~($false)))) => (~((eigen__2 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 5.80/6.04 thf(sP37,plain,sP37 <=> ((~(((~((sP30 => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 5.80/6.04 thf(sP38,plain,sP38 <=> ((~((sP30 => (~(((f3 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP38])])). % 5.80/6.04 thf(sP39,plain,sP39 <=> ((f2 = (^[X1:$o]:X1)) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP39])])). % 5.80/6.04 thf(sP40,plain,sP40 <=> (f1 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP40])])). % 5.80/6.04 thf(sP41,plain,sP41 <=> (f1 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP41])])). % 5.80/6.04 thf(sP42,plain,sP42 <=> ($false = eigen__8),introduced(definition,[new_symbols(definition,[sP42])])). % 5.80/6.04 thf(sP43,plain,sP43 <=> ((f1 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP43])])). % 5.80/6.04 thf(sP44,plain,sP44 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP44])])). % 5.80/6.04 thf(sP45,plain,sP45 <=> (sP7 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP45])])). % 5.80/6.04 thf(sP46,plain,sP46 <=> (f2 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP46])])). % 5.80/6.04 thf(sP47,plain,sP47 <=> (![X1:$o]:((f1 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP47])])). % 5.80/6.04 thf(sP48,plain,sP48 <=> ((sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP48])])). % 5.80/6.04 thf(sP49,plain,sP49 <=> (eigen__5 = eigen__4),introduced(definition,[new_symbols(definition,[sP49])])). % 5.80/6.04 thf(sP50,plain,sP50 <=> (eigen__6 = eigen__4),introduced(definition,[new_symbols(definition,[sP50])])). % 5.80/6.04 thf(sP51,plain,sP51 <=> ((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f3 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP51])])). % 5.80/6.04 thf(sP52,plain,sP52 <=> (f2 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP52])])). % 5.80/6.04 thf(sP53,plain,sP53 <=> (![X1:$o]:((f2 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP53])])). % 5.80/6.04 thf(sP54,plain,sP54 <=> (![X1:$o]:((f0 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP54])])). % 5.80/6.04 thf(sP55,plain,sP55 <=> ((f0 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP55])])). % 5.80/6.04 thf(sP56,plain,sP56 <=> ((f0 @ (~($false))) = (~($false))),introduced(definition,[new_symbols(definition,[sP56])])). % 5.80/6.04 thf(sP57,plain,sP57 <=> (sP40 => (~((eigen__1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP57])])). % 5.80/6.04 thf(sP58,plain,sP58 <=> (sP5 => (~(sP26))),introduced(definition,[new_symbols(definition,[sP58])])). % 5.80/6.04 thf(sP59,plain,sP59 <=> (sP52 => (~((eigen__2 = eigen__2)))),introduced(definition,[new_symbols(definition,[sP59])])). % 5.80/6.04 thf(sP60,plain,sP60 <=> eigen__5,introduced(definition,[new_symbols(definition,[sP60])])). % 5.80/6.04 thf(sP61,plain,sP61 <=> (f1 @ (~($false))),introduced(definition,[new_symbols(definition,[sP61])])). % 5.80/6.04 thf(sP62,plain,sP62 <=> eigen__16,introduced(definition,[new_symbols(definition,[sP62])])). % 5.80/6.04 thf(sP63,plain,sP63 <=> ((~($false)) = eigen__17),introduced(definition,[new_symbols(definition,[sP63])])). % 5.80/6.04 thf(sP64,plain,sP64 <=> (f1 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP64])])). % 5.80/6.04 thf(sP65,plain,sP65 <=> (sP27 => (eigen__10 = eigen__11)),introduced(definition,[new_symbols(definition,[sP65])])). % 5.80/6.04 thf(sP66,plain,sP66 <=> (sP10 = $false),introduced(definition,[new_symbols(definition,[sP66])])). % 5.80/6.04 thf(sP67,plain,sP67 <=> eigen__4,introduced(definition,[new_symbols(definition,[sP67])])). % 5.80/6.04 thf(sP68,plain,sP68 <=> ((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP68])])). % 5.80/6.04 thf(sP69,plain,sP69 <=> ((f2 @ (~($false))) = $false),introduced(definition,[new_symbols(definition,[sP69])])). % 5.80/6.04 thf(sP70,plain,sP70 <=> ((~((sP68 => (~((sP40 => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(sP43))),introduced(definition,[new_symbols(definition,[sP70])])). % 5.80/6.04 thf(sP71,plain,sP71 <=> ((f2 @ eigen__17) = eigen__17),introduced(definition,[new_symbols(definition,[sP71])])). % 5.80/6.04 thf(sP72,plain,sP72 <=> ((f2 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP72])])). % 5.80/6.04 thf(sP73,plain,sP73 <=> ((~(sP21)) => (~(sP28))),introduced(definition,[new_symbols(definition,[sP73])])). % 5.80/6.04 thf(sP74,plain,sP74 <=> (sP24 = (~($false))),introduced(definition,[new_symbols(definition,[sP74])])). % 5.80/6.04 thf(sP75,plain,sP75 <=> ((f1 @ eigen__11) = (~(eigen__11))),introduced(definition,[new_symbols(definition,[sP75])])). % 5.80/6.04 thf(sP76,plain,sP76 <=> (sP35 = $false),introduced(definition,[new_symbols(definition,[sP76])])). % 5.80/6.04 thf(sP77,plain,sP77 <=> (![X1:$o]:((f1 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP77])])). % 5.80/6.04 thf(sP78,plain,sP78 <=> (f3 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP78])])). % 5.80/6.04 thf(sP79,plain,sP79 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP72))))) => (~(sP39))))) => (~((sP46 => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP79])])). % 5.80/6.04 thf(sP80,plain,sP80 <=> (sP33 = $false),introduced(definition,[new_symbols(definition,[sP80])])). % 5.80/6.04 thf(sP81,plain,sP81 <=> (![X1:$o]:((f1 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP81])])). % 5.80/6.04 thf(sP82,plain,sP82 <=> (f3 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP82])])). % 5.80/6.04 thf(sP83,plain,sP83 <=> (eigen__11 = eigen__8),introduced(definition,[new_symbols(definition,[sP83])])). % 5.80/6.04 thf(sP84,plain,sP84 <=> (![X1:$o]:((f0 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP84])])). % 5.80/6.04 thf(sP85,plain,sP85 <=> (f3 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP85])])). % 5.80/6.04 thf(sP86,plain,sP86 <=> eigen__17,introduced(definition,[new_symbols(definition,[sP86])])). % 5.80/6.04 thf(sP87,plain,sP87 <=> eigen__6,introduced(definition,[new_symbols(definition,[sP87])])). % 5.80/6.04 thf(sP88,plain,sP88 <=> ((f0 @ sP60) = sP60),introduced(definition,[new_symbols(definition,[sP88])])). % 5.80/6.04 thf(sP89,plain,sP89 <=> ((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP40 => (~((X1 = eigen__1))))))))) => (~((sP64 => (~((X1 = eigen__2))))))))) => (~((sP41 => (~((X1 = eigen__3))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP89])])). % 5.80/6.04 thf(sP90,plain,sP90 <=> (eigen__10 = eigen__11),introduced(definition,[new_symbols(definition,[sP90])])). % 5.80/6.04 thf(sP91,plain,sP91 <=> (f0 @ $false),introduced(definition,[new_symbols(definition,[sP91])])). % 5.80/6.04 thf(sP92,plain,sP92 <=> eigen__28,introduced(definition,[new_symbols(definition,[sP92])])). % 5.80/6.04 thf(sP93,plain,sP93 <=> (![X1:$o]:((f3 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP93])])). % 5.80/6.04 thf(sP94,plain,sP94 <=> ((~((((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => (~(sP57))))) => (~((sP64 => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP94])])). % 5.80/6.04 thf(sP95,plain,sP95 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP95])])). % 5.80/6.04 thf(sP96,plain,sP96 <=> (sP32 = (~($false))),introduced(definition,[new_symbols(definition,[sP96])])). % 5.80/6.04 thf(sP97,plain,sP97 <=> (sP30 => (~((sP82 => (~(((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP97])])). % 5.80/6.04 thf(sP98,plain,sP98 <=> ((~(sP70)) => (~(sP17))),introduced(definition,[new_symbols(definition,[sP98])])). % 5.80/6.04 thf(sP99,plain,sP99 <=> (eigen__3 = eigen__3),introduced(definition,[new_symbols(definition,[sP99])])). % 5.80/6.04 thf(sP100,plain,sP100 <=> ((~((sP58 => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))))) => (~((sP7 => (~((eigen__0 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP100])])). % 5.80/6.04 thf(sP101,plain,sP101 <=> (![X1:$i]:(~(((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP101])])). % 5.80/6.04 thf(sP102,plain,sP102 <=> (sP82 => (~(((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP102])])). % 5.80/6.04 thf(sP103,plain,sP103 <=> (f3 @ $false),introduced(definition,[new_symbols(definition,[sP103])])). % 5.80/6.04 thf(sP104,plain,sP104 <=> (f0 @ sP67),introduced(definition,[new_symbols(definition,[sP104])])). % 5.80/6.04 thf(sP105,plain,sP105 <=> (f1 @ eigen__11),introduced(definition,[new_symbols(definition,[sP105])])). % 5.80/6.04 thf(sP106,plain,sP106 <=> (sP58 => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP106])])). % 5.80/6.04 thf(sP107,plain,sP107 <=> (sP5 => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP107])])). % 5.80/6.04 thf(sP108,plain,sP108 <=> ((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0),introduced(definition,[new_symbols(definition,[sP108])])). % 5.80/6.04 thf(sP109,plain,sP109 <=> $false,introduced(definition,[new_symbols(definition,[sP109])])). % 5.80/6.04 thf(sP110,plain,sP110 <=> (![X1:$i]:(~(((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP110])])). % 5.80/6.04 thf(sP111,plain,sP111 <=> (![X1:$o]:((f2 @ X1) = (~(sP109)))),introduced(definition,[new_symbols(definition,[sP111])])). % 5.80/6.04 thf(sP112,plain,sP112 <=> ((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP5 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP7 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~(sP109)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP112])])). % 5.80/6.04 thf(sP113,plain,sP113 <=> (f0 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP113])])). % 5.80/6.04 thf(sP114,plain,sP114 <=> eigen__10,introduced(definition,[new_symbols(definition,[sP114])])). % 5.80/6.04 thf(sP115,plain,sP115 <=> (f0 @ (~(sP109))),introduced(definition,[new_symbols(definition,[sP115])])). % 5.80/6.04 thf(sP116,plain,sP116 <=> (f0 @ sP60),introduced(definition,[new_symbols(definition,[sP116])])). % 5.80/6.04 thf(sP117,plain,sP117 <=> eigen__8,introduced(definition,[new_symbols(definition,[sP117])])). % 5.80/6.04 thf(sP118,plain,sP118 <=> (sP61 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP118])])). % 5.80/6.04 thf(sP119,plain,sP119 <=> (sP40 => (~(sP89))),introduced(definition,[new_symbols(definition,[sP119])])). % 5.80/6.04 thf(sP120,plain,sP120 <=> (((f2 = (^[X1:$o]:sP109)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:sP109)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(sP72))),introduced(definition,[new_symbols(definition,[sP120])])). % 5.80/6.04 thf(sP121,plain,sP121 <=> (![X1:$o]:((f3 @ X1) = sP109)),introduced(definition,[new_symbols(definition,[sP121])])). % 5.80/6.04 thf(sP122,plain,sP122 <=> (f2 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP122])])). % 5.80/6.04 thf(sP123,plain,sP123 <=> (f3 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP123])])). % 5.80/6.04 thf(sP124,plain,sP124 <=> (f2 = (^[X1:$o]:sP109)),introduced(definition,[new_symbols(definition,[sP124])])). % 5.80/6.04 thf(sP125,plain,sP125 <=> (f2 @ sP86),introduced(definition,[new_symbols(definition,[sP125])])). % 5.80/6.04 thf(sP126,plain,sP126 <=> (sP86 = sP62),introduced(definition,[new_symbols(definition,[sP126])])). % 5.80/6.04 thf(sP127,plain,sP127 <=> (![X1:$o]:((f3 @ X1) = (~(sP109)))),introduced(definition,[new_symbols(definition,[sP127])])). % 5.80/6.04 thf(sP128,plain,sP128 <=> (f2 @ sP62),introduced(definition,[new_symbols(definition,[sP128])])). % 5.80/6.04 thf(sP129,plain,sP129 <=> (sP3 = sP109),introduced(definition,[new_symbols(definition,[sP129])])). % 5.80/6.04 thf(sP130,plain,sP130 <=> (eigen__2 = eigen__2),introduced(definition,[new_symbols(definition,[sP130])])). % 5.80/6.04 thf(sP131,plain,sP131 <=> (sP68 => (~(sP119))),introduced(definition,[new_symbols(definition,[sP131])])). % 5.80/6.04 thf(sP132,plain,sP132 <=> (![X1:$o]:((eigen__11 = X1) => (X1 = eigen__11))),introduced(definition,[new_symbols(definition,[sP132])])). % 5.80/6.04 thf(sP133,plain,sP133 <=> ((eps @ (^[X1:$i]:((~(((~(((sP85 => (~((X1 = eigen__0)))) => (~((sP82 => (~((X1 = eigen__1))))))))) => (~((sP123 => (~((X1 = eigen__2))))))))) => (~((sP78 => (~((X1 = eigen__3))))))))) = eigen__3),introduced(definition,[new_symbols(definition,[sP133])])). % 5.80/6.04 thf(sP134,plain,sP134 <=> (sP78 => (~(sP133))),introduced(definition,[new_symbols(definition,[sP134])])). % 5.80/6.04 thf(sP135,plain,sP135 <=> (f1 = (^[X1:$o]:sP109)),introduced(definition,[new_symbols(definition,[sP135])])). % 5.80/6.04 thf(sP136,plain,sP136 <=> (f2 @ (~(sP109))),introduced(definition,[new_symbols(definition,[sP136])])). % 5.80/6.04 thf(sP137,plain,sP137 <=> eigen__11,introduced(definition,[new_symbols(definition,[sP137])])). % 5.80/6.04 thf(sP138,plain,sP138 <=> ((~(sP120)) => (~(sP39))),introduced(definition,[new_symbols(definition,[sP138])])). % 5.80/6.04 thf(sP139,plain,sP139 <=> (sP114 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP139])])). % 5.80/6.04 thf(sP140,plain,sP140 <=> (sP124 => (~(((eps @ (^[X1:$i]:((~(((~(((sP124 => (~((X1 = eigen__0)))) => (~((sP122 => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP140])])). % 5.80/6.04 thf(sP141,plain,sP141 <=> (f0 = (^[X1:$o]:(~(sP109)))),introduced(definition,[new_symbols(definition,[sP141])])). % 5.80/6.04 thf(sP142,plain,sP142 <=> (sP104 = (~(sP109))),introduced(definition,[new_symbols(definition,[sP142])])). % 5.80/6.04 thf(sP143,plain,sP143 <=> ((~(((sP124 => (~((eigen__2 = eigen__0)))) => (~((sP122 => (~((eigen__2 = eigen__1))))))))) => (~(sP59))),introduced(definition,[new_symbols(definition,[sP143])])). % 5.80/6.04 thf(sP144,plain,sP144 <=> (sP46 => (~(((eps @ (^[X1:$i]:((~(((~(((sP124 => (~((X1 = eigen__0)))) => (~((sP122 => (~((X1 = eigen__1))))))))) => (~((sP52 => (~((X1 = eigen__2))))))))) => (~((sP46 => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP144])])). % 5.80/6.04 thf(sP145,plain,sP145 <=> (sP87 = sP60),introduced(definition,[new_symbols(definition,[sP145])])). % 5.80/6.04 thf(sP146,plain,sP146 <=> ((sP135 => (~((eigen__1 = eigen__0)))) => (~(sP57))),introduced(definition,[new_symbols(definition,[sP146])])). % 5.80/6.04 thf(def_case,definition,(case = (^[X1:$o>$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(eps @ (^[X6:$i]:((~(((~((((X1 = (^[X7:$o]:sP109)) => (~((X6 = X2)))) => (~(((X1 = (^[X7:$o]:(~(X7)))) => (~((X6 = X3))))))))) => (~(((X1 = (^[X7:$o]:X7)) => (~((X6 = X4))))))))) => (~(((X1 = (^[X7:$o]:(~(sP109)))) => (~((X6 = X5)))))))))))))))). % 5.80/6.04 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP5 => (~((X5 = X1)))) => (~((sP113 => (~((X5 = X2))))))))) => (~((sP7 => (~((X5 = X3))))))))) => (~((sP141 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP135 => (~((X5 = X1)))) => (~((sP40 => (~((X5 = X2))))))))) => (~((sP64 => (~((X5 = X3))))))))) => (~((sP41 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP124 => (~((X5 = X1)))) => (~((sP122 => (~((X5 = X2))))))))) => (~((sP52 => (~((X5 = X3))))))))) => (~((sP46 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP85 => (~((X5 = X1)))) => (~((sP82 => (~((X5 = X2))))))))) => (~((sP123 => (~((X5 = X3))))))))) => (~((sP78 => (~((X5 = X4))))))))) = X4))))))))))). % 5.80/6.04 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP5 => (~((X5 = X1)))) => (~((sP113 => (~((X5 = X2))))))))) => (~((sP7 => (~((X5 = X3))))))))) => (~((sP141 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP135 => (~((X5 = X1)))) => (~((sP40 => (~((X5 = X2))))))))) => (~((sP64 => (~((X5 = X3))))))))) => (~((sP41 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP124 => (~((X5 = X1)))) => (~((sP122 => (~((X5 = X2))))))))) => (~((sP52 => (~((X5 = X3))))))))) => (~((sP46 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP85 => (~((X5 = X1)))) => (~((sP82 => (~((X5 = X2))))))))) => (~((sP123 => (~((X5 = X3))))))))) => (~((sP78 => (~((X5 = X4))))))))) = X4)))))))))))),inference(assume_negation,[status(cth)],[conj])). % 5.80/6.04 thf(h2,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:(~(((~(((~((((eps @ (^[X4:$i]:((~(((~(((sP5 => (~((X4 = eigen__0)))) => (~((sP113 => (~((X4 = X1))))))))) => (~((sP7 => (~((X4 = X2))))))))) => (~((sP141 => (~((X4 = X3))))))))) = eigen__0) => (~(((eps @ (^[X4:$i]:((~(((~(((sP135 => (~((X4 = eigen__0)))) => (~((sP40 => (~((X4 = X1))))))))) => (~((sP64 => (~((X4 = X2))))))))) => (~((sP41 => (~((X4 = X3))))))))) = X1)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP124 => (~((X4 = eigen__0)))) => (~((sP122 => (~((X4 = X1))))))))) => (~((sP52 => (~((X4 = X2))))))))) => (~((sP46 => (~((X4 = X3))))))))) = X2)))))) => (~(((eps @ (^[X4:$i]:((~(((~(((sP85 => (~((X4 = eigen__0)))) => (~((sP82 => (~((X4 = X1))))))))) => (~((sP123 => (~((X4 = X2))))))))) => (~((sP78 => (~((X4 = X3))))))))) = X3))))))))))),introduced(assumption,[])). % 5.80/6.04 thf(h3,assumption,(~((![X1:$i]:(![X2:$i]:(~(((~(((~((((eps @ (^[X3:$i]:((~(((~(((sP5 => (~((X3 = eigen__0)))) => (~((sP113 => (~((X3 = eigen__1))))))))) => (~((sP7 => (~((X3 = X1))))))))) => (~((sP141 => (~((X3 = X2))))))))) = eigen__0) => (~(((eps @ (^[X3:$i]:((~(((~(((sP135 => (~((X3 = eigen__0)))) => (~((sP40 => (~((X3 = eigen__1))))))))) => (~((sP64 => (~((X3 = X1))))))))) => (~((sP41 => (~((X3 = X2))))))))) = eigen__1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP124 => (~((X3 = eigen__0)))) => (~((sP122 => (~((X3 = eigen__1))))))))) => (~((sP52 => (~((X3 = X1))))))))) => (~((sP46 => (~((X3 = X2))))))))) = X1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP85 => (~((X3 = eigen__0)))) => (~((sP82 => (~((X3 = eigen__1))))))))) => (~((sP123 => (~((X3 = X1))))))))) => (~((sP78 => (~((X3 = X2))))))))) = X2)))))))))),introduced(assumption,[])). % 5.80/6.04 thf(h4,assumption,(~((![X1:$i]:(~(((~(((~((((eps @ (^[X2:$i]:((~(((~(((sP5 => (~((X2 = eigen__0)))) => (~((sP113 => (~((X2 = eigen__1))))))))) => (~((sP7 => (~((X2 = eigen__2))))))))) => (~((sP141 => (~((X2 = X1))))))))) = eigen__0) => (~(((eps @ (^[X2:$i]:((~(((~(((sP135 => (~((X2 = eigen__0)))) => (~((sP40 => (~((X2 = eigen__1))))))))) => (~((sP64 => (~((X2 = eigen__2))))))))) => (~((sP41 => (~((X2 = X1))))))))) = eigen__1)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP124 => (~((X2 = eigen__0)))) => (~((sP122 => (~((X2 = eigen__1))))))))) => (~((sP52 => (~((X2 = eigen__2))))))))) => (~((sP46 => (~((X2 = X1))))))))) = eigen__2)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP85 => (~((X2 = eigen__0)))) => (~((sP82 => (~((X2 = eigen__1))))))))) => (~((sP123 => (~((X2 = eigen__2))))))))) => (~((sP78 => (~((X2 = X1))))))))) = X1))))))))),introduced(assumption,[])). % 5.80/6.04 thf(h5,assumption,((~(((~((sP108 => (~(sP89))))) => (~(sP6))))) => (~(sP133))),introduced(assumption,[])). % 5.80/6.04 thf(h6,assumption,((~((sP108 => (~(sP89))))) => (~(sP6))),introduced(assumption,[])). % 5.80/6.04 thf(h7,assumption,(~(sP133)),introduced(assumption,[])). % 5.80/6.04 thf(h8,assumption,(sP108 => (~(sP89))),introduced(assumption,[])). % 5.80/6.04 thf(h9,assumption,(~(sP6)),introduced(assumption,[])). % 5.80/6.04 thf(h10,assumption,(~(sP108)),introduced(assumption,[])). % 5.80/6.04 thf(h11,assumption,(~(sP89)),introduced(assumption,[])). % 5.80/6.04 thf(h12,assumption,sP91,introduced(assumption,[])). % 5.80/6.04 thf(h13,assumption,sP109,introduced(assumption,[])). % 5.80/6.04 thf(h14,assumption,(~(sP91)),introduced(assumption,[])). % 5.80/6.04 thf(h15,assumption,(~(sP109)),introduced(assumption,[])). % 5.80/6.04 thf(1,plain,$false,inference(tab_false,[status(thm),assumptions([h12,h13,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 5.80/6.04 thf(h16,assumption,sP115,introduced(assumption,[])). % 5.80/6.04 thf(h17,assumption,(~(sP115)),introduced(assumption,[])). % 5.80/6.04 thf(2,plain,$false,inference(tab_false,[status(thm),assumptions([h16,h13,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 5.80/6.04 thf(h18,assumption,sP10,introduced(assumption,[])). % 5.80/6.04 thf(h19,assumption,(~(sP10)),introduced(assumption,[])). % 5.80/6.04 thf(h20,assumption,sP61,introduced(assumption,[])). % 5.80/6.04 thf(h21,assumption,(~(sP61)),introduced(assumption,[])). % 5.80/6.04 thf(3,plain,$false,inference(tab_false,[status(thm),assumptions([h20,h13,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 5.80/6.04 thf(h22,assumption,sP24,introduced(assumption,[])). % 5.80/6.04 thf(h23,assumption,(~(sP24)),introduced(assumption,[])). % 5.80/6.04 thf(4,plain,$false,inference(tab_false,[status(thm),assumptions([h22,h13,h21,h15,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13])). % 5.80/6.04 thf(h24,assumption,sP136,introduced(assumption,[])). % 5.80/6.04 thf(h25,assumption,(~(sP136)),introduced(assumption,[])). % 5.80/6.04 thf(h26,assumption,sP103,introduced(assumption,[])). % 5.80/6.04 thf(h27,assumption,(~(sP103)),introduced(assumption,[])). % 5.80/6.04 thf(h28,assumption,sP3,introduced(assumption,[])). % 5.80/6.04 thf(h29,assumption,(~(sP3)),introduced(assumption,[])). % 5.80/6.04 thf(5,plain,((sP25 | sP87) | sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(6,plain,((sP50 | ~(sP87)) | ~(sP67)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(7,plain,((sP145 | ~(sP87)) | ~(sP60)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(8,plain,((sP49 | sP60) | sP67),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(9,plain,((~(sP35) | sP91) | ~(sP25)),inference(mating_rule,[status(thm)],[])). % 5.80/6.04 thf(10,plain,((~(sP35) | sP104) | ~(sP50)),inference(mating_rule,[status(thm)],[])). % 5.80/6.04 thf(11,plain,((~(sP35) | sP116) | ~(sP145)),inference(mating_rule,[status(thm)],[])). % 5.80/6.04 thf(12,plain,((~(sP116) | sP104) | ~(sP49)),inference(mating_rule,[status(thm)],[])). % 5.80/6.04 thf(13,plain,~(sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(14,plain,(~(sP12) | sP55),inference(all_rule,[status(thm)],[])). % 5.80/6.04 thf(15,plain,(~(sP84) | sP56),inference(all_rule,[status(thm)],[])). % 5.80/6.04 thf(16,plain,((~(sP55) | sP91) | sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(17,plain,((~(sP56) | sP115) | sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(18,plain,(~(sP18) | sP55),inference(all_rule,[status(thm)],[])). % 5.80/6.04 thf(19,plain,((sP76 | sP35) | sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(20,plain,(sP54 | ~(sP76)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 5.80/6.04 thf(21,plain,((sP88 | ~(sP116)) | ~(sP60)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(22,plain,((sP88 | sP116) | sP60),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(23,plain,(sP84 | ~(sP88)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 5.80/6.04 thf(24,plain,((sP142 | ~(sP104)) | sP109),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(25,plain,(sP18 | ~(sP142)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 5.80/6.04 thf(26,plain,(~(sP113) | sP12),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(27,plain,(~(sP7) | sP84),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(28,plain,(sP112 | sP113),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(29,plain,(sP107 | sP108),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(30,plain,(~(sP141) | sP18),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(31,plain,(sP45 | sP7),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(32,plain,((~(sP48) | ~(sP107)) | ~(sP112)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(33,plain,(sP28 | sP141),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(34,plain,((~(sP21) | sP48) | ~(sP45)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(35,plain,((~(sP73) | sP21) | ~(sP28)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(36,plain,sP26,inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(37,plain,(sP5 | ~(sP54)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(38,plain,((~(sP58) | ~(sP5)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(39,plain,(sP106 | sP58),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(40,plain,(sP100 | ~(sP106)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(41,plain,(sP4 | ~(sP100)),inference(prop_rule,[status(thm)],[])). % 5.80/6.04 thf(42,plain,(~(sP101) | ~(sP4)),inference(all_rule,[status(thm)],[])). % 6.03/6.39 % SZS status Theorem % 6.03/6.39 % Mode: mode454 % 6.03/6.39 % Inferences: 1505 % 6.03/6.39 % SZS output start Proof % 6.03/6.39 thf(ty_eigen__14, type, eigen__14 : $o). % 6.03/6.39 thf(ty_eigen__2, type, eigen__2 : $i). % 6.03/6.39 thf(ty_eigen__16, type, eigen__16 : $o). % 6.03/6.39 thf(ty_eps, type, eps : (($i>$o)>$i)). % 6.03/6.39 thf(ty_eigen__1, type, eigen__1 : $i). % 6.03/6.39 thf(ty_eigen__0, type, eigen__0 : $i). % 6.03/6.39 thf(ty_eigen__4, type, eigen__4 : $o). % 6.03/6.39 thf(ty_eigen__19, type, eigen__19 : $o). % 6.03/6.39 thf(ty_f0, type, f0 : ($o>$o)). % 6.03/6.39 thf(ty_eigen__3, type, eigen__3 : $i). % 6.03/6.39 thf(ty_eigen__8, type, eigen__8 : $o). % 6.03/6.39 thf(ty_eigen__9, type, eigen__9 : $o). % 6.03/6.39 thf(ty_f3, type, f3 : ($o>$o)). % 6.03/6.39 thf(ty_eigen__18, type, eigen__18 : $o). % 6.03/6.39 thf(ty_f2, type, f2 : ($o>$o)). % 6.03/6.39 thf(ty_f1, type, f1 : ($o>$o)). % 6.03/6.39 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 6.03/6.39 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((~(((~(((~((((eps @ (^[X2:$i]:((~(((~((((f0 = (^[X3:$o]:$false)) => (~((X2 = eigen__0)))) => (~(((f0 = (^[X3:$o]:(~(X3)))) => (~((X2 = eigen__1))))))))) => (~(((f0 = (^[X3:$o]:X3)) => (~((X2 = eigen__2))))))))) => (~(((f0 = (^[X3:$o]:(~($false)))) => (~((X2 = X1))))))))) = eigen__0) => (~(((eps @ (^[X2:$i]:((~(((~((((f1 = (^[X3:$o]:$false)) => (~((X2 = eigen__0)))) => (~(((f1 = (^[X3:$o]:(~(X3)))) => (~((X2 = eigen__1))))))))) => (~(((f1 = (^[X3:$o]:X3)) => (~((X2 = eigen__2))))))))) => (~(((f1 = (^[X3:$o]:(~($false)))) => (~((X2 = X1))))))))) = eigen__1)))))) => (~(((eps @ (^[X2:$i]:((~(((~((((f2 = (^[X3:$o]:$false)) => (~((X2 = eigen__0)))) => (~(((f2 = (^[X3:$o]:(~(X3)))) => (~((X2 = eigen__1))))))))) => (~(((f2 = (^[X3:$o]:X3)) => (~((X2 = eigen__2))))))))) => (~(((f2 = (^[X3:$o]:(~($false)))) => (~((X2 = X1))))))))) = eigen__2)))))) => (~(((eps @ (^[X2:$i]:((~(((~((((f3 = (^[X3:$o]:$false)) => (~((X2 = eigen__0)))) => (~(((f3 = (^[X3:$o]:(~(X3)))) => (~((X2 = eigen__1))))))))) => (~(((f3 = (^[X3:$o]:X3)) => (~((X2 = eigen__2))))))))) => (~(((f3 = (^[X3:$o]:(~($false)))) => (~((X2 = X1))))))))) = X1)))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 6.03/6.39 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~(((~(((~((((eps @ (^[X4:$i]:((~(((~((((f0 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f0 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f0 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f0 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = eigen__0) => (~(((eps @ (^[X4:$i]:((~(((~((((f1 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f1 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f1 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f1 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X1)))))) => (~(((eps @ (^[X4:$i]:((~(((~((((f2 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f2 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f2 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f2 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X2)))))) => (~(((eps @ (^[X4:$i]:((~(((~((((f3 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f3 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f3 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f3 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 6.03/6.39 thf(h1, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 6.03/6.39 thf(eigendef_eigen__14, definition, eigen__14 = (eps__1 @ (^[X1:$o]:(~(((f0 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__14])])). % 6.03/6.39 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~((((f0 = (^[X6:$o]:$false)) => (~((X5 = X1)))) => (~(((f0 = (^[X6:$o]:(~(X6)))) => (~((X5 = X2))))))))) => (~(((f0 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~(((f0 = (^[X6:$o]:(~($false)))) => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~((((f1 = (^[X6:$o]:$false)) => (~((X5 = X1)))) => (~(((f1 = (^[X6:$o]:(~(X6)))) => (~((X5 = X2))))))))) => (~(((f1 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~(((f1 = (^[X6:$o]:(~($false)))) => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~((((f2 = (^[X6:$o]:$false)) => (~((X5 = X1)))) => (~(((f2 = (^[X6:$o]:(~(X6)))) => (~((X5 = X2))))))))) => (~(((f2 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~(((f2 = (^[X6:$o]:(~($false)))) => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~((((f3 = (^[X6:$o]:$false)) => (~((X5 = X1)))) => (~(((f3 = (^[X6:$o]:(~(X6)))) => (~((X5 = X2))))))))) => (~(((f3 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~(((f3 = (^[X6:$o]:(~($false)))) => (~((X5 = X4))))))))) = X4))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 6.03/6.39 thf(eigendef_eigen__18, definition, eigen__18 = (eps__1 @ (^[X1:$o]:(~(((f1 @ X1) = $false))))), introduced(definition,[new_symbols(definition,[eigen__18])])). % 6.03/6.39 thf(eigendef_eigen__8, definition, eigen__8 = (eps__1 @ (^[X1:$o]:(~(((f2 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 6.03/6.39 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(~(((~(((~((((eps @ (^[X3:$i]:((~(((~((((f0 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~(((f0 = (^[X4:$o]:(~(X4)))) => (~((X3 = eigen__1))))))))) => (~(((f0 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f0 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = eigen__0) => (~(((eps @ (^[X3:$i]:((~(((~((((f1 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~(((f1 = (^[X4:$o]:(~(X4)))) => (~((X3 = eigen__1))))))))) => (~(((f1 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f1 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = eigen__1)))))) => (~(((eps @ (^[X3:$i]:((~(((~((((f2 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~(((f2 = (^[X4:$o]:(~(X4)))) => (~((X3 = eigen__1))))))))) => (~(((f2 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f2 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = X1)))))) => (~(((eps @ (^[X3:$i]:((~(((~((((f3 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~(((f3 = (^[X4:$o]:(~(X4)))) => (~((X3 = eigen__1))))))))) => (~(((f3 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f3 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 6.03/6.39 thf(eigendef_eigen__4, definition, eigen__4 = (eps__1 @ (^[X1:$o]:(~(((f3 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 6.03/6.39 thf(eigendef_eigen__16, definition, eigen__16 = (eps__1 @ (^[X1:$o]:(~(((f1 @ X1) = (~($false))))))), introduced(definition,[new_symbols(definition,[eigen__16])])). % 6.03/6.39 thf(eigendef_eigen__9, definition, eigen__9 = (eps__1 @ (^[X1:$o]:(~(((f2 @ X1) = X1))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 6.03/6.39 thf(eigendef_eigen__19, definition, eigen__19 = (eps__1 @ (^[X1:$o]:(~(((f1 @ X1) = (~(X1))))))), introduced(definition,[new_symbols(definition,[eigen__19])])). % 6.03/6.39 thf(sP1,plain,sP1 <=> ((f3 @ (~($false))) = (~($false))),introduced(definition,[new_symbols(definition,[sP1])])). % 6.03/6.39 thf(sP2,plain,sP2 <=> ((f0 @ eigen__14) = $false),introduced(definition,[new_symbols(definition,[sP2])])). % 6.03/6.39 thf(sP3,plain,sP3 <=> (f3 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 6.03/6.39 thf(sP4,plain,sP4 <=> ((f0 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP4])])). % 6.03/6.39 thf(sP5,plain,sP5 <=> ((f1 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP5])])). % 6.03/6.39 thf(sP6,plain,sP6 <=> ($false = eigen__4),introduced(definition,[new_symbols(definition,[sP6])])). % 6.03/6.39 thf(sP7,plain,sP7 <=> (eigen__9 = eigen__8),introduced(definition,[new_symbols(definition,[sP7])])). % 6.03/6.39 thf(sP8,plain,sP8 <=> eigen__14,introduced(definition,[new_symbols(definition,[sP8])])). % 6.03/6.39 thf(sP9,plain,sP9 <=> ((f1 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP9])])). % 6.03/6.39 thf(sP10,plain,sP10 <=> eigen__19,introduced(definition,[new_symbols(definition,[sP10])])). % 6.03/6.39 thf(sP11,plain,sP11 <=> ((f0 = (^[X1:$o]:$false)) => (~((eigen__0 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP11])])). % 6.03/6.39 thf(sP12,plain,sP12 <=> (f1 @ (~($false))),introduced(definition,[new_symbols(definition,[sP12])])). % 6.03/6.39 thf(sP13,plain,sP13 <=> (![X1:$o]:((f1 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP13])])). % 6.03/6.39 thf(sP14,plain,sP14 <=> ((f2 = (^[X1:$o]:X1)) => (~((eigen__2 = eigen__2)))),introduced(definition,[new_symbols(definition,[sP14])])). % 6.03/6.39 thf(sP15,plain,sP15 <=> (sP11 => (~(((f0 = (^[X1:$o]:(~(X1)))) => (~((eigen__0 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 6.03/6.39 thf(sP16,plain,sP16 <=> ((f0 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f0 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP16])])). % 6.03/6.39 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:(~(((~(((~((((eps @ (^[X4:$i]:((~(((~((((f0 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f0 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f0 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f0 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = eigen__0) => (~(((eps @ (^[X4:$i]:((~(((~((((f1 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f1 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f1 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f1 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X1)))))) => (~(((eps @ (^[X4:$i]:((~(((~((((f2 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~(((f2 = (^[X5:$o]:(~(X5)))) => (~((X4 = X1))))))))) => (~(((f2 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f2 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X2)))))) => (~(((eps @ (^[X4:$i]:((~(((~((((f3 = (^[X5:$o]:$false)) => (~((X4 = eigen__0)))) => (~((sP3 => (~((X4 = X1))))))))) => (~(((f3 = (^[X5:$o]:X5)) => (~((X4 = X2))))))))) => (~(((f3 = (^[X5:$o]:(~($false)))) => (~((X4 = X3))))))))) = X3))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 6.03/6.39 thf(sP18,plain,sP18 <=> (eigen__3 = eigen__3),introduced(definition,[new_symbols(definition,[sP18])])). % 6.03/6.39 thf(sP19,plain,sP19 <=> (![X1:$o]:((f0 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP19])])). % 6.03/6.39 thf(sP20,plain,sP20 <=> (![X1:$o]:((f1 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP20])])). % 6.03/6.39 thf(sP21,plain,sP21 <=> (f0 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP21])])). % 6.03/6.39 thf(sP22,plain,sP22 <=> ((~($false)) = eigen__4),introduced(definition,[new_symbols(definition,[sP22])])). % 6.03/6.39 thf(sP23,plain,sP23 <=> (((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP23])])). % 6.03/6.39 thf(sP24,plain,sP24 <=> (![X1:$i]:(~(((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 6.03/6.39 thf(sP25,plain,sP25 <=> ((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f1 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP25])])). % 6.03/6.39 thf(sP26,plain,sP26 <=> ((f2 @ $false) = $false),introduced(definition,[new_symbols(definition,[sP26])])). % 6.03/6.39 thf(sP27,plain,sP27 <=> (f1 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP27])])). % 6.03/6.39 thf(sP28,plain,sP28 <=> (f1 @ $false),introduced(definition,[new_symbols(definition,[sP28])])). % 6.03/6.39 thf(sP29,plain,sP29 <=> ((~(((~((((f3 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP3 => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 6.03/6.39 thf(sP30,plain,sP30 <=> ((~(((~((((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f1 = (^[X1:$o]:(~(X1)))) => (~(sP25)))))))) => (~(sP5))))) => (~((sP27 => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 6.03/6.39 thf(sP31,plain,sP31 <=> ((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP31])])). % 6.03/6.39 thf(sP32,plain,sP32 <=> ((f0 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~(((f0 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP32])])). % 6.03/6.39 thf(sP33,plain,sP33 <=> (![X1:$i]:(~(((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f1 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP33])])). % 6.03/6.39 thf(sP34,plain,sP34 <=> (f2 @ (~($false))),introduced(definition,[new_symbols(definition,[sP34])])). % 6.03/6.39 thf(sP35,plain,sP35 <=> (sP28 = $false),introduced(definition,[new_symbols(definition,[sP35])])). % 6.03/6.39 thf(sP36,plain,sP36 <=> (![X1:$o]:((f2 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP36])])). % 6.03/6.39 thf(sP37,plain,sP37 <=> (f1 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP37])])). % 6.03/6.39 thf(sP38,plain,sP38 <=> ((f2 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP38])])). % 6.03/6.39 thf(sP39,plain,sP39 <=> ((~(sP15)) => (~(((f0 = (^[X1:$o]:X1)) => (~((eigen__0 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP39])])). % 6.03/6.39 thf(sP40,plain,sP40 <=> (sP10 = eigen__16),introduced(definition,[new_symbols(definition,[sP40])])). % 6.03/6.39 thf(sP41,plain,sP41 <=> ((~((((f3 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP3 => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~((((f3 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP41])])). % 6.03/6.39 thf(sP42,plain,sP42 <=> ((~(((~((((f3 = (^[X1:$o]:$false)) => (~((eigen__3 = eigen__0)))) => (~((sP3 => (~((eigen__3 = eigen__1))))))))) => (~(((f3 = (^[X1:$o]:X1)) => (~((eigen__3 = eigen__2))))))))) => (~(((f3 = (^[X1:$o]:(~($false)))) => (~(sP18)))))),introduced(definition,[new_symbols(definition,[sP42])])). % 6.03/6.39 thf(sP43,plain,sP43 <=> ((~((((f2 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~(((f2 = (^[X1:$o]:(~(X1)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))))) => (~(((f2 = (^[X1:$o]:X1)) => (~(sP31)))))),introduced(definition,[new_symbols(definition,[sP43])])). % 6.03/6.39 thf(sP44,plain,sP44 <=> (f2 @ $false),introduced(definition,[new_symbols(definition,[sP44])])). % 6.03/6.39 thf(sP45,plain,sP45 <=> (f3 @ eigen__4),introduced(definition,[new_symbols(definition,[sP45])])). % 6.03/6.39 thf(sP46,plain,sP46 <=> (f3 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP46])])). % 6.03/6.39 thf(sP47,plain,sP47 <=> ((f2 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~(((f2 = (^[X2:$o]:(~(X2)))) => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f2 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP47])])). % 6.03/6.39 thf(sP48,plain,sP48 <=> (eigen__18 = sP10),introduced(definition,[new_symbols(definition,[sP48])])). % 6.03/6.39 thf(sP49,plain,sP49 <=> ((f2 @ eigen__9) = eigen__9),introduced(definition,[new_symbols(definition,[sP49])])). % 6.03/6.39 thf(sP50,plain,sP50 <=> ((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3),introduced(definition,[new_symbols(definition,[sP50])])). % 6.03/6.39 thf(sP51,plain,sP51 <=> (![X1:$o]:((f3 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP51])])). % 6.03/6.39 thf(sP52,plain,sP52 <=> (sP8 = $false),introduced(definition,[new_symbols(definition,[sP52])])). % 6.03/6.39 thf(sP53,plain,sP53 <=> (f2 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP53])])). % 6.03/6.39 thf(sP54,plain,sP54 <=> (((f1 = (^[X1:$o]:$false)) => (~((eigen__1 = eigen__0)))) => (~((sP37 => (~((eigen__1 = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP54])])). % 6.03/6.39 thf(sP55,plain,sP55 <=> ((f2 = (^[X1:$o]:X1)) => (~(sP31))),introduced(definition,[new_symbols(definition,[sP55])])). % 6.03/6.39 thf(sP56,plain,sP56 <=> ((f0 @ (~($false))) = (~($false))),introduced(definition,[new_symbols(definition,[sP56])])). % 6.03/6.39 thf(sP57,plain,sP57 <=> (f2 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP57])])). % 6.03/6.39 thf(sP58,plain,sP58 <=> (sP12 = $false),introduced(definition,[new_symbols(definition,[sP58])])). % 6.03/6.39 thf(sP59,plain,sP59 <=> eigen__8,introduced(definition,[new_symbols(definition,[sP59])])). % 6.03/6.39 thf(sP60,plain,sP60 <=> (![X1:$o]:((f0 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP60])])). % 6.03/6.39 thf(sP61,plain,sP61 <=> ((~((((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP37 => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP37 => (~(sP25)))))))) => (~(sP5))),introduced(definition,[new_symbols(definition,[sP61])])). % 6.03/6.39 thf(sP62,plain,sP62 <=> (sP12 = (~($false))),introduced(definition,[new_symbols(definition,[sP62])])). % 6.03/6.39 thf(sP63,plain,sP63 <=> (sP16 => (~(sP32))),introduced(definition,[new_symbols(definition,[sP63])])). % 6.03/6.39 thf(sP64,plain,sP64 <=> ((~(((~(sP23)) => (~(sP31))))) => (~(sP50))),introduced(definition,[new_symbols(definition,[sP64])])). % 6.03/6.39 thf(sP65,plain,sP65 <=> (![X1:$o]:((f3 @ X1) = (~($false)))),introduced(definition,[new_symbols(definition,[sP65])])). % 6.03/6.39 thf(sP66,plain,sP66 <=> ((~(sP23)) => (~(sP31))),introduced(definition,[new_symbols(definition,[sP66])])). % 6.03/6.39 thf(sP67,plain,sP67 <=> (![X1:$o]:((f2 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP67])])). % 6.03/6.39 thf(sP68,plain,sP68 <=> (f0 = (^[X1:$o]:(~(X1)))),introduced(definition,[new_symbols(definition,[sP68])])). % 6.03/6.39 thf(sP69,plain,sP69 <=> (![X1:$i]:(![X2:$i]:(~(((~(((~((((eps @ (^[X3:$i]:((~(((~(((sP21 => (~((X3 = eigen__0)))) => (~((sP68 => (~((X3 = eigen__1))))))))) => (~(((f0 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f0 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = eigen__0) => (~(((eps @ (^[X3:$i]:((~(((~((((f1 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~((sP37 => (~((X3 = eigen__1))))))))) => (~(((f1 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~((sP27 => (~((X3 = X2))))))))) = eigen__1)))))) => (~(((eps @ (^[X3:$i]:((~(((~((((f2 = (^[X4:$o]:$false)) => (~((X3 = eigen__0)))) => (~((sP57 => (~((X3 = eigen__1))))))))) => (~(((f2 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~((sP53 => (~((X3 = X2))))))))) = X1)))))) => (~(((eps @ (^[X3:$i]:((~(((~(((sP46 => (~((X3 = eigen__0)))) => (~((sP3 => (~((X3 = eigen__1))))))))) => (~(((f3 = (^[X4:$o]:X4)) => (~((X3 = X1))))))))) => (~(((f3 = (^[X4:$o]:(~($false)))) => (~((X3 = X2))))))))) = X2)))))))),introduced(definition,[new_symbols(definition,[sP69])])). % 6.03/6.39 thf(sP70,plain,sP70 <=> ((f1 @ sP10) = (~(sP10))),introduced(definition,[new_symbols(definition,[sP70])])). % 6.03/6.39 thf(sP71,plain,sP71 <=> ((~($false)) = eigen__9),introduced(definition,[new_symbols(definition,[sP71])])). % 6.03/6.39 thf(sP72,plain,sP72 <=> (f1 @ eigen__16),introduced(definition,[new_symbols(definition,[sP72])])). % 6.03/6.39 thf(sP73,plain,sP73 <=> eigen__9,introduced(definition,[new_symbols(definition,[sP73])])). % 6.03/6.39 thf(sP74,plain,sP74 <=> ((f0 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~((sP68 => (~((X1 = eigen__1))))))))) => (~(((f0 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP74])])). % 6.03/6.39 thf(sP75,plain,sP75 <=> (f3 @ (~($false))),introduced(definition,[new_symbols(definition,[sP75])])). % 6.03/6.39 thf(sP76,plain,sP76 <=> ((~(sP63)) => (~(sP74))),introduced(definition,[new_symbols(definition,[sP76])])). % 6.03/6.39 thf(sP77,plain,sP77 <=> (((f2 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP57 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP53 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP57 => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP57 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP53 => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP77])])). % 6.03/6.39 thf(sP78,plain,sP78 <=> (f0 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP78])])). % 6.03/6.39 thf(sP79,plain,sP79 <=> eigen__16,introduced(definition,[new_symbols(definition,[sP79])])). % 6.03/6.39 thf(sP80,plain,sP80 <=> (f1 @ eigen__18),introduced(definition,[new_symbols(definition,[sP80])])). % 6.03/6.39 thf(sP81,plain,sP81 <=> (sP57 => (~(((eps @ (^[X1:$i]:((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP57 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP53 => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP81])])). % 6.03/6.39 thf(sP82,plain,sP82 <=> ((~(((~(sP54)) => (~(((f1 = (^[X1:$o]:X1)) => (~((eigen__1 = eigen__2))))))))) => (~((sP27 => (~((eigen__1 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP82])])). % 6.03/6.39 thf(sP83,plain,sP83 <=> (![X1:$i]:(~(((~(((~((((f2 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP57 => (~((X1 = eigen__1))))))))) => (~(((f2 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP53 => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP83])])). % 6.03/6.39 thf(sP84,plain,sP84 <=> ((~(sP76)) => (~(((f0 = (^[X1:$o]:(~($false)))) => (~(((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~((sP68 => (~((X1 = eigen__1))))))))) => (~((sP78 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP84])])). % 6.03/6.39 thf(sP85,plain,sP85 <=> (((f1 = (^[X1:$o]:$false)) => (~(((eps @ (^[X1:$i]:((~(((~((((f1 = (^[X2:$o]:$false)) => (~((X1 = eigen__0)))) => (~((sP37 => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP37 => (~(sP25)))))),introduced(definition,[new_symbols(definition,[sP85])])). % 6.03/6.39 thf(sP86,plain,sP86 <=> (![X1:$o]:((f1 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP86])])). % 6.03/6.39 thf(sP87,plain,sP87 <=> ((f0 @ $false) = $false),introduced(definition,[new_symbols(definition,[sP87])])). % 6.03/6.39 thf(sP88,plain,sP88 <=> (![X1:$i]:(~(((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~((sP68 => (~((X1 = eigen__1))))))))) => (~((sP78 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3)))))))))),introduced(definition,[new_symbols(definition,[sP88])])). % 6.03/6.39 thf(sP89,plain,sP89 <=> (![X1:$o]:((f3 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP89])])). % 6.03/6.39 thf(sP90,plain,sP90 <=> ((~($false)) = sP59),introduced(definition,[new_symbols(definition,[sP90])])). % 6.03/6.39 thf(sP91,plain,sP91 <=> (f1 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP91])])). % 6.03/6.39 thf(sP92,plain,sP92 <=> ((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~((sP68 => (~((X1 = eigen__1))))))))) => (~((sP78 => (~((X1 = eigen__2))))))))) => (~(((f0 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0),introduced(definition,[new_symbols(definition,[sP92])])). % 6.03/6.39 thf(sP93,plain,sP93 <=> (sP27 => (~(((eps @ (^[X1:$i]:((~(((~(((sP91 => (~((X1 = eigen__0)))) => (~((sP37 => (~((X1 = eigen__1))))))))) => (~(((f1 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP93])])). % 6.03/6.39 thf(sP94,plain,sP94 <=> (f0 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP94])])). % 6.03/6.39 thf(sP95,plain,sP95 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP95])])). % 6.03/6.39 thf(sP96,plain,sP96 <=> ((f3 = (^[X1:$o]:(~($false)))) => (~(sP50))),introduced(definition,[new_symbols(definition,[sP96])])). % 6.03/6.39 thf(sP97,plain,sP97 <=> (![X1:$o]:((f2 @ X1) = $false)),introduced(definition,[new_symbols(definition,[sP97])])). % 6.03/6.39 thf(sP98,plain,sP98 <=> ((~(((~((((f2 = (^[X1:$o]:$false)) => (~((eigen__2 = eigen__0)))) => (~((sP57 => (~((eigen__2 = eigen__1))))))))) => (~(sP14))))) => (~((sP53 => (~((eigen__2 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP98])])). % 6.03/6.39 thf(sP99,plain,sP99 <=> ((f3 @ $false) = (~($false))),introduced(definition,[new_symbols(definition,[sP99])])). % 6.03/6.39 thf(sP100,plain,sP100 <=> (sP37 => (~((eigen__1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP100])])). % 6.03/6.39 thf(sP101,plain,sP101 <=> ($false = sP79),introduced(definition,[new_symbols(definition,[sP101])])). % 6.03/6.39 thf(sP102,plain,sP102 <=> (sP80 = $false),introduced(definition,[new_symbols(definition,[sP102])])). % 6.03/6.39 thf(sP103,plain,sP103 <=> (sP8 = (~($false))),introduced(definition,[new_symbols(definition,[sP103])])). % 6.03/6.39 thf(sP104,plain,sP104 <=> ((sP46 => (~(((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__0)))) => (~((sP3 => (~(((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1))))))),introduced(definition,[new_symbols(definition,[sP104])])). % 6.03/6.39 thf(sP105,plain,sP105 <=> (f3 @ $false),introduced(definition,[new_symbols(definition,[sP105])])). % 6.03/6.39 thf(sP106,plain,sP106 <=> (f1 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP106])])). % 6.03/6.39 thf(sP107,plain,sP107 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(~(((~(((~((((eps @ (^[X5:$i]:((~(((~(((sP21 => (~((X5 = X1)))) => (~((sP68 => (~((X5 = X2))))))))) => (~((sP78 => (~((X5 = X3))))))))) => (~((sP94 => (~((X5 = X4))))))))) = X1) => (~(((eps @ (^[X5:$i]:((~(((~(((sP91 => (~((X5 = X1)))) => (~((sP37 => (~((X5 = X2))))))))) => (~((sP106 => (~((X5 = X3))))))))) => (~((sP27 => (~((X5 = X4))))))))) = X2)))))) => (~(((eps @ (^[X5:$i]:((~(((~((((f2 = (^[X6:$o]:$false)) => (~((X5 = X1)))) => (~((sP57 => (~((X5 = X2))))))))) => (~(((f2 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~((sP53 => (~((X5 = X4))))))))) = X3)))))) => (~(((eps @ (^[X5:$i]:((~(((~(((sP46 => (~((X5 = X1)))) => (~((sP3 => (~((X5 = X2))))))))) => (~(((f3 = (^[X6:$o]:X6)) => (~((X5 = X3))))))))) => (~(((f3 = (^[X6:$o]:(~($false)))) => (~((X5 = X4))))))))) = X4)))))))))),introduced(definition,[new_symbols(definition,[sP107])])). % 6.03/6.39 thf(sP108,plain,sP108 <=> (sP3 => (~(((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP108])])). % 6.03/6.39 thf(sP109,plain,sP109 <=> ((~(sP39)) => (~((sP94 => (~((eigen__0 = eigen__3))))))),introduced(definition,[new_symbols(definition,[sP109])])). % 6.03/6.39 thf(sP110,plain,sP110 <=> (f2 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP110])])). % 6.03/6.39 thf(sP111,plain,sP111 <=> ((f2 @ sP59) = (~($false))),introduced(definition,[new_symbols(definition,[sP111])])). % 6.03/6.39 thf(sP112,plain,sP112 <=> ((f3 = (^[X1:$o]:X1)) => (~(((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~(((f3 = (^[X2:$o]:X2)) => (~((X1 = eigen__2))))))))) => (~(((f3 = (^[X2:$o]:(~($false)))) => (~((X1 = eigen__3))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP112])])). % 6.03/6.39 thf(sP113,plain,sP113 <=> (sP94 => (~(((eps @ (^[X1:$i]:((~(((~(((sP21 => (~((X1 = eigen__0)))) => (~((sP68 => (~((X1 = eigen__1))))))))) => (~((sP78 => (~((X1 = eigen__2))))))))) => (~((sP94 => (~((X1 = eigen__3))))))))) = eigen__3)))),introduced(definition,[new_symbols(definition,[sP113])])). % 6.03/6.39 thf(sP114,plain,sP114 <=> (f0 @ $false),introduced(definition,[new_symbols(definition,[sP114])])). % 6.03/6.39 thf(sP115,plain,sP115 <=> (f0 @ sP8),introduced(definition,[new_symbols(definition,[sP115])])). % 6.03/6.39 thf(sP116,plain,sP116 <=> eigen__18,introduced(definition,[new_symbols(definition,[sP116])])). % 6.03/6.39 thf(sP117,plain,sP117 <=> ((f0 @ (~($false))) = $false),introduced(definition,[new_symbols(definition,[sP117])])). % 6.03/6.39 thf(sP118,plain,sP118 <=> (![X1:$o]:((f2 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP118])])). % 6.03/6.39 thf(sP119,plain,sP119 <=> ((~(sP54)) => (~((sP106 => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP119])])). % 6.03/6.39 thf(sP120,plain,sP120 <=> (f2 = (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP120])])). % 6.03/6.39 thf(sP121,plain,sP121 <=> (f2 @ sP59),introduced(definition,[new_symbols(definition,[sP121])])). % 6.03/6.39 thf(sP122,plain,sP122 <=> (![X1:$i]:(~(((~(((~((((eps @ (^[X2:$i]:((~(((~(((sP21 => (~((X2 = eigen__0)))) => (~((sP68 => (~((X2 = eigen__1))))))))) => (~((sP78 => (~((X2 = eigen__2))))))))) => (~((sP94 => (~((X2 = X1))))))))) = eigen__0) => (~(((eps @ (^[X2:$i]:((~(((~(((sP91 => (~((X2 = eigen__0)))) => (~((sP37 => (~((X2 = eigen__1))))))))) => (~((sP106 => (~((X2 = eigen__2))))))))) => (~((sP27 => (~((X2 = X1))))))))) = eigen__1)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP120 => (~((X2 = eigen__0)))) => (~((sP57 => (~((X2 = eigen__1))))))))) => (~((sP110 => (~((X2 = eigen__2))))))))) => (~((sP53 => (~((X2 = X1))))))))) = eigen__2)))))) => (~(((eps @ (^[X2:$i]:((~(((~(((sP46 => (~((X2 = eigen__0)))) => (~((sP3 => (~((X2 = eigen__1))))))))) => (~(((f3 = (^[X3:$o]:X3)) => (~((X2 = eigen__2))))))))) => (~(((f3 = (^[X3:$o]:(~($false)))) => (~((X2 = X1))))))))) = X1))))))),introduced(definition,[new_symbols(definition,[sP122])])). % 6.03/6.39 thf(sP123,plain,sP123 <=> (f3 = (^[X1:$o]:(~($false)))),introduced(definition,[new_symbols(definition,[sP123])])). % 6.03/6.39 thf(sP124,plain,sP124 <=> (sP34 = $false),introduced(definition,[new_symbols(definition,[sP124])])). % 6.03/6.39 thf(sP125,plain,sP125 <=> (![X1:$o]:((f3 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP125])])). % 6.03/6.39 thf(sP126,plain,sP126 <=> (![X1:$o]:((f0 @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP126])])). % 6.03/6.39 thf(sP127,plain,sP127 <=> (sP123 => (~(sP18))),introduced(definition,[new_symbols(definition,[sP127])])). % 6.03/6.39 thf(sP128,plain,sP128 <=> ((~(((sP120 => (~((eigen__2 = eigen__0)))) => (~((sP57 => (~((eigen__2 = eigen__1))))))))) => (~(sP14))),introduced(definition,[new_symbols(definition,[sP128])])). % 6.03/6.39 thf(sP129,plain,sP129 <=> (f3 = (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP129])])). % 6.03/6.39 thf(sP130,plain,sP130 <=> (eigen__1 = eigen__1),introduced(definition,[new_symbols(definition,[sP130])])). % 6.03/6.39 thf(sP131,plain,sP131 <=> (f1 @ sP10),introduced(definition,[new_symbols(definition,[sP131])])). % 6.03/6.39 thf(sP132,plain,sP132 <=> (sP116 = (~($false))),introduced(definition,[new_symbols(definition,[sP132])])). % 6.03/6.39 thf(sP133,plain,sP133 <=> eigen__4,introduced(definition,[new_symbols(definition,[sP133])])). % 6.03/6.39 thf(sP134,plain,sP134 <=> (sP72 = (~($false))),introduced(definition,[new_symbols(definition,[sP134])])). % 6.03/6.39 thf(sP135,plain,sP135 <=> (sP105 = $false),introduced(definition,[new_symbols(definition,[sP135])])). % 6.03/6.39 thf(sP136,plain,sP136 <=> (sP75 = $false),introduced(definition,[new_symbols(definition,[sP136])])). % 6.03/6.39 thf(sP137,plain,sP137 <=> (sP120 => (~(((eps @ (^[X1:$i]:((~(((~(((sP120 => (~((X1 = eigen__0)))) => (~((sP57 => (~((X1 = eigen__1))))))))) => (~((sP110 => (~((X1 = eigen__2))))))))) => (~((sP53 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP137])])). % 6.03/6.39 thf(sP138,plain,sP138 <=> (![X1:$o]:((f0 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP138])])). % 6.03/6.39 thf(sP139,plain,sP139 <=> (sP37 => (~(sP25))),introduced(definition,[new_symbols(definition,[sP139])])). % 6.03/6.39 thf(sP140,plain,sP140 <=> (sP34 = (~($false))),introduced(definition,[new_symbols(definition,[sP140])])). % 6.03/6.39 thf(sP141,plain,sP141 <=> (f0 @ (~($false))),introduced(definition,[new_symbols(definition,[sP141])])). % 6.03/6.39 thf(sP142,plain,sP142 <=> (sP91 => (~(((eps @ (^[X1:$i]:((~(((~(((sP91 => (~((X1 = eigen__0)))) => (~((sP37 => (~((X1 = eigen__1))))))))) => (~((sP106 => (~((X1 = eigen__2))))))))) => (~((sP27 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP142])])). % 6.03/6.39 thf(sP143,plain,sP143 <=> (f2 @ sP73),introduced(definition,[new_symbols(definition,[sP143])])). % 6.03/6.39 thf(sP144,plain,sP144 <=> (eigen__2 = eigen__2),introduced(definition,[new_symbols(definition,[sP144])])). % 6.03/6.39 thf(sP145,plain,sP145 <=> ((~(sP43)) => (~(sP47))),introduced(definition,[new_symbols(definition,[sP145])])). % 6.03/6.39 thf(sP146,plain,sP146 <=> (sP45 = (~($false))),introduced(definition,[new_symbols(definition,[sP146])])). % 6.03/6.39 thf(sP147,plain,sP147 <=> (sP46 => (~(((eps @ (^[X1:$i]:((~(((~(((sP46 => (~((X1 = eigen__0)))) => (~((sP3 => (~((X1 = eigen__1))))))))) => (~((sP129 => (~((X1 = eigen__2))))))))) => (~((sP123 => (~((X1 = eigen__3))))))))) = eigen__0)))),introduced(definition,[new_symbols(definition,[sP147])])). % 6.03/6.39 thf(sP148,plain,sP148 <=> $false,introduced(definition,[new_symbols(definition,[sP148])])). % 6.03/6.39 thf(sP149,plain,sP149 <=> (![X1:$o]:((f1 @ X1) = (~(X1)))),introduced(definition,[new_symbols(definition,[sP149])])). % 6.03/6.39 thf(def_case,definition,(case = (^[X1:$o>$o]:(^[X2:$i]:(^[X3:$i]:(^[X4:$i]:(^[X5:$i]:(eps @ (^[X6:$i]:((~(((~((((X1 = (^[X7:$o]:sP148)) => (~((X6 = X2)))) => (~(((X1 = (^[X7:$o]:(~(X7)))) => (~((X6 = X3))))))))) => (~(((X1 = (^[X7:$o]:X7)) => (~((X6 = X4))))))))) => (~(((X1 = (^[X7:$o]:(~(sP148)))) => (~((X6 = X5)))))))))))))))). % 6.03/6.39 thf(conj,conjecture,sP107). % 6.03/6.39 thf(h2,negated_conjecture,(~(sP107)),inference(assume_negation,[status(cth)],[conj])). % 6.03/6.39 thf(1,plain,(sP139 | sP25),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(2,plain,(~(sP86) | sP35),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(3,plain,(~(sP91) | sP86),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(4,plain,(sP142 | sP91),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(5,plain,(~(sP138) | sP4),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(6,plain,(~(sP68) | sP138),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(7,plain,(sP32 | sP68),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(8,plain,(sP16 | sP92),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(9,plain,(~(sP67) | sP38),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(10,plain,(~(sP57) | sP67),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(11,plain,(sP81 | sP57),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(12,plain,((~(sP124) | ~(sP34)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(13,plain,(~(sP97) | sP124),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(14,plain,(~(sP120) | sP97),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(15,plain,(sP137 | sP120),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(16,plain,((sP48 | sP116) | sP10),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(17,plain,((sP40 | ~(sP10)) | ~(sP79)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(18,plain,((sP132 | ~(sP116)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(19,plain,((sP101 | sP148) | sP79),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(20,plain,((~(sP35) | ~(sP28)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(21,plain,(~(sP20) | sP35),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(22,plain,(~(sP106) | sP20),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(23,plain,(sP5 | sP106),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(24,plain,((~(sP85) | ~(sP142)) | ~(sP139)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(25,plain,((sP103 | ~(sP8)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(26,plain,((sP52 | sP8) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(27,plain,((~(sP136) | ~(sP75)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(28,plain,((~(sP62) | sP12) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(29,plain,(~(sP126) | sP56),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(30,plain,(~(sP78) | sP126),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(31,plain,(sP74 | sP78),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(32,plain,((~(sP63) | ~(sP16)) | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(33,plain,(~(sP51) | sP136),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(34,plain,(~(sP3) | sP51),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(35,plain,(sP108 | sP3),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(36,plain,(~(sP89) | sP135),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(37,plain,(~(sP46) | sP89),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(38,plain,(sP147 | sP46),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(39,plain,((sP71 | sP148) | ~(sP73)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(40,plain,((sP7 | sP73) | sP59),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(41,plain,((sP90 | sP148) | ~(sP59)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(42,plain,(sP55 | sP31),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(43,plain,((~(sP77) | ~(sP137)) | ~(sP81)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(44,plain,((~(sP80) | sP131) | ~(sP48)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(45,plain,((~(sP131) | sP72) | ~(sP40)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(46,plain,((sP70 | ~(sP131)) | sP10),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(47,plain,((sP70 | sP131) | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(48,plain,(sP149 | ~(sP70)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19])). % 6.03/6.39 thf(49,plain,(sP37 | ~(sP149)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(50,plain,((~(sP80) | sP12) | ~(sP132)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(51,plain,((sP102 | sP80) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(52,plain,(sP86 | ~(sP102)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18])). % 6.03/6.39 thf(53,plain,((~(sP28) | sP72) | ~(sP101)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(54,plain,((sP134 | ~(sP72)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(55,plain,(sP13 | ~(sP134)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16])). % 6.03/6.39 thf(56,plain,(~(sP13) | sP62),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(57,plain,(~(sP27) | sP13),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(58,plain,(sP93 | sP27),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(59,plain,((~(sP61) | sP85) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(60,plain,((~(sP115) | sP141) | ~(sP103)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(61,plain,((~(sP115) | sP114) | ~(sP52)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(62,plain,((sP2 | sP115) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(63,plain,(sP19 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14])). % 6.03/6.39 thf(64,plain,(sP21 | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(65,plain,((~(sP56) | sP141) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(66,plain,((~(sP4) | sP114) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(67,plain,(~(sP60) | sP4),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(68,plain,(~(sP94) | sP60),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(69,plain,(sP113 | sP94),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(70,plain,((~(sP76) | sP63) | ~(sP74)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(71,plain,sP130,inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(72,plain,sP95,inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(73,plain,((sP22 | sP148) | ~(sP133)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(74,plain,((sP6 | sP148) | sP133),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(75,plain,((~(sP135) | ~(sP105)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(76,plain,(~(sP125) | sP135),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(77,plain,(~(sP129) | sP125),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(78,plain,(sP112 | sP129),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(79,plain,((~(sP104) | ~(sP147)) | ~(sP108)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(80,plain,((~(sP34) | sP143) | ~(sP71)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(81,plain,((~(sP143) | sP121) | ~(sP7)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(82,plain,((sP49 | ~(sP143)) | ~(sP73)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(83,plain,((sP49 | sP143) | sP73),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(84,plain,(sP118 | ~(sP49)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9])). % 6.03/6.39 thf(85,plain,(sP110 | ~(sP118)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(86,plain,((~(sP34) | sP121) | ~(sP90)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(87,plain,((sP111 | ~(sP121)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(88,plain,(sP36 | ~(sP111)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8])). % 6.03/6.39 thf(89,plain,sP144,inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(90,plain,((~(sP38) | sP44) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(91,plain,(~(sP36) | sP38),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(92,plain,(~(sP53) | sP36),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(93,plain,(sP47 | sP53),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(94,plain,((~(sP43) | sP77) | ~(sP55)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(95,plain,((~(sP100) | ~(sP37)) | ~(sP130)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(96,plain,(sP54 | sP100),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(97,plain,(sP119 | ~(sP54)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(98,plain,(sP82 | ~(sP119)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(99,plain,((~(sP30) | sP61) | ~(sP93)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(100,plain,(~(sP33) | ~(sP82)),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 6.03/6.39 thf(101,plain,(sP30 | sP33),inference(choice_rule,[status(thm)],[choiceax])). % 6.03/6.39 thf(102,plain,((~(sP11) | ~(sP21)) | ~(sP95)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(103,plain,(sP15 | sP11),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(104,plain,(sP39 | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(105,plain,(sP109 | ~(sP39)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(106,plain,((~(sP84) | sP76) | ~(sP113)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(107,plain,(~(sP88) | ~(sP109)),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(108,plain,(sP84 | sP88),inference(choice_rule,[status(thm)],[choiceax])). % 6.03/6.39 thf(109,plain,sP18,inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(110,plain,((~(sP75) | sP45) | ~(sP22)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(111,plain,((~(sP105) | sP45) | ~(sP6)),inference(mating_rule,[status(thm)],[])). % 6.03/6.39 thf(112,plain,((sP146 | ~(sP45)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(113,plain,(sP65 | ~(sP146)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4])). % 6.03/6.39 thf(114,plain,(sP123 | ~(sP65)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(115,plain,(sP96 | sP50),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(116,plain,((~(sP41) | sP104) | ~(sP112)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(117,plain,((~(sP14) | ~(sP110)) | ~(sP144)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(118,plain,(sP128 | sP14),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(119,plain,(sP98 | ~(sP128)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(120,plain,((~(sP145) | sP43) | ~(sP47)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(121,plain,(~(sP83) | ~(sP98)),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(122,plain,(sP145 | sP83),inference(choice_rule,[status(thm)],[choiceax])). % 6.03/6.39 thf(123,plain,((~(sP23) | ~(sP92)) | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(124,plain,((~(sP127) | ~(sP123)) | ~(sP18)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(125,plain,(sP42 | sP127),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(126,plain,((~(sP29) | sP41) | ~(sP96)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(127,plain,(~(sP24) | ~(sP42)),inference(all_rule,[status(thm)],[])). % 6.03/6.39 thf(128,plain,(sP29 | sP24),inference(choice_rule,[status(thm)],[choiceax])). % 6.03/6.39 thf(129,plain,((~(sP66) | sP23) | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(130,plain,((~(sP64) | sP66) | ~(sP50)),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(131,plain,(sP122 | sP64),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 6.03/6.39 thf(132,plain,(sP69 | ~(sP122)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 6.03/6.39 thf(133,plain,~(sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(134,plain,(sP17 | ~(sP69)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 6.03/6.39 thf(135,plain,((~(sP87) | ~(sP114)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(136,plain,((~(sP117) | ~(sP141)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(137,plain,((~(sP9) | sP28) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(138,plain,((~(sP58) | ~(sP12)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(139,plain,((~(sP26) | ~(sP44)) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(140,plain,((~(sP140) | sP34) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(141,plain,((~(sP99) | sP105) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(142,plain,((~(sP1) | sP75) | sP148),inference(prop_rule,[status(thm)],[])). % 6.03/6.39 thf(143,plain,(sP107 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 6.03/6.39 thf(f0f,axiom,sP87). % 6.03/6.39 thf(f0t,axiom,sP117). % 6.03/6.39 thf(f1f,axiom,sP9). % 6.03/6.39 thf(f1t,axiom,sP58). % 6.03/6.39 thf(f2f,axiom,sP26). % 6.03/6.39 thf(f2t,axiom,sP140). % 6.03/6.39 thf(f3f,axiom,sP99). % 6.03/6.39 thf(f3t,axiom,sP1). % 6.03/6.39 thf(144,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,f0f,f0t,f1f,f1t,f2f,f2t,f3f,f3t,h2])). % 6.03/6.39 thf(145,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[144,h1])). % 6.03/6.39 thf(146,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[145,h0])). % 6.03/6.39 thf(0,theorem,sP107,inference(contra,[status(thm),contra(discharge,[h2])],[144,h2])). % 6.03/6.39 % SZS output end Proof %------------------------------------------------------------------------------