0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.12/0.33	Computer   : n019.cluster.edu
0.12/0.33	Model      : x86_64 x86_64
0.12/0.33	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	RAMPerCPU  : 8042.1875MB
0.12/0.33	OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% DateTime   : Mon Jul  3 05:37:05 EDT 2023
0.12/0.33	% CPUTime    : 
108.49/108.66	% SZS status Theorem
108.49/108.66	% Mode: mode456
108.49/108.66	% Inferences: 1757
108.49/108.66	% SZS output start Proof
108.49/108.66	thf(ty_eigen__106, type, eigen__106 : $o).
108.49/108.66	thf(ty_eigen__108, type, eigen__108 : ($o>$o)).
108.49/108.66	thf(ty_eigen__109, type, eigen__109 : ($o>$o)).
108.49/108.66	thf(ty_eigen__77, type, eigen__77 : ($o>$o)).
108.49/108.66	thf(ty_eigen__79, type, eigen__79 : ($o>$o)).
108.49/108.66	thf(ty_eigen__116, type, eigen__116 : ($o>$o)).
108.49/108.66	thf(ty_eigen__103, type, eigen__103 : (($o>$o)>$o)).
108.49/108.66	thf(ty_eigen__111, type, eigen__111 : (($o>$o)>$o)).
108.49/108.66	thf(ty_eigen__107, type, eigen__107 : $o).
108.49/108.66	thf(ty_eigen__110, type, eigen__110 : (($o>$o)>$o)).
108.49/108.66	thf(ty_eigen__105, type, eigen__105 : $o).
108.49/108.66	thf(ty_eigen__100, type, eigen__100 : ($o>$o)).
108.49/108.66	thf(ty_eigen__101, type, eigen__101 : ($o>$o)).
108.49/108.66	thf(ty_eigen__102, type, eigen__102 : (($o>$o)>$o)).
108.49/108.66	thf(ty_eigen__78, type, eigen__78 : ($o>$o)).
108.49/108.66	thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
108.49/108.66	thf(eigendef_eigen__106, definition, eigen__106 = (eps__0 @ (^[X1:$o]:(~(((eigen__79 @ X1) = (eigen__101 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__106])])).
108.49/108.66	thf(h1, assumption, (![X1:(($o>$o)>$o)>$o]:(![X2:($o>$o)>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
108.49/108.66	thf(eigendef_eigen__110, definition, eigen__110 = (eps__1 @ (^[X1:($o>$o)>$o]:(~((![X2:($o>$o)>$o]:((~(((~(((~(((~(((~(((X1 @ eigen__78) => (X1 @ eigen__108)))) => (X1 @ eigen__109)))) => (X2 @ eigen__109)))) => (~((X2 @ eigen__108)))))) => (X2 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => ((eigen__108 @ $false) = (eigen__109 @ $false))))) => ((eigen__78 @ $false) = (eigen__108 @ $false))))))))), introduced(definition,[new_symbols(definition,[eigen__110])])).
108.49/108.66	thf(h2, assumption, (![X1:($o>$o)>$o]:(![X2:$o>$o]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])).
108.49/108.66	thf(eigendef_eigen__108, definition, eigen__108 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:$o>$o]:(![X3:($o>$o)>$o]:(![X4:($o>$o)>$o]:((~(((~(((~(((~(((~(((X3 @ eigen__78) => (X3 @ X1)))) => (X3 @ X2)))) => (X4 @ X2)))) => (~((X4 @ X1)))))) => (X4 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (X2 @ $false)))) => ((X1 @ $false) = (X2 @ $false))))) => ((eigen__78 @ $false) = (X1 @ $false))))))))))), introduced(definition,[new_symbols(definition,[eigen__108])])).
108.49/108.66	thf(eigendef_eigen__116, definition, eigen__116 = (eps__2 @ (^[X1:$o>$o]:(~((((X1 @ $false) = (eigen__77 @ $false)) => ((eigen__77 @ $false) = (X1 @ $false))))))), introduced(definition,[new_symbols(definition,[eigen__116])])).
108.49/108.66	thf(eigendef_eigen__109, definition, eigen__109 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:($o>$o)>$o]:(![X3:($o>$o)>$o]:((~(((~(((~(((~(((~(((X2 @ eigen__78) => (X2 @ eigen__108)))) => (X2 @ X1)))) => (X3 @ X1)))) => (~((X3 @ eigen__108)))))) => (X3 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (X1 @ $false)))) => ((eigen__108 @ $false) = (X1 @ $false))))) => ((eigen__78 @ $false) = (eigen__108 @ $false)))))))))), introduced(definition,[new_symbols(definition,[eigen__109])])).
108.49/108.66	thf(eigendef_eigen__105, definition, eigen__105 = (eps__0 @ (^[X1:$o]:(~(((eigen__100 @ X1) = (eigen__101 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__105])])).
108.49/108.66	thf(eigendef_eigen__77, definition, eigen__77 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:$o>$o]:(((X2 @ $false) = (X1 @ $false)) => ((X1 @ $false) = (X2 @ $false)))))))), introduced(definition,[new_symbols(definition,[eigen__77])])).
108.49/108.66	thf(eigendef_eigen__100, definition, eigen__100 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:$o>$o]:(![X3:($o>$o)>$o]:(![X4:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X3 @ X1))) => (X3 @ X2)))) => (~((X4 @ X1)))))) => (X4 @ X2)))) => (X4 @ eigen__79)))) => (~((X3 @ eigen__79)))))) => ((~((((eigen__79 @ $false) = (X1 @ $false)) => (~(((eigen__79 @ $false) = (X2 @ $false))))))) => (~(((X1 @ $false) = (X2 @ $false))))))))))))), introduced(definition,[new_symbols(definition,[eigen__100])])).
108.49/108.66	thf(eigendef_eigen__101, definition, eigen__101 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:($o>$o)>$o]:(![X3:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X2 @ eigen__100))) => (X2 @ X1)))) => (~((X3 @ eigen__100)))))) => (X3 @ X1)))) => (X3 @ eigen__79)))) => (~((X2 @ eigen__79)))))) => ((~((((eigen__79 @ $false) = (eigen__100 @ $false)) => (~(((eigen__79 @ $false) = (X1 @ $false))))))) => (~(((eigen__100 @ $false) = (X1 @ $false)))))))))))), introduced(definition,[new_symbols(definition,[eigen__101])])).
108.49/108.66	thf(eigendef_eigen__78, definition, eigen__78 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:$o>$o]:(![X3:$o>$o]:(![X4:($o>$o)>$o]:(![X5:($o>$o)>$o]:((~(((~(((~(((~(((~(((X4 @ X1) => (X4 @ X2)))) => (X4 @ X3)))) => (X5 @ X3)))) => (~((X5 @ X2)))))) => (X5 @ X1)))) => ((~(((~(((X1 @ $false) = (X3 @ $false)))) => ((X2 @ $false) = (X3 @ $false))))) => ((X1 @ $false) = (X2 @ $false)))))))))))), introduced(definition,[new_symbols(definition,[eigen__78])])).
108.49/108.66	thf(eigendef_eigen__102, definition, eigen__102 = (eps__1 @ (^[X1:($o>$o)>$o]:(~((![X2:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X1 @ eigen__100))) => (X1 @ eigen__101)))) => (~((X2 @ eigen__100)))))) => (X2 @ eigen__101)))) => (X2 @ eigen__79)))) => (~((X1 @ eigen__79)))))) => ((~((((eigen__79 @ $false) = (eigen__100 @ $false)) => (~(((eigen__79 @ $false) = (eigen__101 @ $false))))))) => (~(((eigen__100 @ $false) = (eigen__101 @ $false))))))))))), introduced(definition,[new_symbols(definition,[eigen__102])])).
108.49/108.66	thf(eigendef_eigen__103, definition, eigen__103 = (eps__1 @ (^[X1:($o>$o)>$o]:(~(((~(((~(((~(((~(((~(((~((eigen__102 @ eigen__100))) => (eigen__102 @ eigen__101)))) => (~((X1 @ eigen__100)))))) => (X1 @ eigen__101)))) => (X1 @ eigen__79)))) => (~((eigen__102 @ eigen__79)))))) => ((~((((eigen__79 @ $false) = (eigen__100 @ $false)) => (~(((eigen__79 @ $false) = (eigen__101 @ $false))))))) => (~(((eigen__100 @ $false) = (eigen__101 @ $false)))))))))), introduced(definition,[new_symbols(definition,[eigen__103])])).
108.49/108.66	thf(eigendef_eigen__111, definition, eigen__111 = (eps__1 @ (^[X1:($o>$o)>$o]:(~(((~(((~(((~(((~(((~(((eigen__110 @ eigen__78) => (eigen__110 @ eigen__108)))) => (eigen__110 @ eigen__109)))) => (X1 @ eigen__109)))) => (~((X1 @ eigen__108)))))) => (X1 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => ((eigen__108 @ $false) = (eigen__109 @ $false))))) => ((eigen__78 @ $false) = (eigen__108 @ $false)))))))), introduced(definition,[new_symbols(definition,[eigen__111])])).
108.49/108.66	thf(eigendef_eigen__79, definition, eigen__79 = (eps__2 @ (^[X1:$o>$o]:(~((![X2:$o>$o]:(![X3:$o>$o]:(![X4:($o>$o)>$o]:(![X5:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X4 @ X2))) => (X4 @ X3)))) => (~((X5 @ X2)))))) => (X5 @ X3)))) => (X5 @ X1)))) => (~((X4 @ X1)))))) => ((~((((X1 @ $false) = (X2 @ $false)) => (~(((X1 @ $false) = (X3 @ $false))))))) => (~(((X2 @ $false) = (X3 @ $false)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__79])])).
108.49/108.66	thf(eigendef_eigen__107, definition, eigen__107 = (eps__0 @ (^[X1:$o]:(~(((eigen__79 @ X1) = (eigen__100 @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__107])])).
108.49/108.66	thf(sP1,plain,sP1 <=> (![X1:$o>$o]:(![X2:$o>$o]:(![X3:$o>$o]:(![X4:($o>$o)>$o]:(![X5:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X4 @ X2))) => (X4 @ X3)))) => (~((X5 @ X2)))))) => (X5 @ X3)))) => (X5 @ X1)))) => (~((X4 @ X1)))))) => ((~((((X1 @ $false) = (X2 @ $false)) => (~(((X1 @ $false) = (X3 @ $false))))))) => (~(((X2 @ $false) = (X3 @ $false))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
108.49/108.66	thf(sP2,plain,sP2 <=> ($false = eigen__107),introduced(definition,[new_symbols(definition,[sP2])])).
108.49/108.66	thf(sP3,plain,sP3 <=> (![X1:($o>$o)>$o]:(![X2:($o>$o)>$o]:((~(((~(((~(((~(((~(((X1 @ eigen__78) => (X1 @ eigen__108)))) => (X1 @ eigen__109)))) => (X2 @ eigen__109)))) => (~((X2 @ eigen__108)))))) => (X2 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => ((eigen__108 @ $false) = (eigen__109 @ $false))))) => ((eigen__78 @ $false) = (eigen__108 @ $false)))))),introduced(definition,[new_symbols(definition,[sP3])])).
108.49/108.66	thf(sP4,plain,sP4 <=> ((~(((~(((~(((~(((~(((eigen__110 @ eigen__78) => (eigen__110 @ eigen__108)))) => (eigen__110 @ eigen__109)))) => (eigen__111 @ eigen__109)))) => (~((eigen__111 @ eigen__108)))))) => (eigen__111 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => ((eigen__108 @ $false) = (eigen__109 @ $false))))) => ((eigen__78 @ $false) = (eigen__108 @ $false)))),introduced(definition,[new_symbols(definition,[sP4])])).
108.49/108.66	thf(sP5,plain,sP5 <=> (![X1:$o]:(![X2:$o]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
108.49/108.66	thf(sP6,plain,sP6 <=> (eigen__108 @ $false),introduced(definition,[new_symbols(definition,[sP6])])).
108.49/108.66	thf(sP7,plain,sP7 <=> (sP1 => (~((![X1:$o>$o]:(![X2:$o>$o]:(![X3:$o>$o]:(![X4:($o>$o)>$o]:(![X5:($o>$o)>$o]:((~(((~(((~(((~(((~(((X4 @ X1) => (X4 @ X2)))) => (X4 @ X3)))) => (X5 @ X3)))) => (~((X5 @ X2)))))) => (X5 @ X1)))) => ((~(((~(((X1 @ $false) = (X3 @ $false)))) => ((X2 @ $false) = (X3 @ $false))))) => ((X1 @ $false) = (X2 @ $false)))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
108.49/108.66	thf(sP8,plain,sP8 <=> (eigen__103 @ eigen__100),introduced(definition,[new_symbols(definition,[sP8])])).
108.49/108.66	thf(sP9,plain,sP9 <=> (eigen__105 = $false),introduced(definition,[new_symbols(definition,[sP9])])).
108.49/108.66	thf(sP10,plain,sP10 <=> (eigen__100 @ eigen__105),introduced(definition,[new_symbols(definition,[sP10])])).
108.49/108.66	thf(sP11,plain,sP11 <=> (![X1:($o>$o)>$o]:((~(((~(((~(((~(((~(((eigen__110 @ eigen__78) => (eigen__110 @ eigen__108)))) => (eigen__110 @ eigen__109)))) => (X1 @ eigen__109)))) => (~((X1 @ eigen__108)))))) => (X1 @ eigen__78)))) => ((~(((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => (sP6 = (eigen__109 @ $false))))) => ((eigen__78 @ $false) = sP6)))),introduced(definition,[new_symbols(definition,[sP11])])).
108.49/108.66	thf(sP12,plain,sP12 <=> eigen__107,introduced(definition,[new_symbols(definition,[sP12])])).
108.49/108.66	thf(sP13,plain,sP13 <=> (![X1:$o]:((eigen__79 @ X1) = (eigen__101 @ X1))),introduced(definition,[new_symbols(definition,[sP13])])).
108.49/108.66	thf(sP14,plain,sP14 <=> ((~(((eigen__78 @ $false) = (eigen__109 @ $false)))) => (sP6 = (eigen__109 @ $false))),introduced(definition,[new_symbols(definition,[sP14])])).
108.49/108.66	thf(sP15,plain,sP15 <=> (eigen__79 @ sP12),introduced(definition,[new_symbols(definition,[sP15])])).
108.49/108.66	thf(sP16,plain,sP16 <=> (eigen__102 @ eigen__79),introduced(definition,[new_symbols(definition,[sP16])])).
108.49/108.66	thf(sP17,plain,sP17 <=> (![X1:$o>$o]:(![X2:($o>$o)>$o]:(![X3:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X2 @ eigen__100))) => (X2 @ X1)))) => (~((X3 @ eigen__100)))))) => (X3 @ X1)))) => (X3 @ eigen__79)))) => (~((X2 @ eigen__79)))))) => ((~((((eigen__79 @ $false) = (eigen__100 @ $false)) => (~(((eigen__79 @ $false) = (X1 @ $false))))))) => (~(((eigen__100 @ $false) = (X1 @ $false))))))))),introduced(definition,[new_symbols(definition,[sP17])])).
108.49/108.66	thf(sP18,plain,sP18 <=> (eigen__79 = eigen__100),introduced(definition,[new_symbols(definition,[sP18])])).
108.49/108.66	thf(sP19,plain,sP19 <=> (![X1:$o>$o]:(![X2:$o>$o]:(((X2 @ $false) = (X1 @ $false)) => ((X1 @ $false) = (X2 @ $false))))),introduced(definition,[new_symbols(definition,[sP19])])).
108.49/108.66	thf(sP20,plain,sP20 <=> (eigen__106 = sP12),introduced(definition,[new_symbols(definition,[sP20])])).
108.49/108.66	thf(sP21,plain,sP21 <=> (sP6 = (eigen__109 @ $false)),introduced(definition,[new_symbols(definition,[sP21])])).
108.49/108.66	thf(sP22,plain,sP22 <=> ((eigen__78 @ $false) = (eigen__109 @ $false)),introduced(definition,[new_symbols(definition,[sP22])])).
108.49/108.66	thf(sP23,plain,sP23 <=> ((~(((~((eigen__102 @ eigen__100))) => (eigen__102 @ eigen__101)))) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP23])])).
108.49/108.66	thf(sP24,plain,sP24 <=> (eigen__101 @ eigen__105),introduced(definition,[new_symbols(definition,[sP24])])).
108.49/108.66	thf(sP25,plain,sP25 <=> (eigen__109 @ $false),introduced(definition,[new_symbols(definition,[sP25])])).
108.49/108.66	thf(sP26,plain,sP26 <=> ((~(((~(((~(sP23)) => (eigen__103 @ eigen__101)))) => (eigen__103 @ eigen__79)))) => (~(sP16))),introduced(definition,[new_symbols(definition,[sP26])])).
108.49/108.66	thf(sP27,plain,sP27 <=> ((eigen__100 @ $false) = (eigen__101 @ $false)),introduced(definition,[new_symbols(definition,[sP27])])).
108.49/108.66	thf(sP28,plain,sP28 <=> (![X1:$o]:((eigen__79 @ X1) = (eigen__100 @ X1))),introduced(definition,[new_symbols(definition,[sP28])])).
108.49/108.66	thf(sP29,plain,sP29 <=> (eigen__78 @ $false),introduced(definition,[new_symbols(definition,[sP29])])).
108.49/108.66	thf(sP30,plain,sP30 <=> (![X1:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((eigen__102 @ eigen__100))) => (eigen__102 @ eigen__101)))) => (~((X1 @ eigen__100)))))) => (X1 @ eigen__101)))) => (X1 @ eigen__79)))) => (~(sP16))))) => ((~((((eigen__79 @ $false) = (eigen__100 @ $false)) => (~(((eigen__79 @ $false) = (eigen__101 @ $false))))))) => (~(sP27))))),introduced(definition,[new_symbols(definition,[sP30])])).
108.49/108.66	thf(sP31,plain,sP31 <=> ((eigen__79 @ $false) = (eigen__100 @ $false)),introduced(definition,[new_symbols(definition,[sP31])])).
108.49/108.66	thf(sP32,plain,sP32 <=> eigen__105,introduced(definition,[new_symbols(definition,[sP32])])).
108.49/108.66	thf(sP33,plain,sP33 <=> (![X1:$o>$o]:(![X2:$o>$o]:(![X3:($o>$o)>$o]:(![X4:($o>$o)>$o]:((~(((~(((~(((~(((~(((X3 @ eigen__78) => (X3 @ X1)))) => (X3 @ X2)))) => (X4 @ X2)))) => (~((X4 @ X1)))))) => (X4 @ eigen__78)))) => ((~(((~((sP29 = (X2 @ $false)))) => ((X1 @ $false) = (X2 @ $false))))) => (sP29 = (X1 @ $false)))))))),introduced(definition,[new_symbols(definition,[sP33])])).
108.49/108.66	thf(sP34,plain,sP34 <=> ((~((sP31 => (~(((eigen__79 @ $false) = (eigen__101 @ $false))))))) => (~(sP27))),introduced(definition,[new_symbols(definition,[sP34])])).
108.49/108.66	thf(sP35,plain,sP35 <=> (![X1:$o>$o]:(![X2:($o>$o)>$o]:(![X3:($o>$o)>$o]:((~(((~(((~(((~(((~(((X2 @ eigen__78) => (X2 @ eigen__108)))) => (X2 @ X1)))) => (X3 @ X1)))) => (~((X3 @ eigen__108)))))) => (X3 @ eigen__78)))) => ((~(((~((sP29 = (X1 @ $false)))) => (sP6 = (X1 @ $false))))) => (sP29 = sP6)))))),introduced(definition,[new_symbols(definition,[sP35])])).
108.49/108.66	thf(sP36,plain,sP36 <=> (eigen__102 @ eigen__100),introduced(definition,[new_symbols(definition,[sP36])])).
108.49/108.66	thf(sP37,plain,sP37 <=> (eigen__101 @ eigen__106),introduced(definition,[new_symbols(definition,[sP37])])).
108.49/108.66	thf(sP38,plain,sP38 <=> (sP12 = eigen__106),introduced(definition,[new_symbols(definition,[sP38])])).
108.49/108.66	thf(sP39,plain,sP39 <=> (sP29 = sP6),introduced(definition,[new_symbols(definition,[sP39])])).
108.49/108.66	thf(sP40,plain,sP40 <=> ((~(sP36)) => (eigen__102 @ eigen__101)),introduced(definition,[new_symbols(definition,[sP40])])).
108.49/108.66	thf(sP41,plain,sP41 <=> ($false = sP32),introduced(definition,[new_symbols(definition,[sP41])])).
108.49/108.66	thf(sP42,plain,sP42 <=> (eigen__100 = eigen__101),introduced(definition,[new_symbols(definition,[sP42])])).
108.49/108.66	thf(sP43,plain,sP43 <=> ((eigen__79 @ eigen__106) = sP37),introduced(definition,[new_symbols(definition,[sP43])])).
108.49/108.66	thf(sP44,plain,sP44 <=> (sP12 = $false),introduced(definition,[new_symbols(definition,[sP44])])).
108.49/108.66	thf(sP45,plain,sP45 <=> ((~(sP23)) => (eigen__103 @ eigen__101)),introduced(definition,[new_symbols(definition,[sP45])])).
108.49/108.66	thf(sP46,plain,sP46 <=> (![X1:($o>$o)>$o]:(![X2:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X1 @ eigen__100))) => (X1 @ eigen__101)))) => (~((X2 @ eigen__100)))))) => (X2 @ eigen__101)))) => (X2 @ eigen__79)))) => (~((X1 @ eigen__79)))))) => sP34))),introduced(definition,[new_symbols(definition,[sP46])])).
108.49/108.66	thf(sP47,plain,sP47 <=> (sP12 = sP32),introduced(definition,[new_symbols(definition,[sP47])])).
108.49/108.66	thf(sP48,plain,sP48 <=> (sP31 => (~(((eigen__79 @ $false) = (eigen__101 @ $false))))),introduced(definition,[new_symbols(definition,[sP48])])).
108.49/108.66	thf(sP49,plain,sP49 <=> ((~(sP45)) => (eigen__103 @ eigen__79)),introduced(definition,[new_symbols(definition,[sP49])])).
108.49/108.66	thf(sP50,plain,sP50 <=> (![X1:$o>$o]:(![X2:$o>$o]:(![X3:$o>$o]:(![X4:($o>$o)>$o]:(![X5:($o>$o)>$o]:((~(((~(((~(((~(((~(((X4 @ X1) => (X4 @ X2)))) => (X4 @ X3)))) => (X5 @ X3)))) => (~((X5 @ X2)))))) => (X5 @ X1)))) => ((~(((~(((X1 @ $false) = (X3 @ $false)))) => ((X2 @ $false) = (X3 @ $false))))) => ((X1 @ $false) = (X2 @ $false))))))))),introduced(definition,[new_symbols(definition,[sP50])])).
108.49/108.66	thf(sP51,plain,sP51 <=> ((~(sP14)) => sP39),introduced(definition,[new_symbols(definition,[sP51])])).
108.49/108.66	thf(sP52,plain,sP52 <=> (((eigen__116 @ $false) = (eigen__77 @ $false)) => ((eigen__77 @ $false) = (eigen__116 @ $false))),introduced(definition,[new_symbols(definition,[sP52])])).
108.49/108.66	thf(sP53,plain,sP53 <=> ((~(sP7)) => (~(sP19))),introduced(definition,[new_symbols(definition,[sP53])])).
108.49/108.66	thf(sP54,plain,sP54 <=> (eigen__79 @ $false),introduced(definition,[new_symbols(definition,[sP54])])).
108.49/108.66	thf(sP55,plain,sP55 <=> (eigen__100 @ $false),introduced(definition,[new_symbols(definition,[sP55])])).
108.49/108.66	thf(sP56,plain,sP56 <=> (eigen__101 @ $false),introduced(definition,[new_symbols(definition,[sP56])])).
108.49/108.66	thf(sP57,plain,sP57 <=> (![X1:($o>$o)>($o>$o)>$o]:((~(((![X2:$o>$o]:(![X3:$o>$o]:(![X4:$o>$o]:(![X5:($o>$o)>$o]:(![X6:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X5 @ X3))) => (X5 @ X4)))) => (~((X6 @ X3)))))) => (X6 @ X4)))) => (X6 @ X2)))) => (~((X5 @ X2)))))) => ((~((((X1 @ X3) @ X2) => (~(((X1 @ X4) @ X2)))))) => (~(((X1 @ X4) @ X3)))))))))) => (~((![X2:$o>$o]:(![X3:$o>$o]:(![X4:$o>$o]:(![X5:($o>$o)>$o]:(![X6:($o>$o)>$o]:((~(((~(((~(((~(((~(((X5 @ X2) => (X5 @ X3)))) => (X5 @ X4)))) => (X6 @ X4)))) => (~((X6 @ X3)))))) => (X6 @ X2)))) => ((~(((~(((X1 @ X4) @ X2))) => ((X1 @ X4) @ X3)))) => ((X1 @ X3) @ X2))))))))))))) => (~((![X2:$o>$o]:(![X3:$o>$o]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP57])])).
108.49/108.66	thf(sP58,plain,sP58 <=> (eigen__79 = eigen__101),introduced(definition,[new_symbols(definition,[sP58])])).
108.49/108.66	thf(sP59,plain,sP59 <=> (eigen__103 @ eigen__101),introduced(definition,[new_symbols(definition,[sP59])])).
108.49/108.66	thf(sP60,plain,sP60 <=> (eigen__102 @ eigen__101),introduced(definition,[new_symbols(definition,[sP60])])).
108.49/108.66	thf(sP61,plain,sP61 <=> ((~(sP26)) => sP34),introduced(definition,[new_symbols(definition,[sP61])])).
108.49/108.66	thf(sP62,plain,sP62 <=> (sP32 = sP12),introduced(definition,[new_symbols(definition,[sP62])])).
108.49/108.66	thf(sP63,plain,sP63 <=> (![X1:$o>$o]:(![X2:$o>$o]:(![X3:($o>$o)>$o]:(![X4:($o>$o)>$o]:((~(((~(((~(((~(((~(((~((X3 @ X1))) => (X3 @ X2)))) => (~((X4 @ X1)))))) => (X4 @ X2)))) => (X4 @ eigen__79)))) => (~((X3 @ eigen__79)))))) => ((~(((sP54 = (X1 @ $false)) => (~((sP54 = (X2 @ $false))))))) => (~(((X1 @ $false) = (X2 @ $false)))))))))),introduced(definition,[new_symbols(definition,[sP63])])).
108.49/108.66	thf(sP64,plain,sP64 <=> (eigen__106 = $false),introduced(definition,[new_symbols(definition,[sP64])])).
108.49/108.66	thf(sP65,plain,sP65 <=> (eigen__79 @ eigen__106),introduced(definition,[new_symbols(definition,[sP65])])).
108.49/108.66	thf(sP66,plain,sP66 <=> $false,introduced(definition,[new_symbols(definition,[sP66])])).
108.49/108.66	thf(sP67,plain,sP67 <=> (![X1:$o]:((eigen__100 @ X1) = (eigen__101 @ X1))),introduced(definition,[new_symbols(definition,[sP67])])).
108.49/108.66	thf(sP68,plain,sP68 <=> (![X1:$o]:(((eigen__116 @ sP66) = X1) => (X1 = (eigen__116 @ sP66)))),introduced(definition,[new_symbols(definition,[sP68])])).
108.49/108.66	thf(sP69,plain,sP69 <=> (eigen__106 = sP32),introduced(definition,[new_symbols(definition,[sP69])])).
108.49/108.66	thf(sP70,plain,sP70 <=> eigen__106,introduced(definition,[new_symbols(definition,[sP70])])).
108.49/108.66	thf(sP71,plain,sP71 <=> (sP15 = (eigen__100 @ sP12)),introduced(definition,[new_symbols(definition,[sP71])])).
108.49/108.66	thf(sP72,plain,sP72 <=> (eigen__100 @ sP12),introduced(definition,[new_symbols(definition,[sP72])])).
108.49/108.66	thf(sP73,plain,sP73 <=> (sP66 = sP70),introduced(definition,[new_symbols(definition,[sP73])])).
108.49/108.66	thf(sP74,plain,sP74 <=> (sP10 = sP24),introduced(definition,[new_symbols(definition,[sP74])])).
108.49/108.66	thf(sP75,plain,sP75 <=> (sP32 = sP70),introduced(definition,[new_symbols(definition,[sP75])])).
108.49/108.66	thf(sP76,plain,sP76 <=> (![X1:$o>$o]:(((X1 @ sP66) = (eigen__77 @ sP66)) => ((eigen__77 @ sP66) = (X1 @ sP66)))),introduced(definition,[new_symbols(definition,[sP76])])).
108.49/108.66	thf(ramsey_l_3_3_4,conjecture,(~(sP57))).
108.49/108.66	thf(h3,negated_conjecture,sP57,inference(assume_negation,[status(cth)],[ramsey_l_3_3_4])).
108.49/108.66	thf(1,plain,(~(sP68) | sP52),inference(all_rule,[status(thm)],[])).
108.49/108.66	thf(2,plain,(~(sP5) | sP68),inference(all_rule,[status(thm)],[])).
108.49/108.66	thf(3,plain,(sP76 | ~(sP52)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__116])).
108.49/108.66	thf(4,plain,((sP22 | ~(sP29)) | ~(sP25)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(5,plain,((sP22 | sP29) | sP25),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(6,plain,((sP21 | ~(sP6)) | ~(sP25)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(7,plain,((sP21 | sP6) | sP25),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(8,plain,(sP14 | ~(sP21)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(9,plain,(sP14 | ~(sP22)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(10,plain,((sP39 | ~(sP29)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(11,plain,((sP39 | sP29) | sP6),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(12,plain,(sP51 | ~(sP39)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(13,plain,(sP51 | ~(sP14)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(14,plain,(sP4 | ~(sP51)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(15,plain,(sP11 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__111])).
108.49/108.66	thf(16,plain,(sP3 | ~(sP11)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__110])).
108.49/108.66	thf(17,plain,(sP35 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__109])).
108.49/108.66	thf(18,plain,(sP33 | ~(sP35)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__108])).
108.49/108.66	thf(19,plain,((sP62 | ~(sP32)) | ~(sP12)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(20,plain,((~(sP10) | sP72) | ~(sP62)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(21,plain,((~(sP10) | sP55) | ~(sP9)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(22,plain,((sP75 | ~(sP32)) | ~(sP70)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(23,plain,((~(sP24) | sP37) | ~(sP75)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(24,plain,((sP9 | sP32) | sP66),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(25,plain,((~(sP24) | sP56) | ~(sP9)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(26,plain,((sP47 | ~(sP12)) | ~(sP32)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(27,plain,((~(sP72) | sP10) | ~(sP47)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(28,plain,((~(sP55) | sP10) | ~(sP41)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(29,plain,((sP69 | ~(sP70)) | ~(sP32)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(30,plain,((~(sP37) | sP24) | ~(sP69)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(31,plain,((sP41 | sP66) | sP32),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(32,plain,((~(sP56) | sP24) | ~(sP41)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(33,plain,((sP74 | ~(sP10)) | ~(sP24)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(34,plain,((sP74 | sP10) | sP24),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(35,plain,((sP20 | ~(sP70)) | ~(sP12)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(36,plain,((~(sP65) | sP15) | ~(sP20)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(37,plain,((~(sP65) | sP54) | ~(sP64)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(38,plain,((sP64 | sP70) | sP66),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(39,plain,((~(sP37) | sP56) | ~(sP64)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(40,plain,((sP38 | ~(sP12)) | ~(sP70)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(41,plain,((~(sP15) | sP65) | ~(sP38)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(42,plain,((~(sP54) | sP65) | ~(sP73)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(43,plain,((sP73 | sP66) | sP70),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(44,plain,((~(sP56) | sP37) | ~(sP73)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(45,plain,((sP43 | ~(sP65)) | ~(sP37)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(46,plain,((sP43 | sP65) | sP37),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(47,plain,((~(sP15) | sP54) | ~(sP44)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(48,plain,((sP44 | sP12) | sP66),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(49,plain,((~(sP72) | sP55) | ~(sP44)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(50,plain,((~(sP54) | sP15) | ~(sP2)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(51,plain,((sP2 | sP66) | sP12),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(52,plain,((~(sP55) | sP72) | ~(sP2)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(53,plain,((sP71 | ~(sP15)) | ~(sP72)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(54,plain,((sP71 | sP15) | sP72),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(55,plain,(sP28 | ~(sP71)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__107])).
108.49/108.66	thf(56,plain,(sP18 | ~(sP28)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(57,plain,((~(sP16) | sP36) | ~(sP18)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(58,plain,(sP13 | ~(sP43)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__106])).
108.49/108.66	thf(59,plain,(sP58 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(60,plain,((~(sP16) | sP60) | ~(sP58)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(61,plain,(sP40 | ~(sP60)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(62,plain,(sP40 | ~(sP36)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(63,plain,(sP67 | ~(sP74)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__105])).
108.49/108.66	thf(64,plain,(sP42 | ~(sP67)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(65,plain,((~(sP8) | sP59) | ~(sP42)),inference(mating_rule,[status(thm)],[])).
108.49/108.66	thf(66,plain,(sP23 | sP8),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(67,plain,(sP23 | ~(sP40)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(68,plain,(sP45 | ~(sP59)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(69,plain,(sP45 | ~(sP23)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(70,plain,(sP49 | ~(sP45)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(71,plain,(sP26 | sP16),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(72,plain,(sP26 | ~(sP49)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(73,plain,((~(sP31) | ~(sP54)) | sP55),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(74,plain,((~(sP31) | sP54) | ~(sP55)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(75,plain,(sP48 | sP31),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(76,plain,((~(sP27) | ~(sP55)) | sP56),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(77,plain,((~(sP27) | sP55) | ~(sP56)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(78,plain,(sP34 | sP27),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(79,plain,(sP34 | ~(sP48)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(80,plain,(sP61 | ~(sP34)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(81,plain,(sP61 | ~(sP26)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(82,plain,(sP30 | ~(sP61)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__103])).
108.49/108.66	thf(83,plain,(sP46 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__102])).
108.49/108.66	thf(84,plain,(sP17 | ~(sP46)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__101])).
108.49/108.66	thf(85,plain,(sP63 | ~(sP17)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__100])).
108.49/108.66	thf(86,plain,(sP1 | ~(sP63)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__79])).
108.49/108.66	thf(87,plain,(sP50 | ~(sP33)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__78])).
108.49/108.66	thf(88,plain,((~(sP7) | ~(sP1)) | ~(sP50)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(89,plain,(sP19 | ~(sP76)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__77])).
108.49/108.66	thf(90,plain,((~(sP53) | sP7) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(91,plain,~(sP66),inference(prop_rule,[status(thm)],[])).
108.49/108.66	thf(92,plain,sP5,inference(@eq_sym,[status(thm)],[])).
108.49/108.66	thf(93,plain,(~(sP57) | sP53),inference(all_rule,[status(thm)],[])).
108.49/108.66	thf(94,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,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,h3])).
108.49/108.66	thf(95,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[94,h2])).
108.49/108.66	thf(96,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[95,h1])).
108.49/108.66	thf(97,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[96,h0])).
108.49/108.66	thf(0,theorem,(~(sP57)),inference(contra,[status(thm),contra(discharge,[h3])],[94,h3])).
108.49/108.66	% SZS output end Proof
108.49/108.66	EOF