%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:49 PM UTC 2026 % Result : Theorem 0.14s 0.45s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.36 % Computer : n027.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 04:34:43 UTC 2026 % 0.09/0.36 % CPUTime : % 0.14/0.45 % SZS status Theorem % 0.14/0.45 % Mode: mode213 % 0.14/0.45 % Inferences: 364 % 0.14/0.45 % SZS output start Proof % 0.14/0.45 thf(ty_eigen__6, type, eigen__6 : ($i>$o)). % 0.14/0.45 thf(ty_eigen__2, type, eigen__2 : ($i>$o)). % 0.14/0.45 thf(ty_eigen__7, type, eigen__7 : ($i>$o)). % 0.14/0.45 thf(ty_eigen__1, type, eigen__1 : ($i>$o)). % 0.14/0.45 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.45 thf(ty_eigen__4, type, eigen__4 : $i). % 0.14/0.45 thf(ty_rb, type, rb : ($i>$i>$o)). % 0.14/0.45 thf(ty_eigen__5, type, eigen__5 : $i). % 0.14/0.45 thf(ty_eigen__3, type, eigen__3 : $i). % 0.14/0.45 thf(ty_eigen__8, type, eigen__8 : $i). % 0.14/0.45 thf(ty_eigen__9, type, eigen__9 : $i). % 0.14/0.45 thf(ty_ra, type, ra : ($i>$i>$o)). % 0.14/0.45 thf(sP1,plain,sP1 <=> ((ra @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.45 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((ra @ X1) @ X2) => (~(((ra @ X1) @ X3)))))) => ((ra @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.45 thf(sP3,plain,sP3 <=> (((ra @ eigen__8) @ eigen__8) => (eigen__6 @ eigen__8)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.14/0.45 thf(sP4,plain,sP4 <=> ((~((sP1 => (~(((ra @ eigen__0) @ eigen__3)))))) => ((ra @ eigen__4) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP4])])). % 0.14/0.45 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:((~((((rb @ eigen__5) @ X1) => (~(((rb @ eigen__5) @ X2)))))) => ((rb @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.14/0.45 thf(sP6,plain,sP6 <=> (![X1:$i]:((rb @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.14/0.45 thf(sP7,plain,sP7 <=> ((rb @ eigen__8) @ eigen__9),introduced(definition,[new_symbols(definition,[sP7])])). % 0.14/0.45 thf(sP8,plain,sP8 <=> (((ra @ eigen__4) @ eigen__3) => (eigen__1 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP8])])). % 0.14/0.45 thf(sP9,plain,sP9 <=> (![X1:$i]:(((ra @ eigen__0) @ X1) => ((~((![X2:$i]:(((ra @ X1) @ X2) => (eigen__1 @ X2))))) => (![X2:$i]:(((rb @ X1) @ X2) => (eigen__2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.14/0.45 thf(sP10,plain,sP10 <=> (![X1:$i]:((~((sP1 => (~(((ra @ eigen__0) @ X1)))))) => ((ra @ eigen__4) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.14/0.45 thf(sP11,plain,sP11 <=> (sP7 => (eigen__7 @ eigen__9)),introduced(definition,[new_symbols(definition,[sP11])])). % 0.14/0.45 thf(sP12,plain,sP12 <=> ((rb @ eigen__4) @ eigen__4),introduced(definition,[new_symbols(definition,[sP12])])). % 0.14/0.45 thf(sP13,plain,sP13 <=> (eigen__7 @ eigen__9),introduced(definition,[new_symbols(definition,[sP13])])). % 0.14/0.45 thf(sP14,plain,sP14 <=> (![X1:$i]:(![X2:$i]:((~((((ra @ eigen__0) @ X1) => (~(((ra @ eigen__0) @ X2)))))) => ((ra @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.14/0.45 thf(sP15,plain,sP15 <=> (![X1:$i]:(((rb @ eigen__8) @ X1) => (eigen__7 @ X1))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.14/0.45 thf(sP16,plain,sP16 <=> ((~((((rb @ eigen__5) @ eigen__8) => (~(((rb @ eigen__5) @ eigen__9)))))) => sP7),introduced(definition,[new_symbols(definition,[sP16])])). % 0.14/0.45 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rb @ X1) @ X2) => (~(((rb @ X1) @ X3)))))) => ((rb @ X2) @ X3))))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.14/0.45 thf(sP18,plain,sP18 <=> (((rb @ eigen__5) @ eigen__8) => ((~((![X1:$i]:(((ra @ eigen__8) @ X1) => (eigen__6 @ X1))))) => sP15)),introduced(definition,[new_symbols(definition,[sP18])])). % 0.14/0.45 thf(sP19,plain,sP19 <=> (((rb @ eigen__5) @ eigen__8) => (~(((rb @ eigen__5) @ eigen__9)))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.14/0.45 thf(sP20,plain,sP20 <=> (![X1:$i]:(((ra @ eigen__4) @ X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.14/0.45 thf(sP21,plain,sP21 <=> (sP1 => ((~(sP20)) => (![X1:$i]:(((rb @ eigen__4) @ X1) => (eigen__2 @ X1))))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.14/0.45 thf(sP22,plain,sP22 <=> ((ra @ eigen__4) @ eigen__3),introduced(definition,[new_symbols(definition,[sP22])])). % 0.14/0.45 thf(sP23,plain,sP23 <=> ((ra @ eigen__8) @ eigen__8),introduced(definition,[new_symbols(definition,[sP23])])). % 0.14/0.45 thf(sP24,plain,sP24 <=> (![X1:$i]:((ra @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP24])])). % 0.14/0.45 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rb @ eigen__5) @ X1) => ((~((![X2:$i]:(((ra @ X1) @ X2) => (eigen__6 @ X2))))) => (![X2:$i]:(((rb @ X1) @ X2) => (eigen__7 @ X2)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.14/0.45 thf(sP26,plain,sP26 <=> (![X1:$i]:(((rb @ eigen__4) @ X1) => (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.14/0.45 thf(sP27,plain,sP27 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP27])])). % 0.14/0.45 thf(sP28,plain,sP28 <=> (![X1:$i]:(((ra @ eigen__8) @ X1) => (eigen__6 @ X1))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.14/0.45 thf(sP29,plain,sP29 <=> (sP12 => (eigen__2 @ eigen__4)),introduced(definition,[new_symbols(definition,[sP29])])). % 0.14/0.45 thf(sP30,plain,sP30 <=> ((rb @ eigen__5) @ eigen__9),introduced(definition,[new_symbols(definition,[sP30])])). % 0.14/0.45 thf(sP31,plain,sP31 <=> (eigen__2 @ eigen__4),introduced(definition,[new_symbols(definition,[sP31])])). % 0.14/0.45 thf(sP32,plain,sP32 <=> (sP1 => (~(((ra @ eigen__0) @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP32])])). % 0.14/0.45 thf(sP33,plain,sP33 <=> ((~(sP28)) => sP15),introduced(definition,[new_symbols(definition,[sP33])])). % 0.14/0.45 thf(sP34,plain,sP34 <=> (![X1:$i]:((~((((rb @ eigen__5) @ eigen__8) => (~(((rb @ eigen__5) @ X1)))))) => ((rb @ eigen__8) @ X1))),introduced(definition,[new_symbols(definition,[sP34])])). % 0.14/0.45 thf(sP35,plain,sP35 <=> ((ra @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP35])])). % 0.14/0.45 thf(sP36,plain,sP36 <=> ((rb @ eigen__5) @ eigen__8),introduced(definition,[new_symbols(definition,[sP36])])). % 0.14/0.45 thf(sP37,plain,sP37 <=> (eigen__6 @ eigen__8),introduced(definition,[new_symbols(definition,[sP37])])). % 0.14/0.45 thf(sP38,plain,sP38 <=> ((~(sP20)) => sP26),introduced(definition,[new_symbols(definition,[sP38])])). % 0.14/0.45 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.14/0.45 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.14/0.45 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.14/0.45 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.14/0.45 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.14/0.45 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.14/0.45 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.14/0.45 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.14/0.45 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.14/0.45 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.14/0.45 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.14/0.45 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.14/0.45 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.14/0.45 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.14/0.45 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.14/0.45 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.14/0.45 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.14/0.45 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.14/0.45 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.14/0.45 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.14/0.45 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.14/0.45 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.14/0.45 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.14/0.45 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.14/0.45 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.14/0.45 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 0.14/0.45 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.14/0.45 thf(def_mvalid,definition,(mvalid = (!!))). % 0.14/0.45 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.14/0.45 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.14/0.45 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.14/0.45 thf(conj,conjecture,(~(((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((~((~((![X4:$i]:(((ra @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))))))) => ((~((![X4:$i]:(((ra @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((ra @ X1) @ X4) => (X3 @ X4)))))))) => (~((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((~((~((![X4:$i]:(((rb @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))))))) => ((~((![X4:$i]:(((rb @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((rb @ X1) @ X4) => (X3 @ X4)))))))))))))). % 0.14/0.45 thf(h0,negated_conjecture,((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((![X4:$i]:(((ra @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))) => ((~((![X4:$i]:(((ra @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((ra @ X1) @ X4) => (X3 @ X4)))))))) => (~((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((![X4:$i]:(((rb @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))) => ((~((![X4:$i]:(((rb @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((rb @ X1) @ X4) => (X3 @ X4))))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.14/0.45 thf(h1,assumption,(~((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((![X4:$i]:(((ra @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))) => ((~((![X4:$i]:(((ra @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((ra @ X1) @ X4) => (X3 @ X4)))))))))),introduced(assumption,[])). % 0.14/0.45 thf(h2,assumption,(~((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((![X4:$i]:(((rb @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))) => ((~((![X4:$i]:(((rb @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((rb @ X1) @ X4) => (X3 @ X4)))))))))),introduced(assumption,[])). % 0.14/0.45 thf(h3,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(((ra @ eigen__0) @ X3) => ((~((![X4:$i]:(((ra @ X3) @ X4) => (X1 @ X4))))) => (![X4:$i]:(((rb @ X3) @ X4) => (X2 @ X4)))))) => ((~((![X3:$i]:(((ra @ eigen__0) @ X3) => (X1 @ X3))))) => (![X3:$i]:(((ra @ eigen__0) @ X3) => (X2 @ X3))))))))),introduced(assumption,[])). % 0.14/0.45 thf(h4,assumption,(~((![X1:$i>$o]:((![X2:$i]:(((ra @ eigen__0) @ X2) => ((~((![X3:$i]:(((ra @ X2) @ X3) => (eigen__1 @ X3))))) => (![X3:$i]:(((rb @ X2) @ X3) => (X1 @ X3)))))) => ((~((![X2:$i]:(((ra @ eigen__0) @ X2) => (eigen__1 @ X2))))) => (![X2:$i]:(((ra @ eigen__0) @ X2) => (X1 @ X2)))))))),introduced(assumption,[])). % 0.14/0.45 thf(h5,assumption,(~((sP9 => ((~((![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__1 @ X1))))) => (![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__2 @ X1))))))),introduced(assumption,[])). % 0.14/0.45 thf(h6,assumption,sP9,introduced(assumption,[])). % 0.14/0.45 thf(h7,assumption,(~(((~((![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__1 @ X1))))) => (![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__2 @ X1)))))),introduced(assumption,[])). % 0.14/0.45 thf(h8,assumption,(~((![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__1 @ X1))))),introduced(assumption,[])). % 0.14/0.45 thf(h9,assumption,(~((![X1:$i]:(((ra @ eigen__0) @ X1) => (eigen__2 @ X1))))),introduced(assumption,[])). % 0.14/0.45 thf(h10,assumption,(~((sP35 => sP27))),introduced(assumption,[])). % 0.14/0.45 thf(h11,assumption,sP35,introduced(assumption,[])). % 0.14/0.45 thf(h12,assumption,(~(sP27)),introduced(assumption,[])). % 0.14/0.45 thf(h13,assumption,(~((sP1 => sP31))),introduced(assumption,[])). % 0.14/0.45 thf(h14,assumption,sP1,introduced(assumption,[])). % 0.14/0.45 thf(h15,assumption,(~(sP31)),introduced(assumption,[])). % 0.14/0.45 thf(1,plain,(~(sP6) | sP12),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(2,plain,(~(sP2) | sP14),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(3,plain,(~(sP14) | sP10),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(4,plain,(~(sP10) | sP4),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(5,plain,((~(sP4) | sP32) | sP22),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(6,plain,((~(sP32) | ~(sP1)) | ~(sP35)),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(7,plain,(~(sP20) | sP8),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(8,plain,((~(sP8) | ~(sP22)) | sP27),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(9,plain,(~(sP26) | sP29),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(10,plain,((~(sP29) | ~(sP12)) | sP31),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(11,plain,(~(sP9) | sP21),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(12,plain,((~(sP21) | ~(sP1)) | sP38),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(13,plain,((~(sP38) | sP20) | sP26),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(ax2,axiom,(mreflexive @ rb)). % 0.14/0.45 thf(14,plain,sP6,inference(preprocess,[status(thm)],[ax2]). % 0.14/0.45 thf(ax5,axiom,(meuclidean @ ra)). % 0.14/0.45 thf(15,plain,sP2,inference(preprocess,[status(thm)],[ax5]). % 0.14/0.45 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h6,h11,h12,h14,h15])). % 0.14/0.45 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,16,h14,h15])). % 0.14/0.45 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h6,h7,h5,h4,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h9,17,h13])). % 0.14/0.45 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h7,h5,h4,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,18,h11,h12])). % 0.14/0.45 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h8,19,h10])). % 0.14/0.45 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9])). % 0.14/0.45 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,21,h6,h7])). % 0.14/0.45 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,22,h5])). % 0.14/0.45 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,23,h4])). % 0.14/0.45 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,24,h3])). % 0.14/0.45 thf(h16,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:((![X3:$i]:(((rb @ eigen__5) @ X3) => ((~((![X4:$i]:(((ra @ X3) @ X4) => (X1 @ X4))))) => (![X4:$i]:(((rb @ X3) @ X4) => (X2 @ X4)))))) => ((~((![X3:$i]:(((rb @ eigen__5) @ X3) => (X1 @ X3))))) => (![X3:$i]:(((rb @ eigen__5) @ X3) => (X2 @ X3))))))))),introduced(assumption,[])). % 0.14/0.45 thf(h17,assumption,(~((![X1:$i>$o]:((![X2:$i]:(((rb @ eigen__5) @ X2) => ((~((![X3:$i]:(((ra @ X2) @ X3) => (eigen__6 @ X3))))) => (![X3:$i]:(((rb @ X2) @ X3) => (X1 @ X3)))))) => ((~((![X2:$i]:(((rb @ eigen__5) @ X2) => (eigen__6 @ X2))))) => (![X2:$i]:(((rb @ eigen__5) @ X2) => (X1 @ X2)))))))),introduced(assumption,[])). % 0.14/0.45 thf(h18,assumption,(~((sP25 => ((~((![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__6 @ X1))))) => (![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__7 @ X1))))))),introduced(assumption,[])). % 0.14/0.45 thf(h19,assumption,sP25,introduced(assumption,[])). % 0.14/0.45 thf(h20,assumption,(~(((~((![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__6 @ X1))))) => (![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__7 @ X1)))))),introduced(assumption,[])). % 0.14/0.45 thf(h21,assumption,(~((![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__6 @ X1))))),introduced(assumption,[])). % 0.14/0.45 thf(h22,assumption,(~((![X1:$i]:(((rb @ eigen__5) @ X1) => (eigen__7 @ X1))))),introduced(assumption,[])). % 0.14/0.45 thf(h23,assumption,(~((sP36 => sP37))),introduced(assumption,[])). % 0.14/0.45 thf(h24,assumption,sP36,introduced(assumption,[])). % 0.14/0.45 thf(h25,assumption,(~(sP37)),introduced(assumption,[])). % 0.14/0.45 thf(h26,assumption,(~((sP30 => sP13))),introduced(assumption,[])). % 0.14/0.45 thf(h27,assumption,sP30,introduced(assumption,[])). % 0.14/0.45 thf(h28,assumption,(~(sP13)),introduced(assumption,[])). % 0.14/0.45 thf(26,plain,(~(sP24) | sP23),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(27,plain,(~(sP28) | sP3),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(28,plain,((~(sP3) | ~(sP23)) | sP37),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(29,plain,(~(sP15) | sP11),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(30,plain,((~(sP11) | ~(sP7)) | sP13),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(31,plain,(~(sP25) | sP18),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(32,plain,((~(sP18) | ~(sP36)) | sP33),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(33,plain,((~(sP33) | sP28) | sP15),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(34,plain,(~(sP5) | sP34),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(35,plain,(~(sP34) | sP16),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(36,plain,((~(sP16) | sP19) | sP7),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(37,plain,((~(sP19) | ~(sP36)) | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 0.14/0.45 thf(38,plain,(~(sP17) | sP5),inference(all_rule,[status(thm)],[])). % 0.14/0.45 thf(ax1,axiom,(mreflexive @ ra)). % 0.14/0.45 thf(39,plain,sP24,inference(preprocess,[status(thm)],[ax1]). % 0.14/0.45 thf(ax6,axiom,(meuclidean @ rb)). % 0.14/0.45 thf(40,plain,sP17,inference(preprocess,[status(thm)],[ax6]). % 0.14/0.45 thf(41,plain,$false,inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h19,h20,h18,h17,h16,h2,h0])],[26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,h19,h24,h25,h27,h28])). % 0.14/0.45 thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h19,h20,h18,h17,h16,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,41,h27,h28])). % 0.14/0.45 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h19,h20,h18,h17,h16,h2,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__9)],[h22,42,h26])). % 0.14/0.45 thf(44,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h19,h20,h18,h17,h16,h2,h0]),tab_negimp(discharge,[h24,h25])],[h23,43,h24,h25])). % 0.14/0.45 thf(45,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h18,h17,h16,h2,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__8)],[h21,44,h23])). % 0.14/0.45 thf(46,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h17,h16,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,45,h21,h22])). % 0.14/0.45 thf(47,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h17,h16,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,46,h19,h20])). % 0.14/0.45 thf(48,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h16,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__7)],[h17,47,h18])). % 0.14/0.45 thf(49,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__6)],[h16,48,h17])). % 0.14/0.45 thf(50,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[h2,49,h16])). % 0.14/0.45 thf(51,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,25,50,h1,h2])). % 0.14/0.45 thf(0,theorem,(~(((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((~((~((![X4:$i]:(((ra @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))))))) => ((~((![X4:$i]:(((ra @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((ra @ X1) @ X4) => (X3 @ X4)))))))) => (~((![X1:$i]:(![X2:$i>$o]:(![X3:$i>$o]:((~((~((![X4:$i]:(((rb @ X1) @ X4) => ((~((![X5:$i]:(((ra @ X4) @ X5) => (X2 @ X5))))) => (![X5:$i]:(((rb @ X4) @ X5) => (X3 @ X5)))))))))) => ((~((![X4:$i]:(((rb @ X1) @ X4) => (X2 @ X4))))) => (![X4:$i]:(((rb @ X1) @ X4) => (X3 @ X4))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[51,h0])). % 0.14/0.45 % SZS output end Proof %------------------------------------------------------------------------------