%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n026.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 01:02:26 PM UTC 2026 % Result : Theorem 12.97s 13.38s % Output : Proof 12.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0. % 0.00/0.03 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.36 % Computer : n026.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 : Fri Sep 4 20:25:10 UTC 2026 % 0.13/0.36 % CPUTime : % 12.97/13.38 % SZS status Theorem % 12.97/13.38 % Mode: mode454 % 12.97/13.38 % Inferences: 57 % 12.97/13.38 % SZS output start Proof % 12.97/13.38 thf(ty_relr, type, relr : ($i>$i>$o)). % 12.97/13.38 thf(ty_eigen__6, type, eigen__6 : $i). % 12.97/13.38 thf(ty_eigen__2, type, eigen__2 : $i). % 12.97/13.38 thf(ty_eigen__1, type, eigen__1 : ($i>$o)). % 12.97/13.38 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 12.97/13.38 thf(ty_eigen__4, type, eigen__4 : $i). % 12.97/13.38 thf(ty_eigen__5, type, eigen__5 : $i). % 12.97/13.38 thf(ty_reli, type, reli : ($i>$i>$o)). % 12.97/13.38 thf(ty_eigen__3, type, eigen__3 : $i). % 12.97/13.38 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 12.97/13.38 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__2) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 12.97/13.38 thf(h1, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 12.97/13.38 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7))) => (![X7:$i]:(((reli @ X6) @ X7) => (X1 @ X7)))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7))))))) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (X1 @ X7)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 12.97/13.38 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__1 @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 12.97/13.38 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i>$o]:(~((![X2:$i>$o]:(![X3:$i]:(![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 12.97/13.38 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__1 @ X6)))))))))) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__1 @ X6))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 12.97/13.38 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__3) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4))))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 12.97/13.38 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3)))))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 12.97/13.38 thf(sP1,plain,sP1 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__1 @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 12.97/13.38 thf(sP2,plain,sP2 <=> (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). % 12.97/13.38 thf(sP3,plain,sP3 <=> (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 12.97/13.38 thf(sP4,plain,sP4 <=> ((![X1:$i]:(((reli @ eigen__6) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__1 @ X2)))))) => ((![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__0 @ X1))) => (![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__1 @ X1))))),introduced(definition,[new_symbols(definition,[sP4])])). % 12.97/13.38 thf(sP5,plain,sP5 <=> (![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => ((![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7))) => (![X7:$i]:(((reli @ X6) @ X7) => (X1 @ X7)))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (eigen__0 @ X7))))))) => (![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => (X1 @ X7))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 12.97/13.38 thf(sP6,plain,sP6 <=> (((reli @ eigen__2) @ eigen__3) => ((![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))) => (![X1:$i]:(((reli @ eigen__3) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 12.97/13.38 thf(sP7,plain,sP7 <=> (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__1 @ X2))))),introduced(definition,[new_symbols(definition,[sP7])])). % 12.97/13.38 thf(sP8,plain,sP8 <=> ((reli @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP8])])). % 12.97/13.38 thf(sP9,plain,sP9 <=> (((reli @ eigen__3) @ eigen__4) => (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 12.97/13.38 thf(sP10,plain,sP10 <=> (sP8 => sP2),introduced(definition,[new_symbols(definition,[sP10])])). % 12.97/13.38 thf(sP11,plain,sP11 <=> (![X1:$i]:(((reli @ eigen__6) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 12.97/13.38 thf(sP12,plain,sP12 <=> (((relr @ eigen__5) @ eigen__6) => (![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__1 @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 12.97/13.38 thf(sP13,plain,sP13 <=> ((![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__0 @ X1))) => (![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__1 @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 12.97/13.38 thf(sP14,plain,sP14 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP14])])). % 12.97/13.38 thf(sP15,plain,sP15 <=> (((relr @ eigen__5) @ eigen__6) => sP11),introduced(definition,[new_symbols(definition,[sP15])])). % 12.97/13.38 thf(sP16,plain,sP16 <=> (sP8 => sP7),introduced(definition,[new_symbols(definition,[sP16])])). % 12.97/13.38 thf(sP17,plain,sP17 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3)))))) => ((![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP17])])). % 12.97/13.38 thf(sP18,plain,sP18 <=> ((![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))) => (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5))))))))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 12.97/13.38 thf(sP19,plain,sP19 <=> (![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 12.97/13.38 thf(sP20,plain,sP20 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 12.97/13.38 thf(sP21,plain,sP21 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5)))))))))) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5))))))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 12.97/13.38 thf(sP22,plain,sP22 <=> (sP3 => (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 12.97/13.38 thf(sP23,plain,sP23 <=> (sP8 => (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 12.97/13.38 thf(sP24,plain,sP24 <=> (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 12.97/13.38 thf(sP25,plain,sP25 <=> (((reli @ eigen__3) @ eigen__4) => sP22),introduced(definition,[new_symbols(definition,[sP25])])). % 12.97/13.38 thf(sP26,plain,sP26 <=> (![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:(![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 12.97/13.38 thf(sP27,plain,sP27 <=> (![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => ((![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__1 @ X6)))))))))) => (![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__0 @ X6))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (eigen__1 @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 12.97/13.38 thf(sP28,plain,sP28 <=> (sP20 => (![X1:$i]:(((reli @ eigen__3) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 12.97/13.38 thf(sP29,plain,sP29 <=> (![X1:$i]:(((relr @ eigen__5) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 12.97/13.38 thf(sP30,plain,sP30 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__1 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 12.97/13.38 thf(sP31,plain,sP31 <=> (![X1:$i]:(((reli @ eigen__4) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 12.97/13.38 thf(sP32,plain,sP32 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP32])])). % 12.97/13.38 thf(sP33,plain,sP33 <=> (((relr @ eigen__5) @ eigen__6) => sP19),introduced(definition,[new_symbols(definition,[sP33])])). % 12.97/13.38 thf(sP34,plain,sP34 <=> ((relr @ eigen__5) @ eigen__6),introduced(definition,[new_symbols(definition,[sP34])])). % 12.97/13.38 thf(sP35,plain,sP35 <=> ((reli @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP35])])). % 12.97/13.38 thf(sP36,plain,sP36 <=> (![X1:$i]:(((reli @ eigen__6) @ X1) => (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP36])])). % 12.97/13.38 thf(sP37,plain,sP37 <=> (![X1:$i]:(((reli @ eigen__3) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => ((![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__1 @ X5)))))))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 12.97/13.38 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 12.97/13.38 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 12.97/13.38 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 12.97/13.38 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 12.97/13.38 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 12.97/13.38 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 12.97/13.38 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 12.97/13.38 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 12.97/13.38 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 12.97/13.38 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 12.97/13.38 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 12.97/13.38 thf(def_mvalid,definition,(mvalid = (!!))). % 12.97/13.38 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 12.97/13.38 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 12.97/13.38 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 12.97/13.38 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))). % 12.97/13.38 thf(def_cs4_and,definition,(cs4_and = mand)). % 12.97/13.38 thf(def_cs4_or,definition,(cs4_or = mor)). % 12.97/13.38 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))). % 12.97/13.38 thf(def_cs4_true,definition,(cs4_true = mtrue)). % 12.97/13.38 thf(def_cs4_false,definition,(cs4_false = mfalse)). % 12.97/13.38 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))). % 12.97/13.38 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))). % 12.97/13.38 thf(def_cs4_valid,definition,(cs4_valid = mvalid)). % 12.97/13.38 thf(cs4_k,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:(![X4:$i]:(((reli @ X3) @ X4) => ((~((~((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((~((~((![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))))))) => (![X5:$i]:(((reli @ X4) @ X5) => ((~((~((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))))))) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8))))))))))))))))). % 12.97/13.38 thf(h2,negated_conjecture,(~(sP26)),inference(assume_negation,[status(cth)],[cs4_k])). % 12.97/13.38 thf(1,plain,((~(sP13) | ~(sP19)) | sP36),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(2,plain,(~(sP14) | sP17),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(3,plain,(~(sP17) | sP4),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(4,plain,((~(sP4) | ~(sP11)) | sP13),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(5,plain,(~(sP24) | sP23),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(6,plain,((~(sP23) | ~(sP8)) | sP29),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(7,plain,(~(sP37) | sP9),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(8,plain,((~(sP9) | ~(sP35)) | sP24),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(9,plain,(~(sP29) | sP15),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(10,plain,((~(sP15) | ~(sP34)) | sP11),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(11,plain,(~(sP2) | sP33),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(12,plain,((~(sP33) | ~(sP34)) | sP19),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(13,plain,(sP12 | ~(sP36)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(14,plain,(sP12 | sP34),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(15,plain,(sP7 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 12.97/13.38 thf(16,plain,(~(sP3) | sP10),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(17,plain,((~(sP10) | ~(sP8)) | sP2),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(18,plain,(sP16 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(19,plain,(sP16 | sP8),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(20,plain,(sP31 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 12.97/13.38 thf(21,plain,(sP22 | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(22,plain,(sP22 | sP3),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(23,plain,(sP25 | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(24,plain,(sP25 | sP35),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(25,plain,(sP30 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 12.97/13.38 thf(26,plain,(~(sP32) | sP1),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(27,plain,(~(sP1) | sP18),inference(all_rule,[status(thm)],[])). % 12.97/13.38 thf(28,plain,((~(sP18) | ~(sP20)) | sP37),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(29,plain,(sP28 | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(30,plain,(sP28 | sP20),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(31,plain,(sP6 | ~(sP28)),inference(prop_rule,[status(thm)],[])). % 12.97/13.38 thf(32,plain,(sP21 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 12.97/13.38 thf(33,plain,(sP27 | ~(sP21)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 12.97/13.38 thf(34,plain,(sP5 | ~(sP27)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])). % 12.97/13.38 thf(35,plain,(sP26 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 12.97/13.38 thf(refl_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ X1)))). % 12.97/13.38 thf(36,plain,sP14,inference(preprocess,[status(thm)],[refl_axiom_i]). % 12.97/13.38 thf(trans_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ ((mbox @ reli) @ ((mbox @ reli) @ X1)))))). % 12.97/13.38 thf(37,plain,sP32,inference(preprocess,[status(thm)],[trans_axiom_i]). % 12.97/13.38 thf(38,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,h2])). % 12.97/13.38 thf(39,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[38,h1])). % 12.97/13.38 thf(40,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[39,h0])). % 12.97/13.38 thf(0,theorem,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:(![X4:$i]:(((reli @ X3) @ X4) => ((~((~((![X5:$i]:(((reli @ X4) @ X5) => (![X6:$i]:(((relr @ X5) @ X6) => (![X7:$i]:(((reli @ X6) @ X7) => ((~((~((![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))))))) => (![X5:$i]:(((reli @ X4) @ X5) => ((~((~((![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X1 @ X8))))))))))) => (![X6:$i]:(((reli @ X5) @ X6) => (![X7:$i]:(((relr @ X6) @ X7) => (![X8:$i]:(((reli @ X7) @ X8) => (X2 @ X8)))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[38,h2])). % 12.97/13.38 % SZS output end Proof %------------------------------------------------------------------------------