%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG010^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n021.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Oct 9 01:27:38 PM UTC 2025 % Result : Theorem 13.12s 13.60s % Output : Proof 13.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEG010^1 : TPTP v9.2.0. Released v4.1.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Oct 8 12:30:38 EDT 2025 % 0.12/0.34 % CPUTime : % 13.12/13.60 % SZS status Theorem % 13.12/13.60 % Mode: mode454 % 13.12/13.60 % Inferences: 4808 % 13.12/13.60 % SZS output start Proof % 13.12/13.60 thf(ty_reg, type, reg : $tType). % 13.12/13.60 thf(ty_a, type, a : ($i>$i>$o)). % 13.12/13.60 thf(ty_fool, type, fool : ($i>$i>$o)). % 13.12/13.60 thf(ty_eigen__6, type, eigen__6 : $i). % 13.12/13.60 thf(ty_eigen__2, type, eigen__2 : reg). % 13.12/13.60 thf(ty_spain, type, spain : reg). % 13.12/13.60 thf(ty_catalunya, type, catalunya : reg). % 13.12/13.60 thf(ty_eigen__1, type, eigen__1 : $i). % 13.12/13.60 thf(ty_paris, type, paris : reg). % 13.12/13.60 thf(ty_eigen__0, type, eigen__0 : $i). % 13.12/13.60 thf(ty_eigen__10, type, eigen__10 : reg). % 13.12/13.60 thf(ty_eigen__20, type, eigen__20 : reg). % 13.12/13.60 thf(ty_france, type, france : reg). % 13.12/13.60 thf(ty_c, type, c : (reg>reg>$o)). % 13.12/13.60 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.12/13.60 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((a @ eigen__0) @ X1) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.12/13.60 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((fool @ eigen__0) @ X1) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 13.12/13.60 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.12/13.60 thf(h1, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 13.12/13.60 thf(eigendef_eigen__10, definition, eigen__10 = (eps__1 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__10])])). % 13.12/13.60 thf(eigendef_eigen__2, definition, eigen__2 = (eps__1 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 13.12/13.60 thf(eigendef_eigen__20, definition, eigen__20 = (eps__1 @ (^[X1:reg]:(~((((c @ X1) @ eigen__10) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__20])])). % 13.12/13.60 thf(sP1,plain,sP1 <=> (((a @ eigen__0) @ eigen__1) => (~(((~(((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))))) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 13.12/13.60 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ france))) => (![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.12/13.60 thf(sP3,plain,sP3 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.12/13.60 thf(sP4,plain,sP4 <=> (((c @ eigen__2) @ catalunya) => ((c @ eigen__2) @ spain)),introduced(definition,[new_symbols(definition,[sP4])])). % 13.12/13.60 thf(sP5,plain,sP5 <=> ((c @ eigen__20) @ eigen__10),introduced(definition,[new_symbols(definition,[sP5])])). % 13.12/13.60 thf(sP6,plain,sP6 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.12/13.60 thf(sP7,plain,sP7 <=> ((c @ eigen__2) @ eigen__2),introduced(definition,[new_symbols(definition,[sP7])])). % 13.12/13.60 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((a @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.12/13.60 thf(sP9,plain,sP9 <=> (((c @ spain) @ paris) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.12/13.60 thf(sP10,plain,sP10 <=> (![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 13.12/13.60 thf(sP11,plain,sP11 <=> (![X1:reg]:(((c @ X1) @ eigen__10) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP11])])). % 13.12/13.60 thf(sP12,plain,sP12 <=> (((a @ eigen__0) @ eigen__1) => (~(((~((sP3 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~(sP10)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 13.12/13.60 thf(sP13,plain,sP13 <=> (![X1:reg]:(((c @ X1) @ eigen__10) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP13])])). % 13.12/13.60 thf(sP14,plain,sP14 <=> (((c @ eigen__20) @ paris) => ((c @ eigen__20) @ france)),introduced(definition,[new_symbols(definition,[sP14])])). % 13.12/13.60 thf(sP15,plain,sP15 <=> ((c @ eigen__20) @ paris),introduced(definition,[new_symbols(definition,[sP15])])). % 13.12/13.60 thf(sP16,plain,sP16 <=> ((c @ eigen__2) @ catalunya),introduced(definition,[new_symbols(definition,[sP16])])). % 13.12/13.60 thf(sP17,plain,sP17 <=> ((c @ eigen__2) @ spain),introduced(definition,[new_symbols(definition,[sP17])])). % 13.12/13.60 thf(sP18,plain,sP18 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.12/13.60 thf(sP19,plain,sP19 <=> (sP17 => ((c @ spain) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP19])])). % 13.12/13.60 thf(sP20,plain,sP20 <=> (![X1:reg]:(((c @ X1) @ eigen__10) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP20])])). % 13.12/13.60 thf(sP21,plain,sP21 <=> (sP3 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP21])])). % 13.12/13.60 thf(sP22,plain,sP22 <=> (((a @ eigen__0) @ eigen__1) => (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 13.12/13.60 thf(sP23,plain,sP23 <=> (sP5 => sP15),introduced(definition,[new_symbols(definition,[sP23])])). % 13.12/13.60 thf(sP24,plain,sP24 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 13.12/13.60 thf(sP25,plain,sP25 <=> (sP13 => (~(sP11))),introduced(definition,[new_symbols(definition,[sP25])])). % 13.12/13.60 thf(sP26,plain,sP26 <=> ((fool @ eigen__0) @ eigen__6),introduced(definition,[new_symbols(definition,[sP26])])). % 13.12/13.60 thf(sP27,plain,sP27 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 13.12/13.60 thf(sP28,plain,sP28 <=> (sP5 => ((c @ eigen__20) @ france)),introduced(definition,[new_symbols(definition,[sP28])])). % 13.12/13.60 thf(sP29,plain,sP29 <=> ((~(sP18)) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 13.12/13.60 thf(sP30,plain,sP30 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP30])])). % 13.12/13.60 thf(sP31,plain,sP31 <=> (![X1:reg]:((c @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP31])])). % 13.12/13.60 thf(sP32,plain,sP32 <=> ((~(sP21)) => (~(sP10))),introduced(definition,[new_symbols(definition,[sP32])])). % 13.12/13.60 thf(sP33,plain,sP33 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP33])])). % 13.12/13.60 thf(sP34,plain,sP34 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP29)))),introduced(definition,[new_symbols(definition,[sP34])])). % 13.12/13.60 thf(sP35,plain,sP35 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (~((((c @ spain) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))),introduced(definition,[new_symbols(definition,[sP35])])). % 13.12/13.60 thf(sP36,plain,sP36 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__0) @ X2) => (X1 @ X2))) => (![X2:$i]:(((a @ eigen__0) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP36])])). % 13.12/13.60 thf(sP37,plain,sP37 <=> ((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))) => (~(sP33))),introduced(definition,[new_symbols(definition,[sP37])])). % 13.12/13.60 thf(sP38,plain,sP38 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (~((((c @ spain) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP38])])). % 13.12/13.60 thf(sP39,plain,sP39 <=> ((c @ spain) @ eigen__2),introduced(definition,[new_symbols(definition,[sP39])])). % 13.12/13.60 thf(sP40,plain,sP40 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP32)))),introduced(definition,[new_symbols(definition,[sP40])])). % 13.12/13.60 thf(sP41,plain,sP41 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => sP24))),introduced(definition,[new_symbols(definition,[sP41])])). % 13.12/13.60 thf(sP42,plain,sP42 <=> (![X1:reg]:(((c @ eigen__2) @ X1) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP42])])). % 13.12/13.60 thf(sP43,plain,sP43 <=> ((~(sP9)) => (((c @ spain) @ france) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))))))),introduced(definition,[new_symbols(definition,[sP43])])). % 13.12/13.60 thf(sP44,plain,sP44 <=> (sP7 => sP16),introduced(definition,[new_symbols(definition,[sP44])])). % 13.12/13.60 thf(sP45,plain,sP45 <=> (![X1:reg]:(![X2:reg]:(((c @ X1) @ X2) => ((c @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP45])])). % 13.12/13.60 thf(sP46,plain,sP46 <=> (sP39 => ((c @ spain) @ paris)),introduced(definition,[new_symbols(definition,[sP46])])). % 13.12/13.60 thf(sP47,plain,sP47 <=> (sP13 => (~(sP20))),introduced(definition,[new_symbols(definition,[sP47])])). % 13.12/13.60 thf(sP48,plain,sP48 <=> (((c @ spain) @ france) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))))))),introduced(definition,[new_symbols(definition,[sP48])])). % 13.12/13.60 thf(sP49,plain,sP49 <=> ((![X1:$i]:(((fool @ eigen__0) @ X1) => sP24)) => sP6),introduced(definition,[new_symbols(definition,[sP49])])). % 13.12/13.60 thf(sP50,plain,sP50 <=> ((c @ eigen__20) @ france),introduced(definition,[new_symbols(definition,[sP50])])). % 13.12/13.60 thf(sP51,plain,sP51 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => sP24)),introduced(definition,[new_symbols(definition,[sP51])])). % 13.12/13.60 thf(sP52,plain,sP52 <=> (sP26 => sP24),introduced(definition,[new_symbols(definition,[sP52])])). % 13.12/13.60 thf(sP53,plain,sP53 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP29))))),introduced(definition,[new_symbols(definition,[sP53])])). % 13.12/13.60 thf(sP54,plain,sP54 <=> ((c @ spain) @ paris),introduced(definition,[new_symbols(definition,[sP54])])). % 13.12/13.60 thf(sP55,plain,sP55 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP55])])). % 13.12/13.60 thf(sP56,plain,sP56 <=> (sP26 => (~(sP48))),introduced(definition,[new_symbols(definition,[sP56])])). % 13.12/13.60 thf(sP57,plain,sP57 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP57])])). % 13.12/13.60 thf(sP58,plain,sP58 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP58])])). % 13.12/13.60 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 13.12/13.60 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 13.12/13.60 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.12/13.60 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.12/13.60 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 13.12/13.60 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.12/13.60 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 13.12/13.60 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 13.12/13.60 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 13.12/13.60 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 13.12/13.60 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 13.12/13.60 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 13.12/13.60 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 13.12/13.60 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.12/13.60 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 13.12/13.60 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.12/13.60 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 13.12/13.60 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 13.12/13.60 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 13.12/13.60 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 13.12/13.60 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 13.12/13.60 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 13.12/13.60 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 13.12/13.60 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 13.12/13.60 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 13.12/13.60 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))))))))). % 13.12/13.60 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 13.12/13.60 thf(def_mvalid,definition,(mvalid = (!!))). % 13.12/13.60 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.12/13.60 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.12/13.60 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.12/13.60 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 13.12/13.60 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 13.12/13.60 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 13.12/13.60 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 13.12/13.60 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 13.12/13.60 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 13.12/13.60 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 13.12/13.60 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 13.12/13.60 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 13.12/13.60 thf(con,conjecture,sP41). % 13.12/13.60 thf(h2,negated_conjecture,(~(sP41)),inference(assume_negation,[status(cth)],[con])). % 13.12/13.60 thf(1,plain,((~(sP44) | ~(sP7)) | sP16),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(2,plain,(~(sP3) | sP14),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(3,plain,((~(sP14) | ~(sP15)) | sP50),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(4,plain,(~(sP11) | sP23),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(5,plain,((~(sP23) | ~(sP5)) | sP15),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(6,plain,((~(sP4) | ~(sP16)) | sP17),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(7,plain,(~(sP31) | sP7),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(8,plain,(~(sP55) | sP44),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(9,plain,(~(sP30) | sP4),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(10,plain,(sP28 | ~(sP50)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(11,plain,(sP28 | sP5),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(12,plain,(~(sP42) | sP19),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(13,plain,((~(sP19) | ~(sP17)) | sP39),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(14,plain,(sP20 | ~(sP28)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__20])). % 13.12/13.60 thf(15,plain,(~(sP33) | sP46),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(16,plain,((~(sP46) | ~(sP39)) | sP54),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(17,plain,(~(sP57) | sP47),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(18,plain,((~(sP47) | ~(sP13)) | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(19,plain,(sP25 | sP11),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(20,plain,(sP25 | sP13),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(21,plain,(sP27 | ~(sP25)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10])). % 13.12/13.60 thf(22,plain,(~(sP45) | sP42),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(23,plain,(~(sP38) | sP35),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(24,plain,(~(sP35) | sP56),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(25,plain,((~(sP56) | ~(sP26)) | ~(sP48)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(26,plain,(sP52 | sP26),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(27,plain,(sP51 | ~(sP52)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 13.12/13.60 thf(28,plain,(sP18 | sP30),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(29,plain,(sP29 | ~(sP18)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(30,plain,(~(sP10) | sP43),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(31,plain,((~(sP43) | sP9) | sP48),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(32,plain,((~(sP9) | ~(sP54)) | ~(sP27)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(33,plain,(sP48 | sP57),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(34,plain,(sP21 | sP3),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(35,plain,(sP32 | sP10),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(36,plain,(sP32 | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(37,plain,(sP37 | sP33),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(38,plain,(sP37 | sP55),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(39,plain,(sP24 | ~(sP37)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2])). % 13.12/13.60 thf(40,plain,(~(sP2) | sP40),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(41,plain,(~(sP40) | sP12),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(42,plain,((~(sP12) | ~(sP58)) | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(43,plain,(~(sP53) | sP34),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(44,plain,(~(sP34) | sP1),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(45,plain,((~(sP1) | ~(sP58)) | ~(sP29)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(46,plain,(sP22 | ~(sP24)),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(47,plain,(sP22 | sP58),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(48,plain,(sP6 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.12/13.60 thf(49,plain,(~(sP8) | sP36),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(50,plain,(~(sP36) | sP49),inference(all_rule,[status(thm)],[])). % 13.12/13.60 thf(51,plain,((~(sP49) | ~(sP51)) | sP6),inference(prop_rule,[status(thm)],[])). % 13.12/13.60 thf(52,plain,(sP41 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.12/13.60 thf(c_reflexive,axiom,sP31). % 13.12/13.60 thf(c_symmetric,axiom,sP45). % 13.12/13.60 thf(i_axiom_for_fool_a,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ ((mbox @ a) @ X1)))))). % 13.12/13.60 thf(53,plain,sP8,inference(preprocess,[status(thm)],[i_axiom_for_fool_a]). % 13.12/13.60 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))). % 13.12/13.60 thf(54,plain,sP53,inference(preprocess,[status(thm)],[ax1]). % 13.12/13.60 thf(ax2,axiom,(mvalid @ ((mbox @ fool) @ (^[X1:$i]:((ec @ spain) @ france))))). % 13.12/13.60 thf(55,plain,sP38,inference(preprocess,[status(thm)],[ax2]). % 13.12/13.60 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))). % 13.12/13.60 thf(56,plain,sP2,inference(preprocess,[status(thm)],[ax3]). % 13.12/13.60 thf(57,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,c_reflexive,c_symmetric,53,54,55,56,h2])). % 13.12/13.60 thf(58,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[57,h1])). % 13.12/13.60 thf(59,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[58,h0])). % 13.12/13.60 thf(0,theorem,sP41,inference(contra,[status(thm),contra(discharge,[h2])],[57,h2])). % 13.12/13.60 % SZS output end Proof %------------------------------------------------------------------------------