%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG003^1 : 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 : n016.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 01:27:37 PM UTC 2025 % Result : Theorem 13.36s 13.60s % Output : Proof 13.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEG003^1 : TPTP v9.2.0. Released v4.1.0. % 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.11/0.35 % Computer : n016.cluster.edu % 0.11/0.35 % Model : x86_64 x86_64 % 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.35 % Memory : 8042.1875MB % 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.35 % CPULimit : 300 % 0.11/0.35 % WCLimit : 300 % 0.11/0.35 % DateTime : Wed Oct 8 12:30:38 EDT 2025 % 0.11/0.35 % CPUTime : % 13.36/13.60 % SZS status Theorem % 13.36/13.60 % Mode: mode454 % 13.36/13.60 % Inferences: 2696 % 13.36/13.60 % SZS output start Proof % 13.36/13.60 thf(ty_reg, type, reg : $tType). % 13.36/13.60 thf(ty_a, type, a : ($i>$i>$o)). % 13.36/13.60 thf(ty_fool, type, fool : ($i>$i>$o)). % 13.36/13.60 thf(ty_spain, type, spain : reg). % 13.36/13.60 thf(ty_catalunya, type, catalunya : reg). % 13.36/13.60 thf(ty_eigen__1, type, eigen__1 : $i). % 13.36/13.60 thf(ty_paris, type, paris : reg). % 13.36/13.60 thf(ty_eigen__0, type, eigen__0 : $i). % 13.36/13.60 thf(ty_eigen__5, type, eigen__5 : $i). % 13.36/13.60 thf(ty_eigen__9, type, eigen__9 : reg). % 13.36/13.60 thf(ty_france, type, france : reg). % 13.36/13.60 thf(ty_c, type, c : (reg>reg>$o)). % 13.36/13.60 thf(ty_eigen__18, type, eigen__18 : reg). % 13.36/13.60 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.36/13.60 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((a @ eigen__0) @ X1) => (~(((~(((c @ catalunya) @ paris))) => ((c @ spain) @ paris))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.36/13.60 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => (~(((~(((c @ catalunya) @ paris))) => ((c @ spain) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.36/13.60 thf(h1, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 13.36/13.60 thf(eigendef_eigen__18, definition, eigen__18 = (eps__1 @ (^[X1:reg]:(~((((c @ X1) @ eigen__9) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__18])])). % 13.36/13.60 thf(eigendef_eigen__9, definition, eigen__9 = (eps__1 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 13.36/13.60 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((fool @ eigen__0) @ X1) => (~(((~(((c @ catalunya) @ paris))) => ((c @ spain) @ paris))))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 13.36/13.60 thf(sP1,plain,sP1 <=> (((a @ eigen__0) @ eigen__1) => (~(((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~((![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,[sP1])])). % 13.36/13.60 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])])). % 13.36/13.60 thf(sP3,plain,sP3 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.36/13.60 thf(sP4,plain,sP4 <=> (((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,[sP4])])). % 13.36/13.60 thf(sP5,plain,sP5 <=> (![X1:reg]:(((c @ paris) @ X1) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.36/13.60 thf(sP6,plain,sP6 <=> ((c @ eigen__18) @ france),introduced(definition,[new_symbols(definition,[sP6])])). % 13.36/13.60 thf(sP7,plain,sP7 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (~(sP4)))),introduced(definition,[new_symbols(definition,[sP7])])). % 13.36/13.60 thf(sP8,plain,sP8 <=> ((fool @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP8])])). % 13.36/13.60 thf(sP9,plain,sP9 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((a @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.36/13.60 thf(sP10,plain,sP10 <=> (((c @ eigen__18) @ paris) => sP6),introduced(definition,[new_symbols(definition,[sP10])])). % 13.36/13.60 thf(sP11,plain,sP11 <=> (((c @ spain) @ paris) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP11])])). % 13.36/13.60 thf(sP12,plain,sP12 <=> ((c @ catalunya) @ paris),introduced(definition,[new_symbols(definition,[sP12])])). % 13.36/13.60 thf(sP13,plain,sP13 <=> ((~(sP11)) => sP4),introduced(definition,[new_symbols(definition,[sP13])])). % 13.36/13.60 thf(sP14,plain,sP14 <=> ((c @ paris) @ spain),introduced(definition,[new_symbols(definition,[sP14])])). % 13.36/13.60 thf(sP15,plain,sP15 <=> (![X1:reg]:(![X2:reg]:(((c @ X1) @ X2) => ((c @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP15])])). % 13.36/13.60 thf(sP16,plain,sP16 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP16])])). % 13.36/13.60 thf(sP17,plain,sP17 <=> ((~(sP12)) => ((c @ spain) @ paris)),introduced(definition,[new_symbols(definition,[sP17])])). % 13.36/13.60 thf(sP18,plain,sP18 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(sP16)) => (![X2:reg]:((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))))))))))))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.36/13.60 thf(sP19,plain,sP19 <=> (sP14 => ((c @ spain) @ paris)),introduced(definition,[new_symbols(definition,[sP19])])). % 13.36/13.60 thf(sP20,plain,sP20 <=> ((![X1:$i]:(((fool @ eigen__0) @ X1) => (~(sP17)))) => (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP17))))),introduced(definition,[new_symbols(definition,[sP20])])). % 13.36/13.60 thf(sP21,plain,sP21 <=> ((![X1:reg]:(((c @ X1) @ eigen__9) => ((c @ X1) @ spain))) => (~((![X1:reg]:(((c @ X1) @ eigen__9) => ((c @ X1) @ france)))))),introduced(definition,[new_symbols(definition,[sP21])])). % 13.36/13.60 thf(sP22,plain,sP22 <=> ((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~((![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,[sP22])])). % 13.36/13.60 thf(sP23,plain,sP23 <=> ((~(sP16)) => (![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,[sP23])])). % 13.36/13.60 thf(sP24,plain,sP24 <=> (sP8 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP24])])). % 13.36/13.60 thf(sP25,plain,sP25 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP25])])). % 13.36/13.60 thf(sP26,plain,sP26 <=> ((c @ eigen__18) @ paris),introduced(definition,[new_symbols(definition,[sP26])])). % 13.36/13.60 thf(sP27,plain,sP27 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP27])])). % 13.36/13.60 thf(sP28,plain,sP28 <=> (![X1:reg]:(((c @ X1) @ eigen__9) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP28])])). % 13.36/13.60 thf(sP29,plain,sP29 <=> (![X1:reg]:(((c @ catalunya) @ X1) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP29])])). % 13.36/13.60 thf(sP30,plain,sP30 <=> (((c @ eigen__18) @ eigen__9) => sP26),introduced(definition,[new_symbols(definition,[sP30])])). % 13.36/13.60 thf(sP31,plain,sP31 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP22)))),introduced(definition,[new_symbols(definition,[sP31])])). % 13.36/13.60 thf(sP32,plain,sP32 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP32])])). % 13.36/13.60 thf(sP33,plain,sP33 <=> (sP25 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP33])])). % 13.36/13.60 thf(sP34,plain,sP34 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (~(sP4))))),introduced(definition,[new_symbols(definition,[sP34])])). % 13.36/13.60 thf(sP35,plain,sP35 <=> (![X1:reg]:(((c @ X1) @ eigen__9) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP35])])). % 13.36/13.60 thf(sP36,plain,sP36 <=> ((c @ eigen__18) @ eigen__9),introduced(definition,[new_symbols(definition,[sP36])])). % 13.36/13.60 thf(sP37,plain,sP37 <=> ((c @ spain) @ paris),introduced(definition,[new_symbols(definition,[sP37])])). % 13.36/13.60 thf(sP38,plain,sP38 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP17))))),introduced(definition,[new_symbols(definition,[sP38])])). % 13.36/13.60 thf(sP39,plain,sP39 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP39])])). % 13.36/13.60 thf(sP40,plain,sP40 <=> (sP8 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP40])])). % 13.36/13.60 thf(sP41,plain,sP41 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP17)))),introduced(definition,[new_symbols(definition,[sP41])])). % 13.36/13.60 thf(sP42,plain,sP42 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (~(sP17)))),introduced(definition,[new_symbols(definition,[sP42])])). % 13.36/13.60 thf(sP43,plain,sP43 <=> (sP36 => sP6),introduced(definition,[new_symbols(definition,[sP43])])). % 13.36/13.60 thf(sP44,plain,sP44 <=> (((c @ paris) @ catalunya) => sP14),introduced(definition,[new_symbols(definition,[sP44])])). % 13.36/13.60 thf(sP45,plain,sP45 <=> (sP32 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP45])])). % 13.36/13.60 thf(sP46,plain,sP46 <=> ((c @ paris) @ catalunya),introduced(definition,[new_symbols(definition,[sP46])])). % 13.36/13.60 thf(sP47,plain,sP47 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__0) @ X2) => (X1 @ X2))) => (![X2:$i]:(((a @ eigen__0) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP47])])). % 13.36/13.60 thf(sP48,plain,sP48 <=> (sP12 => sP46),introduced(definition,[new_symbols(definition,[sP48])])). % 13.36/13.60 thf(sP49,plain,sP49 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP23))))),introduced(definition,[new_symbols(definition,[sP49])])). % 13.36/13.60 thf(sP50,plain,sP50 <=> (![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,[sP50])])). % 13.36/13.60 thf(sP51,plain,sP51 <=> (![X1:reg]:(((c @ X1) @ eigen__9) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP51])])). % 13.36/13.60 thf(sP52,plain,sP52 <=> (sP32 => (~(sP23))),introduced(definition,[new_symbols(definition,[sP52])])). % 13.36/13.60 thf(sP53,plain,sP53 <=> (sP51 => (~(sP28))),introduced(definition,[new_symbols(definition,[sP53])])). % 13.36/13.60 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 13.36/13.60 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 13.36/13.60 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.36/13.60 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.36/13.60 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 13.36/13.60 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.36/13.60 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 13.36/13.60 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 13.36/13.60 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 13.36/13.60 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 13.36/13.60 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 13.36/13.60 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 13.36/13.60 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 13.36/13.60 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.36/13.60 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 13.36/13.60 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.36/13.60 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 13.36/13.60 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 13.36/13.60 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 13.36/13.60 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 13.36/13.60 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 13.36/13.60 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 13.36/13.60 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)))))))). % 13.36/13.60 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 13.36/13.60 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 13.36/13.60 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 13.36/13.60 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 13.36/13.60 thf(def_mvalid,definition,(mvalid = (!!))). % 13.36/13.60 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.36/13.60 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.36/13.60 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.36/13.60 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 13.36/13.60 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 13.36/13.60 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 13.36/13.60 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 13.36/13.60 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 13.36/13.60 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 13.36/13.60 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 13.36/13.60 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 13.36/13.60 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 13.36/13.60 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(sP12)) => (~((~(sP37))))))))))). % 13.36/13.60 thf(h2,negated_conjecture,(~(sP38)),inference(assume_negation,[status(cth)],[con])). % 13.36/13.60 thf(1,plain,(~(sP25) | sP10),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(2,plain,((~(sP10) | ~(sP26)) | sP6),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(3,plain,(~(sP28) | sP30),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(4,plain,((~(sP30) | ~(sP36)) | sP26),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(5,plain,(~(sP29) | sP48),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(6,plain,((~(sP48) | ~(sP12)) | sP46),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(7,plain,(sP43 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(8,plain,(sP43 | sP36),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(9,plain,(~(sP27) | sP44),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(10,plain,((~(sP44) | ~(sP46)) | sP14),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(11,plain,(sP35 | ~(sP43)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18])). % 13.36/13.60 thf(12,plain,(~(sP5) | sP19),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(13,plain,((~(sP19) | ~(sP14)) | sP37),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(14,plain,(~(sP39) | sP21),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(15,plain,((~(sP21) | ~(sP51)) | ~(sP35)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(16,plain,(sP53 | sP28),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(17,plain,(sP53 | sP51),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(18,plain,(sP3 | ~(sP53)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9])). % 13.36/13.60 thf(19,plain,(~(sP34) | sP7),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(20,plain,(~(sP7) | sP24),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(21,plain,((~(sP24) | ~(sP8)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(22,plain,(sP40 | sP8),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(23,plain,(sP42 | ~(sP40)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 13.36/13.60 thf(24,plain,(~(sP15) | sP29),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(25,plain,(sP16 | sP27),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(26,plain,(sP23 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(27,plain,(~(sP50) | sP13),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(28,plain,((~(sP13) | sP11) | sP4),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(29,plain,((~(sP11) | ~(sP37)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(30,plain,(sP4 | sP39),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(31,plain,(~(sP15) | sP5),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(32,plain,(sP33 | sP25),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(33,plain,(sP22 | sP50),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(34,plain,(sP22 | ~(sP33)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(35,plain,((~(sP17) | sP12) | sP37),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(36,plain,(~(sP2) | sP31),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(37,plain,(~(sP31) | sP1),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(38,plain,((~(sP1) | ~(sP32)) | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(39,plain,(~(sP49) | sP18),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(40,plain,(~(sP18) | sP52),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(41,plain,((~(sP52) | ~(sP32)) | ~(sP23)),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(42,plain,(sP45 | sP17),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(43,plain,(sP45 | sP32),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(44,plain,(sP41 | ~(sP45)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.36/13.60 thf(45,plain,(~(sP9) | sP47),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(46,plain,(~(sP47) | sP20),inference(all_rule,[status(thm)],[])). % 13.36/13.60 thf(47,plain,((~(sP20) | ~(sP42)) | sP41),inference(prop_rule,[status(thm)],[])). % 13.36/13.60 thf(48,plain,(sP38 | ~(sP41)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.36/13.60 thf(c_symmetric,axiom,sP15). % 13.36/13.60 thf(i_axiom_for_fool_a,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ ((mbox @ a) @ X1)))))). % 13.36/13.60 thf(49,plain,sP9,inference(preprocess,[status(thm)],[i_axiom_for_fool_a]). % 13.36/13.60 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))). % 13.36/13.60 thf(50,plain,sP49,inference(preprocess,[status(thm)],[ax1]). % 13.36/13.60 thf(ax2,axiom,(mvalid @ ((mbox @ fool) @ (^[X1:$i]:((ec @ spain) @ france))))). % 13.36/13.60 thf(51,plain,sP34,inference(preprocess,[status(thm)],[ax2]). % 13.36/13.60 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))). % 13.36/13.60 thf(52,plain,sP2,inference(preprocess,[status(thm)],[ax3]). % 13.36/13.60 thf(53,plain,$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,c_symmetric,49,50,51,52,h2])). % 13.36/13.60 thf(54,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[53,h1])). % 13.36/13.60 thf(55,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[54,h0])). % 13.36/13.60 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(sP12)) => (~((~(sP37)))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[53,h2])). % 13.36/13.60 % SZS output end Proof %------------------------------------------------------------------------------