%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG020^1 : 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 : n031.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 01:27:39 PM UTC 2025 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.12 % Problem : GEG020^1 : TPTP v9.2.0. Released v4.1.0. % 0.05/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n031.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 12:30:08 EDT 2025 % 0.12/0.34 % CPUTime : % 0.20/0.52 % SZS status Theorem % 0.20/0.52 % Mode: mode213 % 0.20/0.52 % Inferences: 1414 % 0.20/0.52 % SZS output start Proof % 0.20/0.52 thf(ty_reg, type, reg : $tType). % 0.20/0.52 thf(ty_a, type, a : ($i>$i>$o)). % 0.20/0.52 thf(ty_eigen__6, type, eigen__6 : reg). % 0.20/0.52 thf(ty_eigen__2, type, eigen__2 : reg). % 0.20/0.52 thf(ty_spain, type, spain : reg). % 0.20/0.52 thf(ty_catalunya, type, catalunya : reg). % 0.20/0.52 thf(ty_eigen__1, type, eigen__1 : $i). % 0.20/0.52 thf(ty_paris, type, paris : reg). % 0.20/0.52 thf(ty_eigen__0, type, eigen__0 : $i). % 0.20/0.52 thf(ty_eigen__5, type, eigen__5 : reg). % 0.20/0.52 thf(ty_eigen__11, type, eigen__11 : reg). % 0.20/0.52 thf(ty_eigen__3, type, eigen__3 : reg). % 0.20/0.52 thf(ty_france, type, france : reg). % 0.20/0.52 thf(ty_c, type, c : (reg>reg>$o)). % 0.20/0.52 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.20/0.52 thf(eigendef_eigen__11, definition, eigen__11 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__6) => ((c @ X1) @ spain)))))), introduced(definition,[new_symbols(definition,[eigen__11])])). % 0.20/0.52 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__3) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 0.20/0.52 thf(sP1,plain,sP1 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.52 thf(sP2,plain,sP2 <=> (((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,[sP2])])). % 0.20/0.52 thf(sP3,plain,sP3 <=> (((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,[sP3])])). % 0.20/0.52 thf(sP4,plain,sP4 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))) => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.52 thf(sP5,plain,sP5 <=> ((~(((![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,[sP5])])). % 0.20/0.52 thf(sP6,plain,sP6 <=> ((c @ eigen__11) @ spain),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.52 thf(sP7,plain,sP7 <=> ((![X1:reg]:(((c @ X1) @ eigen__6) => ((c @ X1) @ eigen__2))) => (~((![X1:reg]:(((c @ X1) @ eigen__6) => ((c @ X1) @ spain)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.52 thf(sP8,plain,sP8 <=> ((c @ eigen__11) @ eigen__6),introduced(definition,[new_symbols(definition,[sP8])])). % 0.20/0.52 thf(sP9,plain,sP9 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP9])])). % 0.20/0.52 thf(sP10,plain,sP10 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP5)))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.20/0.52 thf(sP11,plain,sP11 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.20/0.52 thf(sP12,plain,sP12 <=> ((c @ eigen__5) @ eigen__3),introduced(definition,[new_symbols(definition,[sP12])])). % 0.20/0.52 thf(sP13,plain,sP13 <=> (![X1:reg]:(((c @ X1) @ eigen__6) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.20/0.52 thf(sP14,plain,sP14 <=> ((c @ eigen__11) @ catalunya),introduced(definition,[new_symbols(definition,[sP14])])). % 0.20/0.52 thf(sP15,plain,sP15 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP5))))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.20/0.52 thf(sP16,plain,sP16 <=> ((~(sP4)) => (![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,[sP16])])). % 0.20/0.52 thf(sP17,plain,sP17 <=> ((![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ eigen__2))) => (~((![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ france)))))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.20/0.52 thf(sP18,plain,sP18 <=> (sP14 => sP6),introduced(definition,[new_symbols(definition,[sP18])])). % 0.20/0.52 thf(sP19,plain,sP19 <=> (sP12 => ((c @ eigen__5) @ france)),introduced(definition,[new_symbols(definition,[sP19])])). % 0.20/0.52 thf(sP20,plain,sP20 <=> (((c @ eigen__5) @ paris) => ((c @ eigen__5) @ france)),introduced(definition,[new_symbols(definition,[sP20])])). % 0.20/0.52 thf(sP21,plain,sP21 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(sP16)))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.20/0.52 thf(sP22,plain,sP22 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.20/0.52 thf(sP23,plain,sP23 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP23])])). % 0.20/0.52 thf(sP24,plain,sP24 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP24])])). % 0.20/0.52 thf(sP25,plain,sP25 <=> (![X1:reg]:(((c @ X1) @ eigen__6) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.20/0.52 thf(sP26,plain,sP26 <=> ((c @ eigen__5) @ france),introduced(definition,[new_symbols(definition,[sP26])])). % 0.20/0.52 thf(sP27,plain,sP27 <=> (sP8 => sP6),introduced(definition,[new_symbols(definition,[sP27])])). % 0.20/0.52 thf(sP28,plain,sP28 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.20/0.52 thf(sP29,plain,sP29 <=> (sP8 => sP14),introduced(definition,[new_symbols(definition,[sP29])])). % 0.20/0.52 thf(sP30,plain,sP30 <=> (sP11 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.20/0.52 thf(sP31,plain,sP31 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP16))))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.20/0.52 thf(sP32,plain,sP32 <=> (![X1:reg]:(((c @ X1) @ eigen__6) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP32])])). % 0.20/0.52 thf(sP33,plain,sP33 <=> (sP12 => ((c @ eigen__5) @ paris)),introduced(definition,[new_symbols(definition,[sP33])])). % 0.20/0.52 thf(sP34,plain,sP34 <=> ((c @ eigen__5) @ paris),introduced(definition,[new_symbols(definition,[sP34])])). % 0.20/0.52 thf(sP35,plain,sP35 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP35])])). % 0.20/0.52 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.20/0.52 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.20/0.52 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.20/0.52 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.20/0.52 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.20/0.52 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.20/0.52 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.20/0.52 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.20/0.52 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.20/0.52 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.20/0.52 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.20/0.52 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.20/0.52 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.20/0.52 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.20/0.52 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.20/0.52 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.20/0.52 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.20/0.52 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.20/0.52 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.20/0.52 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.20/0.52 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.20/0.52 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.20/0.52 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 0.20/0.52 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.20/0.52 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.20/0.52 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))))))))). % 0.20/0.52 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.20/0.52 thf(def_mvalid,definition,(mvalid = (!!))). % 0.20/0.52 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.20/0.52 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.20/0.52 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.20/0.52 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 0.20/0.52 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 0.20/0.52 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 0.20/0.52 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 0.20/0.52 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 0.20/0.52 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 0.20/0.52 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 0.20/0.52 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 0.20/0.52 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 0.20/0.52 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:(((~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))) => ((~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))))))). % 0.20/0.52 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:(((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))) => ((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france))))))))))))))))),inference(assume_negation,[status(cth)],[con])). % 0.20/0.52 thf(h2,assumption,(~((![X1:$i]:(((a @ eigen__0) @ X1) => (![X2:reg]:(((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris))))))) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))) => ((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))))))) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h3,assumption,(~((sP9 => (![X1:reg]:(((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))) => ((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h4,assumption,sP9,introduced(assumption,[])). % 0.20/0.52 thf(h5,assumption,(~((![X1:reg]:(((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris))))))) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))) => ((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h6,assumption,(~((((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))) => (sP1 => (~(sP28)))))),introduced(assumption,[])). % 0.20/0.52 thf(h7,assumption,((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h8,assumption,(~((sP1 => (~(sP28))))),introduced(assumption,[])). % 0.20/0.52 thf(h9,assumption,(~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h10,assumption,(~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya))))))))),introduced(assumption,[])). % 0.20/0.52 thf(h11,assumption,(~((sP35 => (~(sP24))))),introduced(assumption,[])). % 0.20/0.52 thf(h12,assumption,sP35,introduced(assumption,[])). % 0.20/0.52 thf(h13,assumption,sP24,introduced(assumption,[])). % 0.20/0.52 thf(h14,assumption,sP1,introduced(assumption,[])). % 0.20/0.52 thf(h15,assumption,sP28,introduced(assumption,[])). % 0.20/0.52 thf(1,plain,(~(sP11) | sP20),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(2,plain,((~(sP20) | ~(sP34)) | sP26),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(3,plain,(sP30 | sP11),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(4,plain,(sP5 | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(5,plain,(~(sP15) | sP10),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(6,plain,(~(sP10) | sP3),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(7,plain,((~(sP3) | ~(sP9)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(8,plain,(~(sP24) | sP33),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(9,plain,((~(sP33) | ~(sP12)) | sP34),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(10,plain,(sP19 | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(11,plain,(sP19 | sP12),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(12,plain,(sP22 | ~(sP19)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 0.20/0.52 thf(13,plain,(~(sP28) | sP17),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(14,plain,((~(sP17) | ~(sP35)) | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))). % 0.20/0.52 thf(15,plain,sP15,inference(preprocess,[status(thm)],[ax3]). % 0.20/0.52 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4,h12,h13,h15])). % 0.20/0.52 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h8,16,h14,h15])). % 0.20/0.52 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,17,h12,h13])). % 0.20/0.52 thf(19,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h9,18,h11])). % 0.20/0.52 thf(h16,assumption,(~((sP25 => (~(sP32))))),introduced(assumption,[])). % 0.20/0.52 thf(h17,assumption,sP25,introduced(assumption,[])). % 0.20/0.52 thf(h18,assumption,sP32,introduced(assumption,[])). % 0.20/0.52 thf(20,plain,(~(sP23) | sP18),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(21,plain,((~(sP18) | ~(sP14)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(22,plain,(sP4 | sP23),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(23,plain,(sP16 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(24,plain,(~(sP31) | sP21),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(25,plain,(~(sP21) | sP2),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(26,plain,((~(sP2) | ~(sP9)) | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(27,plain,(~(sP32) | sP29),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(28,plain,((~(sP29) | ~(sP8)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(29,plain,(sP27 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(30,plain,(sP27 | sP8),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(31,plain,(sP13 | ~(sP27)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11])). % 0.20/0.52 thf(32,plain,(~(sP1) | sP7),inference(all_rule,[status(thm)],[])). % 0.20/0.52 thf(33,plain,((~(sP7) | ~(sP25)) | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 0.20/0.52 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))). % 0.20/0.52 thf(34,plain,sP31,inference(preprocess,[status(thm)],[ax1]). % 0.20/0.52 thf(35,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h17,h18,h16,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h4,h17,h18,h14])). % 0.20/0.52 thf(36,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h18,h16,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h8,35,h14,h15])). % 0.20/0.52 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h16,36,h17,h18])). % 0.20/0.52 thf(38,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__6)],[h10,37,h16])). % 0.20/0.52 thf(39,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,19,38,h9,h10])). % 0.20/0.52 thf(40,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,39,h7,h8])). % 0.20/0.52 thf(41,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,40,h6])). % 0.20/0.52 thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,41,h4,h5])). % 0.20/0.52 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,42,h3])). % 0.20/0.52 thf(44,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,43,h2])). % 0.20/0.52 thf(45,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[44,h0])). % 0.20/0.52 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:(((~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris))))))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))) => ((~((~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain))))))))))) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[44,h1])). % 0.20/0.52 % SZS output end Proof %------------------------------------------------------------------------------