%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG016^1 : 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 : n018.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 18.48s 18.86s % Output : Proof 18.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEG016^1 : 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 % 0.14/0.35 % Computer : n018.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Oct 8 12:31:08 EDT 2025 % 0.14/0.35 % CPUTime : % 18.48/18.86 % SZS status Theorem % 18.48/18.86 % Mode: mode485 % 18.48/18.86 % Inferences: 1588 % 18.48/18.86 % SZS output start Proof % 18.48/18.86 thf(ty_reg, type, reg : $tType). % 18.48/18.86 thf(ty_fool, type, fool : ($i>$i>$o)). % 18.48/18.86 thf(ty_eigen__2, type, eigen__2 : reg). % 18.48/18.86 thf(ty_spain, type, spain : reg). % 18.48/18.86 thf(ty_eigen__1, type, eigen__1 : $i). % 18.48/18.86 thf(ty_eigen__0, type, eigen__0 : $i). % 18.48/18.86 thf(ty_eigen__4, type, eigen__4 : reg). % 18.48/18.86 thf(ty_eigen__19, type, eigen__19 : reg). % 18.48/18.86 thf(ty_eigen__3, type, eigen__3 : reg). % 18.48/18.86 thf(ty_eigen__20, type, eigen__20 : reg). % 18.48/18.86 thf(ty_france, type, france : reg). % 18.48/18.86 thf(ty_c, type, c : (reg>reg>$o)). % 18.48/18.86 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 18.48/18.86 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:reg]:(~(((~(((![X2:reg]:(((c @ X2) @ eigen__2) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1)))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 18.48/18.86 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 18.48/18.86 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~((((fool @ eigen__0) @ X1) => (![X2:reg]:(![X3:reg]:((~(((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))) => (![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 18.48/18.86 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:(((fool @ X1) @ X2) => (![X3:reg]:(![X4:reg]:((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))) => (![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 18.48/18.86 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:reg]:(~((![X2:reg]:((~(((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ spain))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 18.48/18.86 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3)))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 18.48/18.86 thf(eigendef_eigen__20, definition, eigen__20 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__4) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__20])])). % 18.48/18.86 thf(eigendef_eigen__19, definition, eigen__19 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__4) => ((c @ X1) @ spain)))))), introduced(definition,[new_symbols(definition,[eigen__19])])). % 18.48/18.86 thf(sP1,plain,sP1 <=> ((![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__2))) => (~((![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__3)))))),introduced(definition,[new_symbols(definition,[sP1])])). % 18.48/18.86 thf(sP2,plain,sP2 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (![X2:reg]:(![X3:reg]:((~(((![X4:reg]:(((c @ X4) @ X2) => ((c @ X4) @ spain))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))) => (![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3)))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 18.48/18.86 thf(sP3,plain,sP3 <=> (((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,[sP3])])). % 18.48/18.86 thf(sP4,plain,sP4 <=> (((c @ eigen__20) @ eigen__3) => ((c @ eigen__20) @ france)),introduced(definition,[new_symbols(definition,[sP4])])). % 18.48/18.86 thf(sP5,plain,sP5 <=> ((c @ eigen__19) @ eigen__4),introduced(definition,[new_symbols(definition,[sP5])])). % 18.48/18.86 thf(sP6,plain,sP6 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP6])])). % 18.48/18.86 thf(sP7,plain,sP7 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__3))),introduced(definition,[new_symbols(definition,[sP7])])). % 18.48/18.86 thf(sP8,plain,sP8 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP8])])). % 18.48/18.86 thf(sP9,plain,sP9 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 18.48/18.86 thf(sP10,plain,sP10 <=> ((c @ eigen__19) @ eigen__2),introduced(definition,[new_symbols(definition,[sP10])])). % 18.48/18.86 thf(sP11,plain,sP11 <=> (((c @ eigen__20) @ eigen__4) => ((c @ eigen__20) @ france)),introduced(definition,[new_symbols(definition,[sP11])])). % 18.48/18.86 thf(sP12,plain,sP12 <=> (![X1:$i]:(((fool @ eigen__0) @ X1) => (~(sP3)))),introduced(definition,[new_symbols(definition,[sP12])])). % 18.48/18.86 thf(sP13,plain,sP13 <=> ((c @ eigen__20) @ france),introduced(definition,[new_symbols(definition,[sP13])])). % 18.48/18.86 thf(sP14,plain,sP14 <=> (((fool @ eigen__0) @ eigen__1) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP14])])). % 18.48/18.86 thf(sP15,plain,sP15 <=> ((c @ eigen__20) @ eigen__4),introduced(definition,[new_symbols(definition,[sP15])])). % 18.48/18.86 thf(sP16,plain,sP16 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 18.48/18.86 thf(sP17,plain,sP17 <=> (![X1:reg]:(((c @ X1) @ eigen__3) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP17])])). % 18.48/18.86 thf(sP18,plain,sP18 <=> ((c @ eigen__19) @ spain),introduced(definition,[new_symbols(definition,[sP18])])). % 18.48/18.86 thf(sP19,plain,sP19 <=> (![X1:reg]:(![X2:reg]:((~(((![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ spain))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))) => (![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 18.48/18.86 thf(sP20,plain,sP20 <=> (((fool @ eigen__0) @ eigen__1) => sP19),introduced(definition,[new_symbols(definition,[sP20])])). % 18.48/18.86 thf(sP21,plain,sP21 <=> (sP15 => ((c @ eigen__20) @ eigen__3)),introduced(definition,[new_symbols(definition,[sP21])])). % 18.48/18.86 thf(sP22,plain,sP22 <=> (sP6 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP22])])). % 18.48/18.86 thf(sP23,plain,sP23 <=> (![X1:reg]:(((c @ X1) @ eigen__4) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP23])])). % 18.48/18.86 thf(sP24,plain,sP24 <=> ((c @ eigen__20) @ eigen__3),introduced(definition,[new_symbols(definition,[sP24])])). % 18.48/18.86 thf(sP25,plain,sP25 <=> ((![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain))) => (~(sP17))),introduced(definition,[new_symbols(definition,[sP25])])). % 18.48/18.86 thf(sP26,plain,sP26 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => sP19))),introduced(definition,[new_symbols(definition,[sP26])])). % 18.48/18.86 thf(sP27,plain,sP27 <=> (sP10 => sP18),introduced(definition,[new_symbols(definition,[sP27])])). % 18.48/18.86 thf(sP28,plain,sP28 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (~(sP3))))),introduced(definition,[new_symbols(definition,[sP28])])). % 18.48/18.86 thf(sP29,plain,sP29 <=> ((fool @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP29])])). % 18.48/18.86 thf(sP30,plain,sP30 <=> ((~(sP25)) => sP16),introduced(definition,[new_symbols(definition,[sP30])])). % 18.48/18.86 thf(sP31,plain,sP31 <=> (sP5 => sP18),introduced(definition,[new_symbols(definition,[sP31])])). % 18.48/18.86 thf(sP32,plain,sP32 <=> (![X1:reg]:((~(((![X2:reg]:(((c @ X2) @ eigen__2) => ((c @ X2) @ spain))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))))) => (![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP32])])). % 18.48/18.86 thf(sP33,plain,sP33 <=> (sP5 => sP10),introduced(definition,[new_symbols(definition,[sP33])])). % 18.48/18.86 thf(sP34,plain,sP34 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP34])])). % 18.48/18.86 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 18.48/18.86 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 18.48/18.86 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 18.48/18.86 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 18.48/18.86 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 18.48/18.86 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 18.48/18.86 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 18.48/18.86 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 18.48/18.86 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 18.48/18.86 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 18.48/18.86 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 18.48/18.86 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 18.48/18.86 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 18.48/18.86 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 18.48/18.86 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 18.48/18.86 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 18.48/18.86 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 18.48/18.86 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 18.48/18.86 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 18.48/18.86 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 18.48/18.86 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 18.48/18.86 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 18.48/18.86 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 18.48/18.86 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 18.48/18.86 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 18.48/18.86 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))))))))). % 18.48/18.86 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 18.48/18.86 thf(def_mvalid,definition,(mvalid = (!!))). % 18.48/18.86 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 18.48/18.86 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 18.48/18.86 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 18.48/18.86 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 18.48/18.86 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 18.48/18.86 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 18.48/18.86 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 18.48/18.86 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 18.48/18.86 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 18.48/18.86 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 18.48/18.86 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 18.48/18.86 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 18.48/18.86 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (![X3:reg]:(![X4:reg]:((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4)))))))))))))))))). % 18.48/18.86 thf(h2,negated_conjecture,(~(sP26)),inference(assume_negation,[status(cth)],[con])). % 18.48/18.86 thf(1,plain,((~(sP4) | ~(sP24)) | sP13),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(2,plain,(~(sP17) | sP4),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(3,plain,(~(sP7) | sP21),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(4,plain,((~(sP21) | ~(sP15)) | sP24),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(5,plain,((~(sP27) | ~(sP10)) | sP18),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(6,plain,(~(sP34) | sP27),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(7,plain,(~(sP23) | sP33),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(8,plain,((~(sP33) | ~(sP5)) | sP10),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(9,plain,(sP11 | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(10,plain,(sP11 | sP15),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(11,plain,(sP31 | ~(sP18)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(12,plain,(sP31 | sP5),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(13,plain,(sP8 | ~(sP11)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20])). % 18.48/18.86 thf(14,plain,(sP6 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19])). % 18.48/18.86 thf(15,plain,((~(sP22) | ~(sP6)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(16,plain,(~(sP9) | sP22),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(17,plain,(sP3 | sP9),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(18,plain,(~(sP28) | sP12),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(19,plain,(~(sP12) | sP14),inference(all_rule,[status(thm)],[])). % 18.48/18.86 thf(20,plain,((~(sP14) | ~(sP29)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(21,plain,(sP1 | sP7),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(22,plain,(sP1 | sP23),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(23,plain,(sP16 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 18.48/18.86 thf(24,plain,(sP25 | sP17),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(25,plain,(sP25 | sP34),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(26,plain,(sP30 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(27,plain,(sP30 | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(28,plain,(sP32 | ~(sP30)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 18.48/18.86 thf(29,plain,(sP19 | ~(sP32)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 18.48/18.86 thf(30,plain,(sP20 | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(31,plain,(sP20 | sP29),inference(prop_rule,[status(thm)],[])). % 18.48/18.86 thf(32,plain,(sP2 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])). % 18.48/18.86 thf(33,plain,(sP26 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 18.48/18.86 thf(ax2,axiom,(mvalid @ ((mbox @ fool) @ (^[X1:$i]:((ec @ spain) @ france))))). % 18.48/18.86 thf(34,plain,sP28,inference(preprocess,[status(thm)],[ax2]). % 18.48/18.86 thf(35,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,h2])). % 18.48/18.86 thf(36,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[35,h1])). % 18.48/18.86 thf(37,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[36,h0])). % 18.48/18.86 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => (![X3:reg]:(![X4:reg]:((~(((![X5:reg]:(((c @ X5) @ X3) => ((c @ X5) @ spain))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))) => (~((~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[35,h2])). % 18.48/18.86 % SZS output end Proof %------------------------------------------------------------------------------