%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV426^2 : TPTP v9.2.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n011.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 03:07:20 PM UTC 2025 % Result : Theorem 13.34s 13.32s % Output : Proof 13.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWV426^2 : TPTP v9.2.0. Released v3.6.0. % 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 14:10:23 EDT 2025 % 0.13/0.34 % CPUTime : % 13.34/13.32 % SZS status Theorem % 13.34/13.32 % Mode: mode454 % 13.34/13.32 % Inferences: 126 % 13.34/13.32 % SZS output start Proof % 13.34/13.32 thf(ty_a, type, a : ($i>$o)). % 13.34/13.32 thf(ty_eigen__2, type, eigen__2 : $i). % 13.34/13.32 thf(ty_s, type, s : ($i>$o)). % 13.34/13.32 thf(ty_eigen__1, type, eigen__1 : $i). % 13.34/13.32 thf(ty_eigen__0, type, eigen__0 : $i). % 13.34/13.32 thf(ty_eigen__3, type, eigen__3 : $i). % 13.34/13.32 thf(ty_t, type, t : ($i>$o)). % 13.34/13.32 thf(ty_rel, type, rel : ($i>$i>$o)). % 13.34/13.32 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.34/13.32 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 13.34/13.32 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__0) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => (s @ X4))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4))))))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.34/13.32 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => ((![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5)))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.34/13.32 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 13.34/13.32 thf(sP1,plain,sP1 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((rel @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (![X4:$i]:(((rel @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 13.34/13.32 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3))))))))) => (![X1:$i]:(((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.34/13.32 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel @ eigen__3) @ X1) => (s @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.34/13.32 thf(sP4,plain,sP4 <=> (((rel @ eigen__1) @ eigen__2) => (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.34/13.32 thf(sP5,plain,sP5 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2)))))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.34/13.32 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((rel @ eigen__3) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2)))))) => (sP3 => (![X1:$i]:(((rel @ eigen__3) @ X1) => (t @ X1))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.34/13.32 thf(sP7,plain,sP7 <=> (((rel @ eigen__2) @ eigen__3) => ((~((a @ eigen__3))) => (![X1:$i]:(((rel @ eigen__3) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2)))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 13.34/13.32 thf(sP8,plain,sP8 <=> (((rel @ eigen__0) @ eigen__1) => sP2),introduced(definition,[new_symbols(definition,[sP8])])). % 13.34/13.32 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.34/13.32 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel @ eigen__3) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2)))))),introduced(definition,[new_symbols(definition,[sP10])])). % 13.34/13.32 thf(sP11,plain,sP11 <=> (sP3 => (![X1:$i]:(((rel @ eigen__3) @ X1) => (t @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])). % 13.34/13.32 thf(sP12,plain,sP12 <=> ((~((a @ eigen__3))) => sP10),introduced(definition,[new_symbols(definition,[sP12])])). % 13.34/13.32 thf(sP13,plain,sP13 <=> ((~((a @ eigen__3))) => (![X1:$i]:(((rel @ eigen__3) @ X1) => (t @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 13.34/13.32 thf(sP14,plain,sP14 <=> ((![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))) => sP5),introduced(definition,[new_symbols(definition,[sP14])])). % 13.34/13.32 thf(sP15,plain,sP15 <=> (((rel @ eigen__2) @ eigen__3) => sP13),introduced(definition,[new_symbols(definition,[sP15])])). % 13.34/13.32 thf(sP16,plain,sP16 <=> ((rel @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP16])])). % 13.34/13.32 thf(sP17,plain,sP17 <=> (a @ eigen__3),introduced(definition,[new_symbols(definition,[sP17])])). % 13.34/13.32 thf(sP18,plain,sP18 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))),introduced(definition,[new_symbols(definition,[sP18])])). % 13.34/13.32 thf(sP19,plain,sP19 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => (s @ X4))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 13.34/13.32 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 13.34/13.32 thf(sP21,plain,sP21 <=> ((rel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP21])])). % 13.34/13.32 thf(sP22,plain,sP22 <=> ((~(sP17)) => sP3),introduced(definition,[new_symbols(definition,[sP22])])). % 13.34/13.32 thf(sP23,plain,sP23 <=> (![X1:$i]:((![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3)))))) => ((![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))) => (![X2:$i]:(((rel @ X1) @ X2) => (t @ X2)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 13.34/13.32 thf(sP24,plain,sP24 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((rel @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP24])])). % 13.34/13.32 thf(sP25,plain,sP25 <=> (![X1:$i]:(((rel @ eigen__3) @ X1) => (t @ X1))),introduced(definition,[new_symbols(definition,[sP25])])). % 13.34/13.32 thf(sP26,plain,sP26 <=> (![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => ((![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 13.34/13.32 thf(sP27,plain,sP27 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (t @ X3))))))))),introduced(definition,[new_symbols(definition,[sP27])])). % 13.34/13.32 thf(sP28,plain,sP28 <=> (sP16 => sP22),introduced(definition,[new_symbols(definition,[sP28])])). % 13.34/13.32 thf(sP29,plain,sP29 <=> (![X1:$i]:((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => (s @ X4))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4))))))))) => (![X2:$i]:(((rel @ X1) @ X2) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => ((![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 13.34/13.32 thf(sP30,plain,sP30 <=> (sP27 => sP19),introduced(definition,[new_symbols(definition,[sP30])])). % 13.34/13.32 thf(sP31,plain,sP31 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => (s @ X4))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4))))))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (t @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 13.34/13.32 thf(sP32,plain,sP32 <=> (sP21 => sP14),introduced(definition,[new_symbols(definition,[sP32])])). % 13.34/13.32 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 13.34/13.32 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.34/13.32 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.34/13.32 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.34/13.32 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 13.34/13.32 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.34/13.32 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 13.34/13.32 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.34/13.32 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 13.34/13.32 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 13.34/13.32 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 13.34/13.32 thf(def_mvalid,definition,(mvalid = (!!))). % 13.34/13.32 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.34/13.32 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.34/13.32 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.34/13.32 thf(def_icl_atom,definition,(icl_atom = (mbox @ rel))). % 13.34/13.32 thf(def_icl_princ,definition,(icl_princ = (^[X1:$i>$o]:X1))). % 13.34/13.32 thf(def_icl_and,definition,(icl_and = mand)). % 13.34/13.32 thf(def_icl_or,definition,(icl_or = mor)). % 13.34/13.32 thf(def_icl_impl,definition,(icl_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mimpl @ X1) @ X2)))))). % 13.34/13.32 thf(def_icl_true,definition,(icl_true = mtrue)). % 13.34/13.32 thf(def_icl_false,definition,(icl_false = mfalse)). % 13.34/13.32 thf(def_icl_says,definition,(icl_says = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mor @ X1) @ X2)))))). % 13.34/13.32 thf(def_iclval,definition,(iclval = mvalid)). % 13.34/13.32 thf(cuc,conjecture,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((~((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((~((![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))))))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5)))))))))))))). % 13.34/13.32 thf(h1,negated_conjecture,(~(sP26)),inference(assume_negation,[status(cth)],[cuc])). % 13.34/13.32 thf(1,plain,(~(sP23) | sP6),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(2,plain,((~(sP6) | ~(sP10)) | sP11),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(3,plain,(~(sP24) | sP23),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(4,plain,(~(sP9) | sP7),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(5,plain,((~(sP7) | ~(sP16)) | sP12),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(6,plain,(~(sP19) | sP4),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(7,plain,((~(sP4) | ~(sP21)) | sP9),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(8,plain,((~(sP12) | sP17) | sP10),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(9,plain,(sP13 | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(10,plain,(sP13 | ~(sP17)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(11,plain,((~(sP11) | ~(sP3)) | sP25),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(12,plain,(~(sP18) | sP28),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(13,plain,((~(sP28) | ~(sP16)) | sP22),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(14,plain,((~(sP22) | sP17) | sP3),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(15,plain,(sP15 | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(16,plain,(sP15 | sP16),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(17,plain,(sP5 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 13.34/13.32 thf(18,plain,(sP14 | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(19,plain,(sP14 | sP18),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(20,plain,(sP32 | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(21,plain,(sP32 | sP21),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(22,plain,(sP20 | ~(sP32)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 13.34/13.32 thf(23,plain,(~(sP1) | sP29),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(24,plain,(~(sP29) | sP30),inference(all_rule,[status(thm)],[])). % 13.34/13.32 thf(25,plain,((~(sP30) | ~(sP27)) | sP19),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(26,plain,(sP2 | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(27,plain,(sP2 | sP27),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(28,plain,(sP8 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 13.34/13.32 thf(29,plain,(sP31 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.34/13.32 thf(30,plain,(sP26 | ~(sP31)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.34/13.32 thf(refl_axiom,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ rel) @ X1)) @ X1)))). % 13.34/13.32 thf(31,plain,sP24,inference(preprocess,[status(thm)],[refl_axiom]). % 13.34/13.32 thf(trans_axiom,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ rel) @ X1)) @ ((mbox @ rel) @ ((mbox @ rel) @ X1)))))). % 13.34/13.32 thf(32,plain,sP1,inference(preprocess,[status(thm)],[trans_axiom]). % 13.34/13.32 thf(33,plain,$false,inference(prop_unsat,[status(thm),assumptions([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,h1])). % 13.34/13.32 thf(34,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[33,h0])). % 13.34/13.32 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((~((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((~((![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))))))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (t @ X5))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[33,h1])). % 13.34/13.32 % SZS output end Proof %------------------------------------------------------------------------------