%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO443^1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n006.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 03:25:36 PM UTC 2025 % Result : Theorem 0.20s 0.41s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SYO443^1 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.35 % Computer : n006.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 : Thu Oct 9 00:58:38 EDT 2025 % 0.14/0.35 % CPUTime : % 0.20/0.41 % SZS status Theorem % 0.20/0.41 % Mode: mode213 % 0.20/0.41 % Inferences: 77 % 0.20/0.41 % SZS output start Proof % 0.20/0.41 thf(ty_eigen__6, type, eigen__6 : $i). % 0.20/0.41 thf(ty_p, type, p : ($i>$o)). % 0.20/0.41 thf(ty_eigen__2, type, eigen__2 : $i). % 0.20/0.41 thf(ty_q, type, q : ($i>$o)). % 0.20/0.41 thf(ty_eigen__1, type, eigen__1 : $i). % 0.20/0.41 thf(ty_eigen__0, type, eigen__0 : $i). % 0.20/0.41 thf(ty_eigen__4, type, eigen__4 : $i). % 0.20/0.41 thf(ty_eigen__5, type, eigen__5 : $i). % 0.20/0.41 thf(ty_eigen__3, type, eigen__3 : $i). % 0.20/0.41 thf(ty_rel_s5, type, rel_s5 : ($i>$i>$o)). % 0.20/0.41 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.41 thf(sP2,plain,sP2 <=> ((rel_s5 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP2])])). % 0.20/0.41 thf(sP3,plain,sP3 <=> ((~((((rel_s5 @ eigen__1) @ eigen__0) => (~(sP2))))) => ((rel_s5 @ eigen__1) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.20/0.41 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s5 @ X1) @ X2) => (~(((rel_s5 @ X2) @ X3)))))) => ((rel_s5 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.41 thf(sP5,plain,sP5 <=> ((rel_s5 @ eigen__0) @ eigen__3),introduced(definition,[new_symbols(definition,[sP5])])). % 0.20/0.41 thf(sP6,plain,sP6 <=> ((p @ eigen__1) => (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (q @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.41 thf(sP7,plain,sP7 <=> (((rel_s5 @ eigen__1) @ eigen__0) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.41 thf(sP8,plain,sP8 <=> ((rel_s5 @ eigen__5) @ eigen__6),introduced(definition,[new_symbols(definition,[sP8])])). % 0.20/0.41 thf(sP9,plain,sP9 <=> ((rel_s5 @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])). % 0.20/0.41 thf(sP10,plain,sP10 <=> (q @ eigen__6),introduced(definition,[new_symbols(definition,[sP10])])). % 0.20/0.41 thf(sP11,plain,sP11 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((p @ X1) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.20/0.41 thf(sP12,plain,sP12 <=> (![X1:$i]:((~((sP9 => (~(((rel_s5 @ eigen__0) @ X1)))))) => ((rel_s5 @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.20/0.41 thf(sP13,plain,sP13 <=> (p @ eigen__3),introduced(definition,[new_symbols(definition,[sP13])])). % 0.20/0.41 thf(sP14,plain,sP14 <=> (![X1:$i]:((~((((rel_s5 @ eigen__0) @ eigen__5) => (~(((rel_s5 @ eigen__5) @ X1)))))) => ((rel_s5 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.20/0.41 thf(sP15,plain,sP15 <=> (((rel_s5 @ eigen__0) @ eigen__1) => sP9),introduced(definition,[new_symbols(definition,[sP15])])). % 0.20/0.41 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i]:(((rel_s5 @ X1) @ X2) => ((rel_s5 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.20/0.41 thf(sP17,plain,sP17 <=> (((rel_s5 @ eigen__0) @ eigen__5) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.20/0.41 thf(sP18,plain,sP18 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => (~((p @ X1))))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.20/0.41 thf(sP19,plain,sP19 <=> (sP5 => (~(sP13))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.20/0.41 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel_s5 @ eigen__1) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.20/0.41 thf(sP21,plain,sP21 <=> (((rel_s5 @ eigen__0) @ eigen__1) => sP6),introduced(definition,[new_symbols(definition,[sP21])])). % 0.20/0.41 thf(sP22,plain,sP22 <=> ((rel_s5 @ eigen__0) @ eigen__5),introduced(definition,[new_symbols(definition,[sP22])])). % 0.20/0.41 thf(sP23,plain,sP23 <=> ((rel_s5 @ eigen__0) @ eigen__6),introduced(definition,[new_symbols(definition,[sP23])])). % 0.20/0.41 thf(sP24,plain,sP24 <=> (((rel_s5 @ eigen__1) @ eigen__2) => (q @ eigen__2)),introduced(definition,[new_symbols(definition,[sP24])])). % 0.20/0.41 thf(sP25,plain,sP25 <=> (p @ eigen__1),introduced(definition,[new_symbols(definition,[sP25])])). % 0.20/0.41 thf(sP26,plain,sP26 <=> ((rel_s5 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP26])])). % 0.20/0.41 thf(sP27,plain,sP27 <=> (q @ eigen__2),introduced(definition,[new_symbols(definition,[sP27])])). % 0.20/0.41 thf(sP28,plain,sP28 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__1) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__1) @ X2)))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.20/0.41 thf(sP29,plain,sP29 <=> (sP23 => sP10),introduced(definition,[new_symbols(definition,[sP29])])). % 0.20/0.41 thf(sP30,plain,sP30 <=> ((~(sP17)) => sP23),introduced(definition,[new_symbols(definition,[sP30])])). % 0.20/0.41 thf(sP31,plain,sP31 <=> (![X1:$i]:(((rel_s5 @ eigen__0) @ X1) => ((rel_s5 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP31])])). % 0.20/0.41 thf(sP32,plain,sP32 <=> ((rel_s5 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP32])])). % 0.20/0.41 thf(sP33,plain,sP33 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s5 @ eigen__0) @ X1) => (~(((rel_s5 @ X1) @ X2)))))) => ((rel_s5 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP33])])). % 0.20/0.41 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 0.20/0.41 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 0.20/0.41 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.20/0.41 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.20/0.41 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 0.20/0.41 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.20/0.41 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 0.20/0.41 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 0.20/0.41 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 0.20/0.41 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 0.20/0.41 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 0.20/0.41 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 0.20/0.41 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 0.20/0.41 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.20/0.41 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.20/0.41 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.20/0.41 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 0.20/0.41 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.20/0.41 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 0.20/0.41 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 0.20/0.41 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.20/0.41 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 0.20/0.41 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)))))))). % 0.20/0.41 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 0.20/0.41 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 0.20/0.41 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 0.20/0.41 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 0.20/0.41 thf(def_mvalid,definition,(mvalid = (!!))). % 0.20/0.41 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.20/0.41 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.20/0.41 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.20/0.41 thf(def_mbox_s5,definition,(mbox_s5 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s5 @ X2) @ X3) => (X1 @ X3))))))). % 0.20/0.41 thf(def_mdia_s5,definition,(mdia_s5 = (^[X1:$i>$o]:(mnot @ (mbox_s5 @ (mnot @ X1)))))). % 0.20/0.41 thf(prove,conjecture,(![X1:$i]:(~(((~((~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2))))))))) => (~(((~((~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))))))). % 0.20/0.41 thf(h0,negated_conjecture,(~((![X1:$i]:(~((((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((p @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2))))) => (~((((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((p @ X2) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3))))))))))))))),inference(assume_negation,[status(cth)],[prove])). % 0.20/0.41 thf(h1,assumption,((sP11 => ((~(sP18)) => sP1)) => (~((((~(sP18)) => sP1) => sP11)))),introduced(assumption,[])). % 0.20/0.41 thf(h2,assumption,(~((sP11 => ((~(sP18)) => sP1)))),introduced(assumption,[])). % 0.20/0.41 thf(h3,assumption,(~((((~(sP18)) => sP1) => sP11))),introduced(assumption,[])). % 0.20/0.41 thf(h4,assumption,sP11,introduced(assumption,[])). % 0.20/0.41 thf(h5,assumption,(~(((~(sP18)) => sP1))),introduced(assumption,[])). % 0.20/0.41 thf(h6,assumption,(~(sP18)),introduced(assumption,[])). % 0.20/0.41 thf(h7,assumption,(~(sP1)),introduced(assumption,[])). % 0.20/0.41 thf(h8,assumption,(~((sP32 => (~(sP25))))),introduced(assumption,[])). % 0.20/0.41 thf(h9,assumption,sP32,introduced(assumption,[])). % 0.20/0.41 thf(h10,assumption,sP25,introduced(assumption,[])). % 0.20/0.41 thf(h11,assumption,(~((sP2 => sP27))),introduced(assumption,[])). % 0.20/0.41 thf(h12,assumption,sP2,introduced(assumption,[])). % 0.20/0.41 thf(h13,assumption,(~(sP27)),introduced(assumption,[])). % 0.20/0.41 thf(1,plain,(~(sP16) | sP31),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(2,plain,(~(sP31) | sP15),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(3,plain,((~(sP15) | ~(sP32)) | sP9),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(4,plain,(~(sP4) | sP28),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(5,plain,(~(sP28) | sP12),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(6,plain,(~(sP12) | sP3),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(7,plain,((~(sP3) | sP7) | sP26),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(8,plain,((~(sP7) | ~(sP9)) | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(9,plain,(~(sP20) | sP24),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(10,plain,((~(sP24) | ~(sP26)) | sP27),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(11,plain,(~(sP11) | sP21),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(12,plain,((~(sP21) | ~(sP32)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(13,plain,((~(sP6) | ~(sP25)) | sP20),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(a2,axiom,(mtransitive @ rel_s5)). % 0.20/0.41 thf(14,plain,sP4,inference(preprocess,[status(thm)],[a2]). % 0.20/0.41 thf(a3,axiom,(msymmetric @ rel_s5)). % 0.20/0.41 thf(15,plain,sP16,inference(preprocess,[status(thm)],[a3]). % 0.20/0.41 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h9,h10,h8,h6,h7,h4,h5,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h4,h9,h10,h12,h13])). % 0.20/0.41 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,16,h12,h13])). % 0.20/0.41 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h7,17,h11])). % 0.20/0.41 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,18,h9,h10])). % 0.20/0.41 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h6,19,h8])). % 0.20/0.41 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,20,h6,h7])). % 0.20/0.41 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,21,h4,h5])). % 0.20/0.41 thf(h14,assumption,((~(sP18)) => sP1),introduced(assumption,[])). % 0.20/0.41 thf(h15,assumption,(~(sP11)),introduced(assumption,[])). % 0.20/0.41 thf(h16,assumption,sP18,introduced(assumption,[])). % 0.20/0.41 thf(h17,assumption,sP1,introduced(assumption,[])). % 0.20/0.41 thf(h18,assumption,(~((sP5 => (sP13 => (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (q @ X1))))))),introduced(assumption,[])). % 0.20/0.41 thf(h19,assumption,sP5,introduced(assumption,[])). % 0.20/0.41 thf(h20,assumption,(~((sP13 => (![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (q @ X1)))))),introduced(assumption,[])). % 0.20/0.41 thf(h21,assumption,sP13,introduced(assumption,[])). % 0.20/0.41 thf(h22,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__3) @ X1) => (q @ X1))))),introduced(assumption,[])). % 0.20/0.41 thf(h23,assumption,(~((((rel_s5 @ eigen__3) @ eigen__4) => (q @ eigen__4)))),introduced(assumption,[])). % 0.20/0.41 thf(h24,assumption,((rel_s5 @ eigen__3) @ eigen__4),introduced(assumption,[])). % 0.20/0.41 thf(h25,assumption,(~((q @ eigen__4))),introduced(assumption,[])). % 0.20/0.41 thf(23,plain,(~(sP18) | sP19),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(24,plain,((~(sP19) | ~(sP5)) | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h21,h22,h19,h20,h18,h16,h14,h15,h3,h1,h0])],[23,24,h16,h19,h21])). % 0.20/0.41 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h19,h20,h18,h16,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,25,h24,h25])). % 0.20/0.41 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h19,h20,h18,h16,h14,h15,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__4)],[h22,26,h23])). % 0.20/0.41 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h16,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,27,h21,h22])). % 0.20/0.41 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h16,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,28,h19,h20])). % 0.20/0.41 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h16,h14,h15,h3,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__3)],[h15,29,h18])). % 0.20/0.41 thf(h26,assumption,(~((sP22 => ((p @ eigen__5) => (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (q @ X1))))))),introduced(assumption,[])). % 0.20/0.41 thf(h27,assumption,sP22,introduced(assumption,[])). % 0.20/0.41 thf(h28,assumption,(~(((p @ eigen__5) => (![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (q @ X1)))))),introduced(assumption,[])). % 0.20/0.41 thf(h29,assumption,(p @ eigen__5),introduced(assumption,[])). % 0.20/0.41 thf(h30,assumption,(~((![X1:$i]:(((rel_s5 @ eigen__5) @ X1) => (q @ X1))))),introduced(assumption,[])). % 0.20/0.41 thf(h31,assumption,(~((sP8 => sP10))),introduced(assumption,[])). % 0.20/0.41 thf(h32,assumption,sP8,introduced(assumption,[])). % 0.20/0.41 thf(h33,assumption,(~(sP10)),introduced(assumption,[])). % 0.20/0.41 thf(31,plain,(~(sP1) | sP29),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(32,plain,((~(sP29) | ~(sP23)) | sP10),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(33,plain,(~(sP4) | sP33),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(34,plain,(~(sP33) | sP14),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(35,plain,(~(sP14) | sP30),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(36,plain,((~(sP30) | sP17) | sP23),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(37,plain,((~(sP17) | ~(sP22)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(38,plain,$false,inference(prop_unsat,[status(thm),assumptions([h32,h33,h31,h29,h30,h27,h28,h26,h17,h14,h15,h3,h1,h0])],[31,32,33,34,35,36,37,14,h17,h27,h32,h33])). % 0.20/0.41 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h31,h29,h30,h27,h28,h26,h17,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,38,h32,h33])). % 0.20/0.41 thf(40,plain,$false,inference(tab_negall,[status(thm),assumptions([h29,h30,h27,h28,h26,h17,h14,h15,h3,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__6)],[h30,39,h31])). % 0.20/0.42 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h27,h28,h26,h17,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h29,h30])],[h28,40,h29,h30])). % 0.20/0.42 thf(42,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h17,h14,h15,h3,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,41,h27,h28])). % 0.20/0.42 thf(43,plain,$false,inference(tab_negall,[status(thm),assumptions([h17,h14,h15,h3,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__5)],[h15,42,h26])). % 0.20/0.42 thf(44,plain,$false,inference(tab_imp,[status(thm),assumptions([h14,h15,h3,h1,h0]),tab_imp(discharge,[h16]),tab_imp(discharge,[h17])],[h14,30,43,h16,h17])). % 0.20/0.42 thf(45,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h3,44,h14,h15])). % 0.20/0.42 thf(46,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,22,45,h2,h3])). % 0.20/0.42 thf(47,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,46,h1])). % 0.20/0.42 thf(0,theorem,(![X1:$i]:(~(((~((~(((~((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3)))))))))) => ((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2))))))))) => (~(((~((~(((~((![X2:$i]:(((rel_s5 @ X1) @ X2) => (~((p @ X2))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => (q @ X2)))))))) => (![X2:$i]:(((rel_s5 @ X1) @ X2) => ((~((~((p @ X2))))) => (![X3:$i]:(((rel_s5 @ X2) @ X3) => (q @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[47,h0])). % 0.20/0.42 % SZS output end Proof %------------------------------------------------------------------------------