%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYN741^7 : TPTP v9.2.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n022.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 03:18:43 PM UTC 2025 % Result : Theorem 0.21s 0.47s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN741^7 : TPTP v9.2.0. Released v5.5.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Oct 8 15:05:08 EDT 2025 % 0.14/0.35 % CPUTime : % 0.21/0.47 % SZS status Theorem % 0.21/0.47 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0 % 0.21/0.47 % Inferences: 669 % 0.21/0.47 % SZS output start Proof % 0.21/0.47 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 0.21/0.47 thf(ty_eigen__1, type, eigen__1 : $i). % 0.21/0.47 thf(ty_v4, type, v4 : ($i>$o)). % 0.21/0.47 thf(ty_v2, type, v2 : ($i>$o)). % 0.21/0.47 thf(ty_v3, type, v3 : ($i>$o)). % 0.21/0.47 thf(ty_v1, type, v1 : ($i>$o)). % 0.21/0.47 thf(sP1,plain,sP1 <=> (![X1:$i]:((~((v3 @ X1))) => ((v2 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v2 @ X3))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v4 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.21/0.47 thf(sP2,plain,sP2 <=> (((rel_s4 @ eigen__1) @ eigen__1) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v3 @ X1)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.21/0.47 thf(sP3,plain,sP3 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v4 @ X1))))) => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v2 @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.21/0.47 thf(sP4,plain,sP4 <=> (((rel_s4 @ eigen__1) @ eigen__1) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v2 @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.21/0.47 thf(sP5,plain,sP5 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v1 @ X1))))))) => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v3 @ X1))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.21/0.47 thf(sP6,plain,sP6 <=> (![X1:$i]:((~((v1 @ X1))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (v1 @ X2))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (v4 @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v2 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.21/0.47 thf(sP7,plain,sP7 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v1 @ X1))))) => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v4 @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v2 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.21/0.47 thf(sP8,plain,sP8 <=> ((~((v1 @ eigen__1))) => sP7),introduced(definition,[new_symbols(definition,[sP8])])). % 0.21/0.47 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v4 @ X1))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.21/0.47 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v4 @ X2))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.21/0.47 thf(sP11,plain,sP11 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v4 @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v2 @ X2)))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.21/0.47 thf(sP12,plain,sP12 <=> ((~(sP9)) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.21/0.47 thf(sP13,plain,sP13 <=> (((rel_s4 @ eigen__1) @ eigen__1) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v2 @ X1)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.21/0.47 thf(sP14,plain,sP14 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v1 @ X2))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.21/0.47 thf(sP15,plain,sP15 <=> ((~((v3 @ eigen__1))) => sP3),introduced(definition,[new_symbols(definition,[sP15])])). % 0.21/0.47 thf(sP16,plain,sP16 <=> ((~((v1 @ eigen__1))) => ((v3 @ eigen__1) => sP12)),introduced(definition,[new_symbols(definition,[sP16])])). % 0.21/0.47 thf(sP17,plain,sP17 <=> ((~((v3 @ eigen__1))) => ((v2 @ eigen__1) => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v2 @ X2))))))))) => sP10))),introduced(definition,[new_symbols(definition,[sP17])])). % 0.21/0.47 thf(sP18,plain,sP18 <=> ((v3 @ eigen__1) => sP12),introduced(definition,[new_symbols(definition,[sP18])])). % 0.21/0.47 thf(sP19,plain,sP19 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v1 @ X1))))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.21/0.47 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v2 @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.21/0.47 thf(sP21,plain,sP21 <=> (v2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP21])])). % 0.21/0.47 thf(sP22,plain,sP22 <=> ((v1 @ eigen__1) => sP5),introduced(definition,[new_symbols(definition,[sP22])])). % 0.21/0.47 thf(sP23,plain,sP23 <=> (sP21 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v3 @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 0.21/0.47 thf(sP24,plain,sP24 <=> (((rel_s4 @ eigen__1) @ eigen__1) => sP19),introduced(definition,[new_symbols(definition,[sP24])])). % 0.21/0.47 thf(sP25,plain,sP25 <=> (((rel_s4 @ eigen__1) @ eigen__1) => (~((v1 @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP25])])). % 0.21/0.47 thf(sP26,plain,sP26 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v4 @ X1))),introduced(definition,[new_symbols(definition,[sP26])])). % 0.21/0.47 thf(sP27,plain,sP27 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP27])])). % 0.21/0.47 thf(sP28,plain,sP28 <=> (sP27 => (~((v3 @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.21/0.47 thf(sP29,plain,sP29 <=> ((~((v4 @ eigen__1))) => sP23),introduced(definition,[new_symbols(definition,[sP29])])). % 0.21/0.47 thf(sP30,plain,sP30 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v2 @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v3 @ X2)))))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.21/0.47 thf(sP31,plain,sP31 <=> ((~(sP9)) => sP10),introduced(definition,[new_symbols(definition,[sP31])])). % 0.21/0.47 thf(sP32,plain,sP32 <=> (v3 @ eigen__1),introduced(definition,[new_symbols(definition,[sP32])])). % 0.21/0.47 thf(sP33,plain,sP33 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v4 @ X2))))),introduced(definition,[new_symbols(definition,[sP33])])). % 0.21/0.47 thf(sP34,plain,sP34 <=> (sP32 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v3 @ X1))))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v3 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP34])])). % 0.21/0.47 thf(sP35,plain,sP35 <=> (![X1:$i]:((~((v4 @ X1))) => ((v2 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (v3 @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v1 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP35])])). % 0.21/0.47 thf(sP36,plain,sP36 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v3 @ X1))))),introduced(definition,[new_symbols(definition,[sP36])])). % 0.21/0.47 thf(sP37,plain,sP37 <=> (sP21 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v2 @ X2))))))))) => sP10)),introduced(definition,[new_symbols(definition,[sP37])])). % 0.21/0.47 thf(sP38,plain,sP38 <=> (sP27 => sP26),introduced(definition,[new_symbols(definition,[sP38])])). % 0.21/0.47 thf(sP39,plain,sP39 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v1 @ X1))),introduced(definition,[new_symbols(definition,[sP39])])). % 0.21/0.47 thf(sP40,plain,sP40 <=> ((~(sP21)) => ((v4 @ eigen__1) => sP31)),introduced(definition,[new_symbols(definition,[sP40])])). % 0.21/0.47 thf(sP41,plain,sP41 <=> (![X1:$i]:((~((v3 @ X1))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (v4 @ X2))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (v2 @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (v3 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP41])])). % 0.21/0.47 thf(sP42,plain,sP42 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP42])])). % 0.21/0.47 thf(sP43,plain,sP43 <=> (sP27 => (v4 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP43])])). % 0.21/0.47 thf(sP44,plain,sP44 <=> (sP27 => sP39),introduced(definition,[new_symbols(definition,[sP44])])). % 0.21/0.47 thf(sP45,plain,sP45 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v2 @ X2))))),introduced(definition,[new_symbols(definition,[sP45])])). % 0.21/0.47 thf(sP46,plain,sP46 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (v3 @ X1))),introduced(definition,[new_symbols(definition,[sP46])])). % 0.21/0.47 thf(sP47,plain,sP47 <=> (sP27 => (~((v4 @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP47])])). % 0.21/0.47 thf(sP48,plain,sP48 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (v3 @ X2))))),introduced(definition,[new_symbols(definition,[sP48])])). % 0.21/0.47 thf(sP49,plain,sP49 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v2 @ X2))))))),introduced(definition,[new_symbols(definition,[sP49])])). % 0.21/0.47 thf(sP50,plain,sP50 <=> (![X1:$i]:((~((v1 @ X1))) => ((v3 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v4 @ X2))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (v1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP50])])). % 0.21/0.48 thf(sP51,plain,sP51 <=> (v4 @ eigen__1),introduced(definition,[new_symbols(definition,[sP51])])). % 0.21/0.48 thf(sP52,plain,sP52 <=> ((~(sP36)) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2)))))))),introduced(definition,[new_symbols(definition,[sP52])])). % 0.21/0.48 thf(sP53,plain,sP53 <=> (sP27 => sP9),introduced(definition,[new_symbols(definition,[sP53])])). % 0.21/0.48 thf(sP54,plain,sP54 <=> ((~(sP48)) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2)))))))),introduced(definition,[new_symbols(definition,[sP54])])). % 0.21/0.48 thf(sP55,plain,sP55 <=> ((~(sP49)) => sP10),introduced(definition,[new_symbols(definition,[sP55])])). % 0.21/0.48 thf(sP56,plain,sP56 <=> (sP27 => (v1 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP56])])). % 0.21/0.48 thf(sP57,plain,sP57 <=> (sP27 => sP21),introduced(definition,[new_symbols(definition,[sP57])])). % 0.21/0.48 thf(sP58,plain,sP58 <=> (![X1:$i]:((~((v2 @ X1))) => ((v4 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v4 @ X2))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v4 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP58])])). % 0.21/0.48 thf(sP59,plain,sP59 <=> (![X1:$i]:((~((v2 @ X1))) => ((v3 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v3 @ X2))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v3 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP59])])). % 0.21/0.48 thf(sP60,plain,sP60 <=> ((~(sP36)) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v3 @ X2)))))))),introduced(definition,[new_symbols(definition,[sP60])])). % 0.21/0.48 thf(sP61,plain,sP61 <=> ((~(sP21)) => sP34),introduced(definition,[new_symbols(definition,[sP61])])). % 0.21/0.48 thf(sP62,plain,sP62 <=> (sP27 => (~(sP21))),introduced(definition,[new_symbols(definition,[sP62])])). % 0.21/0.48 thf(sP63,plain,sP63 <=> (![X1:$i]:((v1 @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2))))))) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v3 @ X2))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((v1 @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 0.21/0.48 thf(sP64,plain,sP64 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((v2 @ X1))))),introduced(definition,[new_symbols(definition,[sP64])])). % 0.21/0.48 thf(sP65,plain,sP65 <=> (v1 @ eigen__1),introduced(definition,[new_symbols(definition,[sP65])])). % 0.21/0.48 thf(sP66,plain,sP66 <=> (sP27 => sP32),introduced(definition,[new_symbols(definition,[sP66])])). % 0.21/0.48 thf(sP67,plain,sP67 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP67])])). % 0.21/0.48 thf(sP68,plain,sP68 <=> (sP51 => sP31),introduced(definition,[new_symbols(definition,[sP68])])). % 0.21/0.48 thf(sP69,plain,sP69 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((v1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP69])])). % 0.21/0.48 thf(sP70,plain,sP70 <=> (sP27 => sP46),introduced(definition,[new_symbols(definition,[sP70])])). % 0.21/0.48 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.21/0.48 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.21/0.48 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.21/0.48 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 0.21/0.48 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 0.21/0.48 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 0.21/0.48 thf(def_mvalid,definition,(mvalid = (!!))). % 0.21/0.48 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 0.21/0.48 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))). % 0.21/0.48 thf(result1,conjecture,(![X1:$i]:(~((~($false)))))). % 0.21/0.48 thf(h0,negated_conjecture,(~((![X1:$i]:$false))),inference(assume_negation,[status(cth)],[result1])). % 0.21/0.48 thf(1,plain,(~(sP63) | sP22),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(2,plain,((~(sP22) | ~(sP65)) | sP5),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(3,plain,((~(sP5) | sP19) | sP52),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(4,plain,((~(sP52) | sP36) | sP69),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(5,plain,(~(sP35) | sP29),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(6,plain,((~(sP29) | sP51) | sP23),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(7,plain,((~(sP23) | ~(sP21)) | sP54),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(8,plain,((~(sP54) | sP48) | sP69),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(9,plain,(~(sP46) | sP66),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(10,plain,((~(sP66) | ~(sP27)) | sP32),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(11,plain,(~(sP48) | sP70),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(12,plain,((~(sP70) | ~(sP27)) | sP46),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(13,plain,(~(sP41) | sP15),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(14,plain,((~(sP15) | sP32) | sP3),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(15,plain,((~(sP3) | sP26) | sP30),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(16,plain,((~(sP30) | sP45) | sP48),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(17,plain,(~(sP1) | sP17),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(18,plain,((~(sP17) | sP32) | sP37),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(19,plain,((~(sP37) | ~(sP21)) | sP55),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(20,plain,((~(sP55) | sP49) | sP10),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(21,plain,(~(sP58) | sP40),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(22,plain,((~(sP40) | sP21) | sP68),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(23,plain,((~(sP68) | ~(sP51)) | sP31),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(24,plain,((~(sP31) | sP9) | sP10),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(25,plain,(~(sP59) | sP61),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(26,plain,((~(sP61) | sP21) | sP34),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(27,plain,((~(sP34) | ~(sP32)) | sP60),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(28,plain,((~(sP60) | sP36) | sP67),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(29,plain,(~(sP10) | sP53),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(30,plain,((~(sP53) | ~(sP27)) | sP9),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(31,plain,(~(sP6) | sP8),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(32,plain,((~(sP8) | sP65) | sP7),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(33,plain,((~(sP7) | sP39) | sP11),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(34,plain,((~(sP11) | sP33) | sP49),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(35,plain,(~(sP36) | sP28),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(36,plain,((~(sP28) | ~(sP27)) | ~(sP32)),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(37,plain,(~(sP20) | sP57),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(38,plain,((~(sP57) | ~(sP27)) | sP21),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(39,plain,(~(sP45) | sP4),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(40,plain,((~(sP4) | ~(sP27)) | sP20),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(41,plain,(~(sP67) | sP2),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(42,plain,((~(sP2) | ~(sP27)) | sP36),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(43,plain,(~(sP39) | sP56),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(44,plain,((~(sP56) | ~(sP27)) | sP65),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(45,plain,(~(sP9) | sP47),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(46,plain,((~(sP47) | ~(sP27)) | ~(sP51)),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(47,plain,(~(sP14) | sP44),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(48,plain,((~(sP44) | ~(sP27)) | sP39),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(49,plain,(~(sP50) | sP16),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(50,plain,((~(sP16) | sP65) | sP18),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(51,plain,((~(sP18) | ~(sP32)) | sP12),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(52,plain,((~(sP12) | sP9) | sP14),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(53,plain,(~(sP26) | sP43),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(54,plain,((~(sP43) | ~(sP27)) | sP51),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(55,plain,(~(sP33) | sP38),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(56,plain,((~(sP38) | ~(sP27)) | sP26),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(57,plain,(~(sP64) | sP62),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(58,plain,((~(sP62) | ~(sP27)) | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(59,plain,(~(sP19) | sP25),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(60,plain,((~(sP25) | ~(sP27)) | ~(sP65)),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(61,plain,(~(sP69) | sP24),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(62,plain,((~(sP24) | ~(sP27)) | sP19),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(63,plain,(~(sP49) | sP13),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(64,plain,((~(sP13) | ~(sP27)) | sP64),inference(prop_rule,[status(thm)],[])). % 0.21/0.48 thf(65,plain,(~(sP42) | sP27),inference(all_rule,[status(thm)],[])). % 0.21/0.48 thf(persat25,axiom,(mvalid @ ((mor @ (mnot @ v1)) @ ((mor @ (mbox_s4 @ (mnot @ v1))) @ ((mor @ (mbox_s4 @ (mnot @ v3))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v1)))))))). % 0.21/0.48 thf(66,plain,sP63,inference(preprocess,[status(thm)],[persat25]). % 0.21/0.48 thf(persat21,axiom,(mvalid @ ((mor @ v4) @ ((mor @ (mnot @ v2)) @ ((mor @ (mbox_s4 @ (mbox_s4 @ v3))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v1)))))))). % 0.21/0.48 thf(67,plain,sP35,inference(preprocess,[status(thm)],[persat21]). % 0.21/0.48 thf(persat16,axiom,(mvalid @ ((mor @ v3) @ ((mor @ (mbox_s4 @ v4)) @ ((mor @ (mbox_s4 @ (mbox_s4 @ v2))) @ (mbox_s4 @ (mbox_s4 @ v3))))))). % 0.21/0.48 thf(68,plain,sP41,inference(preprocess,[status(thm)],[persat16]). % 0.21/0.48 thf(persat15,axiom,(mvalid @ ((mor @ v3) @ ((mor @ (mnot @ v2)) @ ((mor @ (mbox_s4 @ (mbox_s4 @ (mnot @ v2)))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v4)))))))). % 0.21/0.48 thf(69,plain,sP1,inference(preprocess,[status(thm)],[persat15]). % 0.21/0.48 thf(persat10,axiom,(mvalid @ ((mor @ v2) @ ((mor @ (mnot @ v4)) @ ((mor @ (mbox_s4 @ (mnot @ v4))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v4)))))))). % 0.21/0.48 thf(70,plain,sP58,inference(preprocess,[status(thm)],[persat10]). % 0.21/0.48 thf(persat9,axiom,(mvalid @ ((mor @ v2) @ ((mor @ (mnot @ v3)) @ ((mor @ (mbox_s4 @ (mnot @ v3))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v3)))))))). % 0.21/0.48 thf(71,plain,sP59,inference(preprocess,[status(thm)],[persat9]). % 0.21/0.48 thf(persat5,axiom,(mvalid @ ((mor @ v1) @ ((mor @ (mbox_s4 @ v1)) @ ((mor @ (mbox_s4 @ (mbox_s4 @ v4))) @ (mbox_s4 @ (mbox_s4 @ (mnot @ v2)))))))). % 0.21/0.48 thf(72,plain,sP6,inference(preprocess,[status(thm)],[persat5]). % 0.21/0.48 thf(persat3,axiom,(mvalid @ ((mor @ v1) @ ((mor @ (mnot @ v3)) @ ((mor @ (mbox_s4 @ (mnot @ v4))) @ (mbox_s4 @ (mbox_s4 @ v1))))))). % 0.21/0.48 thf(73,plain,sP50,inference(preprocess,[status(thm)],[persat3]). % 0.21/0.48 thf(a1,axiom,(mreflexive @ rel_s4)). % 0.21/0.48 thf(74,plain,sP42,inference(preprocess,[status(thm)],[a1]). % 0.21/0.48 thf(75,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74])). % 0.21/0.48 thf(0,theorem,(![X1:$i]:(~((~($false))))),inference(contra,[status(thm),contra(discharge,[h0])],[75,h0])). % 0.21/0.48 % SZS output end Proof %------------------------------------------------------------------------------