%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO903^10 : TPTP v9.2.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n021.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 03:26:34 PM UTC 2025 % Result : Theorem 0.18s 0.45s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO903^10 : TPTP v9.2.0. Released v8.1.0. % 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 9 01:24:53 EDT 2025 % 0.12/0.34 % CPUTime : % 0.18/0.45 % SZS status Theorem % 0.18/0.45 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0 % 0.18/0.45 % Inferences: 655 % 0.18/0.45 % SZS output start Proof % 0.18/0.45 thf(ty_mworld, type, mworld : $tType). % 0.18/0.45 thf(ty_v4, type, v4 : (mworld>$o)). % 0.18/0.45 thf(ty_v2, type, v2 : (mworld>$o)). % 0.18/0.45 thf(ty_v3, type, v3 : (mworld>$o)). % 0.18/0.45 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 0.18/0.45 thf(ty_v1, type, v1 : (mworld>$o)). % 0.18/0.45 thf(ty_mactual, type, mactual : mworld). % 0.18/0.45 thf(sP1,plain,sP1 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.18/0.45 thf(sP2,plain,sP2 <=> ((v4 @ mactual) => ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v3 @ X2))))))))) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v4 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.18/0.45 thf(sP3,plain,sP3 <=> ((~((v3 @ mactual))) => ((v4 @ mactual) => ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v3 @ X2))))))) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v4 @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.18/0.45 thf(sP4,plain,sP4 <=> ((~((v4 @ mactual))) => ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v1 @ X1))))))) => ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v4 @ X2))))))) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v1 @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.18/0.45 thf(sP5,plain,sP5 <=> (((mrel @ mactual) @ mactual) => (~((v1 @ mactual)))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.18/0.45 thf(sP6,plain,sP6 <=> ((v2 @ mactual) => ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v4 @ X1))))))) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v1 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.18/0.45 thf(sP7,plain,sP7 <=> ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v1 @ X2))))))) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v4 @ X2)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.18/0.45 thf(sP8,plain,sP8 <=> ((v1 @ mactual) => sP6),introduced(definition,[new_symbols(definition,[sP8])])). % 0.18/0.45 thf(sP9,plain,sP9 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.18/0.45 thf(sP10,plain,sP10 <=> (((mrel @ mactual) @ mactual) => (~((v3 @ mactual)))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.18/0.45 thf(sP11,plain,sP11 <=> ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v4 @ X1))))))) => sP9),introduced(definition,[new_symbols(definition,[sP11])])). % 0.18/0.45 thf(sP12,plain,sP12 <=> (((mrel @ mactual) @ mactual) => (~((v4 @ mactual)))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.18/0.45 thf(sP13,plain,sP13 <=> (((mrel @ mactual) @ mactual) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (v3 @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.18/0.45 thf(sP14,plain,sP14 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v1 @ X1))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.18/0.45 thf(sP15,plain,sP15 <=> ((mrel @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP15])])). % 0.18/0.45 thf(sP16,plain,sP16 <=> ((v3 @ mactual) => ((~(sP14)) => sP9)),introduced(definition,[new_symbols(definition,[sP16])])). % 0.18/0.45 thf(sP17,plain,sP17 <=> ((~((v4 @ mactual))) => ((v3 @ mactual) => sP7)),introduced(definition,[new_symbols(definition,[sP17])])). % 0.18/0.45 thf(sP18,plain,sP18 <=> (sP15 => (v1 @ mactual)),introduced(definition,[new_symbols(definition,[sP18])])). % 0.18/0.45 thf(sP19,plain,sP19 <=> (sP15 => (v4 @ mactual)),introduced(definition,[new_symbols(definition,[sP19])])). % 0.18/0.45 thf(sP20,plain,sP20 <=> (v2 @ mactual),introduced(definition,[new_symbols(definition,[sP20])])). % 0.18/0.45 thf(sP21,plain,sP21 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (v4 @ X1))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.18/0.45 thf(sP22,plain,sP22 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v3 @ X2))))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.18/0.45 thf(sP23,plain,sP23 <=> (sP15 => sP21),introduced(definition,[new_symbols(definition,[sP23])])). % 0.18/0.45 thf(sP24,plain,sP24 <=> ((~(sP14)) => sP9),introduced(definition,[new_symbols(definition,[sP24])])). % 0.18/0.45 thf(sP25,plain,sP25 <=> ((v3 @ mactual) => sP7),introduced(definition,[new_symbols(definition,[sP25])])). % 0.18/0.45 thf(sP26,plain,sP26 <=> (v1 @ mactual),introduced(definition,[new_symbols(definition,[sP26])])). % 0.18/0.45 thf(sP27,plain,sP27 <=> (sP15 => (v3 @ mactual)),introduced(definition,[new_symbols(definition,[sP27])])). % 0.18/0.45 thf(sP28,plain,sP28 <=> (sP15 => (![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v3 @ X1)))))),introduced(definition,[new_symbols(definition,[sP28])])). % 0.18/0.45 thf(sP29,plain,sP29 <=> ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v4 @ X2))))))) => sP9),introduced(definition,[new_symbols(definition,[sP29])])). % 0.18/0.45 thf(sP30,plain,sP30 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v4 @ X2))))),introduced(definition,[new_symbols(definition,[sP30])])). % 0.18/0.45 thf(sP31,plain,sP31 <=> (v4 @ mactual),introduced(definition,[new_symbols(definition,[sP31])])). % 0.18/0.45 thf(sP32,plain,sP32 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (v3 @ X1))),introduced(definition,[new_symbols(definition,[sP32])])). % 0.18/0.45 thf(sP33,plain,sP33 <=> (v3 @ mactual),introduced(definition,[new_symbols(definition,[sP33])])). % 0.18/0.45 thf(sP34,plain,sP34 <=> (sP15 => (![X1:mworld]:(((mrel @ mactual) @ X1) => (v1 @ X1)))),introduced(definition,[new_symbols(definition,[sP34])])). % 0.18/0.45 thf(sP35,plain,sP35 <=> ((~(sP14)) => sP29),introduced(definition,[new_symbols(definition,[sP35])])). % 0.18/0.45 thf(sP36,plain,sP36 <=> ((~(sP22)) => (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v4 @ X2)))))))),introduced(definition,[new_symbols(definition,[sP36])])). % 0.18/0.45 thf(sP37,plain,sP37 <=> (sP15 => (![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v4 @ X1)))))),introduced(definition,[new_symbols(definition,[sP37])])). % 0.18/0.45 thf(sP38,plain,sP38 <=> (sP31 => sP36),introduced(definition,[new_symbols(definition,[sP38])])). % 0.18/0.45 thf(sP39,plain,sP39 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (v1 @ X2))))),introduced(definition,[new_symbols(definition,[sP39])])). % 0.18/0.45 thf(sP40,plain,sP40 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v3 @ X1))))),introduced(definition,[new_symbols(definition,[sP40])])). % 0.18/0.45 thf(sP41,plain,sP41 <=> ((~(sP20)) => sP16),introduced(definition,[new_symbols(definition,[sP41])])). % 0.18/0.45 thf(sP42,plain,sP42 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (v1 @ X1))),introduced(definition,[new_symbols(definition,[sP42])])). % 0.18/0.45 thf(sP43,plain,sP43 <=> (sP15 => sP14),introduced(definition,[new_symbols(definition,[sP43])])). % 0.18/0.45 thf(sP44,plain,sP44 <=> ((~(sP33)) => ((~(sP22)) => sP30)),introduced(definition,[new_symbols(definition,[sP44])])). % 0.18/0.45 thf(sP45,plain,sP45 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v4 @ X2))))))),introduced(definition,[new_symbols(definition,[sP45])])). % 0.18/0.45 thf(sP46,plain,sP46 <=> ((~(sP26)) => sP44),introduced(definition,[new_symbols(definition,[sP46])])). % 0.18/0.45 thf(sP47,plain,sP47 <=> ((~(sP22)) => sP30),introduced(definition,[new_symbols(definition,[sP47])])). % 0.18/0.45 thf(sP48,plain,sP48 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (~((v4 @ X1))))),introduced(definition,[new_symbols(definition,[sP48])])). % 0.18/0.45 thf(sP49,plain,sP49 <=> ((~((![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v3 @ X2))))))))) => sP45),introduced(definition,[new_symbols(definition,[sP49])])). % 0.18/0.45 thf(sP50,plain,sP50 <=> ((~(sP26)) => sP2),introduced(definition,[new_symbols(definition,[sP50])])). % 0.18/0.45 thf(sP51,plain,sP51 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:mworld]:(((mrel @ X1) @ X2) => (~((v3 @ X2))))))),introduced(definition,[new_symbols(definition,[sP51])])). % 0.18/0.45 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 0.18/0.45 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 0.18/0.45 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.18/0.45 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 0.18/0.45 thf(result1,conjecture,$false). % 0.18/0.45 thf(h0,negated_conjecture,(~($false)),inference(assume_negation,[status(cth)],[result1])). % 0.18/0.45 thf(1,plain,((~(sP11) | sP48) | sP9),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(2,plain,((~(sP6) | ~(sP20)) | sP11),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(3,plain,((~(sP8) | ~(sP26)) | sP6),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(4,plain,((~(sP29) | sP30) | sP9),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(5,plain,((~(sP35) | sP14) | sP29),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(6,plain,((~(sP4) | sP31) | sP35),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(7,plain,((~(sP7) | sP39) | sP30),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(8,plain,((~(sP25) | ~(sP33)) | sP7),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(9,plain,((~(sP17) | sP31) | sP25),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(10,plain,((~(sP36) | sP22) | sP45),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(11,plain,((~(sP38) | ~(sP31)) | sP36),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(12,plain,((~(sP3) | sP33) | sP38),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(13,plain,((~(sP41) | sP20) | sP16),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(14,plain,((~(sP49) | sP51) | sP45),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(15,plain,((~(sP2) | ~(sP31)) | sP49),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(16,plain,((~(sP50) | sP26) | sP2),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(17,plain,((~(sP16) | ~(sP33)) | sP24),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(18,plain,((~(sP24) | sP14) | sP9),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(19,plain,(~(sP21) | sP19),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(20,plain,((~(sP19) | ~(sP15)) | sP31),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(21,plain,(~(sP30) | sP23),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(22,plain,((~(sP23) | ~(sP15)) | sP21),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(23,plain,(~(sP32) | sP27),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(24,plain,((~(sP27) | ~(sP15)) | sP33),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(25,plain,(~(sP22) | sP13),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(26,plain,((~(sP13) | ~(sP15)) | sP32),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(27,plain,((~(sP47) | sP22) | sP30),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(28,plain,((~(sP44) | sP33) | sP47),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(29,plain,((~(sP46) | sP26) | sP44),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(30,plain,(~(sP42) | sP18),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(31,plain,((~(sP18) | ~(sP15)) | sP26),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(32,plain,(~(sP39) | sP34),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(33,plain,((~(sP34) | ~(sP15)) | sP42),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(34,plain,(~(sP48) | sP12),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(35,plain,((~(sP12) | ~(sP15)) | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(36,plain,(~(sP45) | sP37),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(37,plain,((~(sP37) | ~(sP15)) | sP48),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(38,plain,(~(sP40) | sP10),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(39,plain,((~(sP10) | ~(sP15)) | ~(sP33)),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(40,plain,(~(sP51) | sP28),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(41,plain,((~(sP28) | ~(sP15)) | sP40),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(42,plain,(~(sP14) | sP5),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(43,plain,((~(sP5) | ~(sP15)) | ~(sP26)),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(44,plain,((~(sP43) | ~(sP15)) | sP14),inference(prop_rule,[status(thm)],[])). % 0.18/0.45 thf(45,plain,(~(sP1) | sP15),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(46,plain,(~(sP9) | sP43),inference(all_rule,[status(thm)],[])). % 0.18/0.45 thf(persat34,axiom,(mlocal @ ((mor @ (mnot @ v1)) @ ((mor @ (mnot @ v2)) @ ((mor @ (mbox @ (mnot @ v4))) @ (mbox @ (mbox @ (mnot @ v1)))))))). % 0.18/0.45 thf(47,plain,sP8,inference(preprocess,[status(thm)],[persat34]). % 0.18/0.45 thf(persat32,axiom,(mlocal @ ((mor @ v4) @ ((mor @ (mbox @ (mnot @ v1))) @ ((mor @ (mbox @ (mbox @ v4))) @ (mbox @ (mbox @ (mnot @ v1)))))))). % 0.18/0.45 thf(48,plain,sP4,inference(preprocess,[status(thm)],[persat32]). % 0.18/0.45 thf(persat31,axiom,(mlocal @ ((mor @ v4) @ ((mor @ (mnot @ v3)) @ ((mor @ (mbox @ (mbox @ v1))) @ (mbox @ (mbox @ v4))))))). % 0.18/0.45 thf(49,plain,sP17,inference(preprocess,[status(thm)],[persat31]). % 0.18/0.45 thf(persat26,axiom,(mlocal @ ((mor @ v3) @ ((mor @ (mnot @ v4)) @ ((mor @ (mbox @ (mbox @ v3))) @ (mbox @ (mbox @ (mnot @ v4)))))))). % 0.18/0.45 thf(50,plain,sP3,inference(preprocess,[status(thm)],[persat26]). % 0.18/0.45 thf(persat18,axiom,(mlocal @ ((mor @ v2) @ ((mor @ (mnot @ v3)) @ ((mor @ (mbox @ (mnot @ v1))) @ (mbox @ (mbox @ (mnot @ v1)))))))). % 0.18/0.45 thf(51,plain,sP41,inference(preprocess,[status(thm)],[persat18]). % 0.18/0.45 thf(persat11,axiom,(mlocal @ ((mor @ v1) @ ((mor @ (mnot @ v4)) @ ((mor @ (mbox @ (mbox @ (mnot @ v3)))) @ (mbox @ (mbox @ (mnot @ v4)))))))). % 0.18/0.45 thf(52,plain,sP50,inference(preprocess,[status(thm)],[persat11]). % 0.18/0.45 thf(persat5,axiom,(mlocal @ ((mor @ v1) @ ((mor @ v3) @ ((mor @ (mbox @ (mbox @ v3))) @ (mbox @ (mbox @ v4))))))). % 0.18/0.45 thf(53,plain,sP46,inference(preprocess,[status(thm)],[persat5]). % 0.18/0.45 thf(mrel_reflexive,axiom,sP1). % 0.18/0.45 thf(54,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,mrel_reflexive])). % 0.18/0.45 thf(0,theorem,$false,inference(contra,[status(thm),contra(discharge,[h0])],[54,h0])). % 0.18/0.45 % SZS output end Proof %------------------------------------------------------------------------------