%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PUZ086^1 : 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 : 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 02:15:36 PM UTC 2025 % Result : Theorem 13.41s 13.59s % Output : Proof 13.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : PUZ086^1 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n018.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 : Wed Oct 8 17:26:23 EDT 2025 % 0.12/0.33 % CPUTime : % 13.41/13.59 % SZS status Theorem % 13.41/13.59 % Mode: mode454 % 13.41/13.59 % Inferences: 1301 % 13.41/13.59 % SZS output start Proof % 13.41/13.59 thf(ty_wife, type, wife : (($i>$i>$o)>$i>$i>$o)). % 13.41/13.59 thf(ty_eigen__2, type, eigen__2 : $i). % 13.41/13.59 thf(ty_peter, type, peter : ($i>$i>$o)). % 13.41/13.59 thf(ty_eigen__1, type, eigen__1 : $i). % 13.41/13.59 thf(ty_eigen__0, type, eigen__0 : $i). % 13.41/13.59 thf(ty_john, type, john : ($i>$i>$o)). % 13.41/13.59 thf(ty_place, type, place : ($i>$o)). % 13.41/13.59 thf(ty_time, type, time : ($i>$o)). % 13.41/13.59 thf(ty_appointment, type, appointment : ($i>$o)). % 13.41/13.59 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 13.41/13.59 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((peter @ eigen__0) @ X1) => (![X2:$i]:(((john @ X1) @ X2) => (appointment @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 13.41/13.59 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~(((![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (appointment @ X3))))) => (~((![X2:$i]:(((john @ X1) @ X2) => (![X3:$i]:(((peter @ X2) @ X3) => (appointment @ X3)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 13.41/13.59 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((john @ eigen__1) @ X1) => (appointment @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 13.41/13.59 thf(sP1,plain,sP1 <=> (((peter @ eigen__0) @ eigen__1) => (![X1:$i]:(((john @ eigen__1) @ X1) => (appointment @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])). % 13.41/13.59 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => ((~(((place @ X3) => (~((time @ X3)))))) => (appointment @ X3))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 13.41/13.59 thf(sP3,plain,sP3 <=> (![X1:$i]:(((peter @ eigen__1) @ X1) => (time @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 13.41/13.59 thf(sP4,plain,sP4 <=> (![X1:$i]:(((john @ eigen__1) @ X1) => ((~(((place @ X1) => (~((time @ X1)))))) => (appointment @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 13.41/13.59 thf(sP5,plain,sP5 <=> (![X1:$i]:(((peter @ eigen__1) @ X1) => (![X2:$i]:(((john @ X1) @ X2) => (place @ X2))))),introduced(definition,[new_symbols(definition,[sP5])])). % 13.41/13.59 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((peter @ X1) @ X3) => (![X4:$i]:(((john @ X3) @ X4) => (X2 @ X4))))) => (![X3:$i]:(((john @ X1) @ X3) => (![X4:$i]:(((peter @ X3) @ X4) => (X2 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 13.41/13.59 thf(sP7,plain,sP7 <=> (place @ eigen__2),introduced(definition,[new_symbols(definition,[sP7])])). % 13.41/13.59 thf(sP8,plain,sP8 <=> ((![X1:$i]:(((peter @ eigen__0) @ X1) => (![X2:$i]:(((john @ X1) @ X2) => (appointment @ X2))))) => (![X1:$i]:(((john @ eigen__0) @ X1) => (![X2:$i]:(((peter @ X1) @ X2) => (appointment @ X2)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 13.41/13.59 thf(sP9,plain,sP9 <=> (![X1:$i]:(((john @ eigen__1) @ X1) => (time @ X1))),introduced(definition,[new_symbols(definition,[sP9])])). % 13.41/13.59 thf(sP10,plain,sP10 <=> ((john @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP10])])). % 13.41/13.59 thf(sP11,plain,sP11 <=> (![X1:$i>$o]:((![X2:$i]:(((peter @ eigen__0) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (X1 @ X3))))) => (![X2:$i]:(((john @ eigen__0) @ X2) => (![X3:$i]:(((peter @ X2) @ X3) => (X1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 13.41/13.59 thf(sP12,plain,sP12 <=> (![X1:$i]:(![X2:$i]:(((peter @ X1) @ X2) => (time @ X2)))),introduced(definition,[new_symbols(definition,[sP12])])). % 13.41/13.59 thf(sP13,plain,sP13 <=> (sP10 => sP7),introduced(definition,[new_symbols(definition,[sP13])])). % 13.41/13.59 thf(sP14,plain,sP14 <=> (![X1:$i]:(((john @ eigen__1) @ X1) => (appointment @ X1))),introduced(definition,[new_symbols(definition,[sP14])])). % 13.41/13.59 thf(sP15,plain,sP15 <=> (((wife @ peter) @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP15])])). % 13.41/13.59 thf(sP16,plain,sP16 <=> (appointment @ eigen__2),introduced(definition,[new_symbols(definition,[sP16])])). % 13.41/13.59 thf(sP17,plain,sP17 <=> (sP10 => (time @ eigen__2)),introduced(definition,[new_symbols(definition,[sP17])])). % 13.41/13.59 thf(sP18,plain,sP18 <=> (sP3 => sP9),introduced(definition,[new_symbols(definition,[sP18])])). % 13.41/13.59 thf(sP19,plain,sP19 <=> (sP7 => (~((time @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP19])])). % 13.41/13.59 thf(sP20,plain,sP20 <=> (time @ eigen__2),introduced(definition,[new_symbols(definition,[sP20])])). % 13.41/13.59 thf(sP21,plain,sP21 <=> (sP15 => sP18),introduced(definition,[new_symbols(definition,[sP21])])). % 13.41/13.59 thf(sP22,plain,sP22 <=> (sP10 => sP16),introduced(definition,[new_symbols(definition,[sP22])])). % 13.41/13.59 thf(sP23,plain,sP23 <=> (sP10 => ((~(sP19)) => sP16)),introduced(definition,[new_symbols(definition,[sP23])])). % 13.41/13.59 thf(sP24,plain,sP24 <=> (![X1:$i]:((peter @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP24])])). % 13.41/13.59 thf(sP25,plain,sP25 <=> (![X1:$i]:(((wife @ peter) @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP25])])). % 13.41/13.59 thf(sP26,plain,sP26 <=> (![X1:$i]:(((john @ eigen__1) @ X1) => (place @ X1))),introduced(definition,[new_symbols(definition,[sP26])])). % 13.41/13.59 thf(sP27,plain,sP27 <=> (![X1:$i]:(((john @ eigen__0) @ X1) => (![X2:$i]:(((peter @ X1) @ X2) => (appointment @ X2))))),introduced(definition,[new_symbols(definition,[sP27])])). % 13.41/13.59 thf(sP28,plain,sP28 <=> (![X1:$i]:(![X2:$i]:((((wife @ peter) @ X1) @ X2) => ((![X3:$i]:(((peter @ X2) @ X3) => (time @ X3))) => (![X3:$i]:(((john @ X2) @ X3) => (time @ X3))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 13.41/13.59 thf(sP29,plain,sP29 <=> ((peter @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP29])])). % 13.41/13.59 thf(sP30,plain,sP30 <=> (![X1:$i]:(~(((![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (appointment @ X3))))) => (~((![X2:$i]:(((john @ X1) @ X2) => (![X3:$i]:(((peter @ X2) @ X3) => (appointment @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 13.41/13.59 thf(sP31,plain,sP31 <=> (sP29 => sP4),introduced(definition,[new_symbols(definition,[sP31])])). % 13.41/13.59 thf(sP32,plain,sP32 <=> (![X1:$i]:((((wife @ peter) @ eigen__1) @ X1) => ((![X2:$i]:(((peter @ X1) @ X2) => (time @ X2))) => (![X2:$i]:(((john @ X1) @ X2) => (time @ X2)))))),introduced(definition,[new_symbols(definition,[sP32])])). % 13.41/13.59 thf(sP33,plain,sP33 <=> (sP29 => sP26),introduced(definition,[new_symbols(definition,[sP33])])). % 13.41/13.59 thf(sP34,plain,sP34 <=> (![X1:$i]:(((peter @ eigen__0) @ X1) => (![X2:$i]:(((john @ X1) @ X2) => (appointment @ X2))))),introduced(definition,[new_symbols(definition,[sP34])])). % 13.41/13.59 thf(sP35,plain,sP35 <=> (sP34 => (~(sP27))),introduced(definition,[new_symbols(definition,[sP35])])). % 13.41/13.59 thf(sP36,plain,sP36 <=> ((~(sP19)) => sP16),introduced(definition,[new_symbols(definition,[sP36])])). % 13.41/13.59 thf(sP37,plain,sP37 <=> (![X1:$i]:(![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (place @ X3)))))),introduced(definition,[new_symbols(definition,[sP37])])). % 13.41/13.59 thf(sP38,plain,sP38 <=> (![X1:$i]:(((peter @ eigen__1) @ X1) => (![X2:$i]:(((john @ X1) @ X2) => ((~(((place @ X2) => (~((time @ X2)))))) => (appointment @ X2)))))),introduced(definition,[new_symbols(definition,[sP38])])). % 13.41/13.59 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 13.41/13.59 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 13.41/13.59 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 13.41/13.59 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 13.41/13.59 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 13.41/13.59 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 13.41/13.59 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 13.41/13.59 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 13.41/13.59 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 13.41/13.59 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 13.41/13.59 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 13.41/13.59 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 13.41/13.59 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 13.41/13.59 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 13.41/13.59 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 13.41/13.59 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 13.41/13.59 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 13.41/13.59 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 13.41/13.59 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 13.41/13.59 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 13.41/13.59 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 13.41/13.59 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 13.41/13.59 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)))))))). % 13.41/13.59 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 13.41/13.59 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 13.41/13.59 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 13.41/13.59 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 13.41/13.59 thf(def_mvalid,definition,(mvalid = (!!))). % 13.41/13.59 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 13.41/13.59 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 13.41/13.59 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 13.41/13.59 thf(conj,conjecture,(![X1:$i]:(~(((~((~((![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (appointment @ X3))))))))) => (~((![X2:$i]:(((john @ X1) @ X2) => (![X3:$i]:(((peter @ X2) @ X3) => (appointment @ X3)))))))))))). % 13.41/13.59 thf(h1,negated_conjecture,(~(sP30)),inference(assume_negation,[status(cth)],[conj])). % 13.41/13.59 thf(1,plain,(~(sP9) | sP17),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(2,plain,((~(sP17) | ~(sP10)) | sP20),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(3,plain,(~(sP32) | sP21),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(4,plain,((~(sP21) | ~(sP15)) | sP18),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(5,plain,((~(sP18) | ~(sP3)) | sP9),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(6,plain,(~(sP38) | sP31),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(7,plain,((~(sP31) | ~(sP29)) | sP4),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(8,plain,(~(sP5) | sP33),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(9,plain,((~(sP33) | ~(sP29)) | sP26),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(10,plain,(~(sP2) | sP38),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(11,plain,(~(sP28) | sP32),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(12,plain,(~(sP37) | sP5),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(13,plain,(~(sP12) | sP3),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(14,plain,(~(sP25) | sP15),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(15,plain,(~(sP24) | sP29),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(16,plain,(~(sP6) | sP11),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(17,plain,(~(sP11) | sP8),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(18,plain,((~(sP8) | ~(sP34)) | sP27),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(19,plain,(~(sP4) | sP23),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(20,plain,((~(sP23) | ~(sP10)) | sP36),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(21,plain,((~(sP36) | sP19) | sP16),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(22,plain,((~(sP19) | ~(sP7)) | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(23,plain,(~(sP26) | sP13),inference(all_rule,[status(thm)],[])). % 13.41/13.59 thf(24,plain,((~(sP13) | ~(sP10)) | sP7),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(25,plain,(sP22 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(26,plain,(sP22 | sP10),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(27,plain,(sP14 | ~(sP22)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 13.41/13.59 thf(28,plain,(sP1 | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(29,plain,(sP34 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 13.41/13.59 thf(30,plain,((~(sP35) | ~(sP34)) | ~(sP27)),inference(prop_rule,[status(thm)],[])). % 13.41/13.59 thf(31,plain,(sP30 | sP35),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 13.41/13.59 thf(refl_peter,axiom,(mreflexive @ peter)). % 13.41/13.59 thf(32,plain,sP24,inference(preprocess,[status(thm)],[refl_peter]). % 13.41/13.59 thf(refl_wife_peter,axiom,(mreflexive @ (wife @ peter))). % 13.41/13.59 thf(33,plain,sP25,inference(preprocess,[status(thm)],[refl_wife_peter]). % 13.41/13.59 thf(ax_i,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ peter) @ ((mbox @ john) @ X1))) @ ((mbox @ john) @ ((mbox @ peter) @ X1))))))). % 13.41/13.59 thf(34,plain,sP6,inference(preprocess,[status(thm)],[ax_i]). % 13.41/13.59 thf(ax_a,axiom,(mvalid @ ((mbox @ peter) @ time))). % 13.41/13.59 thf(35,plain,sP12,inference(preprocess,[status(thm)],[ax_a]). % 13.41/13.59 thf(ax_b,axiom,(mvalid @ ((mbox @ peter) @ ((mbox @ john) @ place)))). % 13.41/13.59 thf(36,plain,sP37,inference(preprocess,[status(thm)],[ax_b]). % 13.41/13.59 thf(ax_c,axiom,(mvalid @ ((mbox @ (wife @ peter)) @ ((mimplies @ ((mbox @ peter) @ time)) @ ((mbox @ john) @ time))))). % 13.41/13.59 thf(37,plain,sP28,inference(preprocess,[status(thm)],[ax_c]). % 13.41/13.59 thf(ax_d,axiom,(mvalid @ ((mbox @ peter) @ ((mbox @ john) @ ((mimplies @ ((mand @ place) @ time)) @ appointment))))). % 13.41/13.59 thf(38,plain,sP2,inference(preprocess,[status(thm)],[ax_d]). % 13.41/13.59 thf(39,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,h1])). % 13.41/13.59 thf(40,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[39,h0])). % 13.41/13.59 thf(0,theorem,(![X1:$i]:(~(((~((~((![X2:$i]:(((peter @ X1) @ X2) => (![X3:$i]:(((john @ X2) @ X3) => (appointment @ X3))))))))) => (~((![X2:$i]:(((john @ X1) @ X2) => (![X3:$i]:(((peter @ X2) @ X3) => (appointment @ X3))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[39,h1])). % 13.41/13.59 % SZS output end Proof %------------------------------------------------------------------------------