%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT032^1 : TPTP v9.2.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n004.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 01:08:58 PM UTC 2025 % Result : Theorem 44.18s 44.37s % Output : Proof 44.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : AGT032^1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n004.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 12:29:23 EDT 2025 % 0.13/0.34 % CPUTime : % 44.18/44.37 % SZS status Theorem % 44.18/44.37 % Mode: mode491:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 44.18/44.37 % Inferences: 6093 % 44.18/44.37 % SZS output start Proof % 44.18/44.37 thf(ty_mu, type, mu : $tType). % 44.18/44.37 thf(ty_very_much_likes, type, very_much_likes : (mu>mu>$i>$o)). % 44.18/44.37 thf(ty_jan, type, jan : mu). % 44.18/44.37 thf(ty_a3, type, a3 : ($i>$i>$o)). % 44.18/44.37 thf(ty_a1, type, a1 : ($i>$i>$o)). % 44.18/44.37 thf(ty_cola, type, cola : mu). % 44.18/44.37 thf(ty_a2, type, a2 : ($i>$i>$o)). % 44.18/44.37 thf(ty_eigen__0, type, eigen__0 : $i). % 44.18/44.37 thf(ty_likes, type, likes : (mu>mu>$i>$o)). % 44.18/44.37 thf(ty_piotr, type, piotr : mu). % 44.18/44.37 thf(ty_pepsi, type, pepsi : mu). % 44.18/44.37 thf(sP1,plain,sP1 <=> ((~((![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((very_much_likes @ jan) @ cola) @ X1))))))) => (((likes @ jan) @ cola) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])). % 44.18/44.37 thf(sP2,plain,sP2 <=> ((((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) => ((((a1 @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) @ (@+[X1:$i]:(~((((a1 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))) => (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a1 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1))))))) => (~((((a2 @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))) => (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 44.18/44.37 thf(sP3,plain,sP3 <=> (![X1:$i]:(((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ pepsi) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 44.18/44.37 thf(sP4,plain,sP4 <=> (((a1 @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) @ (@+[X1:$i]:(~((((a1 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))) => (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a1 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 44.18/44.37 thf(sP5,plain,sP5 <=> (((likes @ jan) @ cola) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 44.18/44.37 thf(sP6,plain,sP6 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => ((~(((((likes @ jan) @ cola) @ X1) => ((((a1 @ X1) @ (@+[X2:$i]:(~((((a1 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))))) => (((likes @ jan) @ cola) @ (@+[X2:$i]:(~((((a1 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2))))))) => (~((((a2 @ X1) @ (@+[X2:$i]:(~((((a2 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))))) => (((likes @ jan) @ cola) @ (@+[X2:$i]:(~((((a2 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2))))))))))))) => (((very_much_likes @ jan) @ cola) @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 44.18/44.37 thf(sP7,plain,sP7 <=> (![X1:$i]:(((a1 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 44.18/44.37 thf(sP8,plain,sP8 <=> (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))),introduced(definition,[new_symbols(definition,[sP8])])). % 44.18/44.37 thf(sP9,plain,sP9 <=> (![X1:mu]:(![X2:mu]:((~((![X3:$i]:(((a3 @ eigen__0) @ X3) => (~((((very_much_likes @ X1) @ X2) @ X3))))))) => (((likes @ X1) @ X2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP9])])). % 44.18/44.37 thf(sP10,plain,sP10 <=> (![X1:$i]:(![X2:$i]:(((a2 @ X1) @ X2) => (((likes @ jan) @ pepsi) @ X2)))),introduced(definition,[new_symbols(definition,[sP10])])). % 44.18/44.37 thf(sP11,plain,sP11 <=> (((a3 @ eigen__0) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) => ((~(sP2)) => (((very_much_likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 44.18/44.37 thf(sP12,plain,sP12 <=> (![X1:mu]:(~((((likes @ jan) @ X1) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP12])])). % 44.18/44.37 thf(sP13,plain,sP13 <=> (((a3 @ eigen__0) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) => (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 44.18/44.37 thf(sP14,plain,sP14 <=> (((likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 44.18/44.37 thf(sP15,plain,sP15 <=> (![X1:mu]:(![X2:$i]:(((a2 @ (@+[X3:$i]:(~((((a3 @ eigen__0) @ X3) => (~((((likes @ piotr) @ pepsi) @ X3)))))))) @ X2) => ((((likes @ X1) @ pepsi) @ X2) => (((likes @ X1) @ cola) @ X2))))),introduced(definition,[new_symbols(definition,[sP15])])). % 44.18/44.37 thf(sP16,plain,sP16 <=> ((((likes @ jan) @ pepsi) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))) => sP8),introduced(definition,[new_symbols(definition,[sP16])])). % 44.18/44.37 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(((a3 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))),introduced(definition,[new_symbols(definition,[sP17])])). % 44.18/44.37 thf(sP18,plain,sP18 <=> (![X1:$i]:(![X2:mu]:(![X3:$i]:(((a2 @ X1) @ X3) => ((((likes @ X2) @ pepsi) @ X3) => (((likes @ X2) @ cola) @ X3)))))),introduced(definition,[new_symbols(definition,[sP18])])). % 44.18/44.37 thf(sP19,plain,sP19 <=> ((~(sP2)) => (((very_much_likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 44.18/44.37 thf(sP20,plain,sP20 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (((likes @ jan) @ cola) @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 44.18/44.37 thf(sP21,plain,sP21 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((very_much_likes @ jan) @ cola) @ X1))))),introduced(definition,[new_symbols(definition,[sP21])])). % 44.18/44.37 thf(sP22,plain,sP22 <=> (![X1:$i]:(((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => ((((likes @ jan) @ pepsi) @ X1) => (((likes @ jan) @ cola) @ X1)))),introduced(definition,[new_symbols(definition,[sP22])])). % 44.18/44.37 thf(sP23,plain,sP23 <=> (![X1:$i]:(![X2:$i]:(((a1 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))),introduced(definition,[new_symbols(definition,[sP23])])). % 44.18/44.37 thf(sP24,plain,sP24 <=> (((a2 @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))) => sP8),introduced(definition,[new_symbols(definition,[sP24])])). % 44.18/44.37 thf(sP25,plain,sP25 <=> ((a2 @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 44.18/44.37 thf(sP26,plain,sP26 <=> (sP25 => (((likes @ jan) @ pepsi) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1))))))),introduced(definition,[new_symbols(definition,[sP26])])). % 44.18/44.37 thf(sP27,plain,sP27 <=> (((likes @ jan) @ pepsi) @ (@+[X1:$i]:(~((((a2 @ (@+[X2:$i]:(~((((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) @ X1) => (((likes @ jan) @ cola) @ X1)))))),introduced(definition,[new_symbols(definition,[sP27])])). % 44.18/44.37 thf(sP28,plain,sP28 <=> (![X1:mu]:(![X2:$i]:(((a3 @ eigen__0) @ X2) => ((~(((((likes @ jan) @ X1) @ X2) => ((((a1 @ X2) @ (@+[X3:$i]:(~((((a1 @ X2) @ X3) => (((likes @ jan) @ X1) @ X3)))))) => (((likes @ jan) @ X1) @ (@+[X3:$i]:(~((((a1 @ X2) @ X3) => (((likes @ jan) @ X1) @ X3))))))) => (~((((a2 @ X2) @ (@+[X3:$i]:(~((((a2 @ X2) @ X3) => (((likes @ jan) @ X1) @ X3)))))) => (((likes @ jan) @ X1) @ (@+[X3:$i]:(~((((a2 @ X2) @ X3) => (((likes @ jan) @ X1) @ X3))))))))))))) => (((very_much_likes @ jan) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP28])])). % 44.18/44.37 thf(sP29,plain,sP29 <=> (![X1:$i]:(~((((a3 @ X1) @ (@+[X2:$i]:(~((((a3 @ X1) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))) => (~((((likes @ piotr) @ pepsi) @ (@+[X2:$i]:(~((((a3 @ X1) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 44.18/44.37 thf(sP30,plain,sP30 <=> (((very_much_likes @ jan) @ cola) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP30])])). % 44.18/44.37 thf(sP31,plain,sP31 <=> (((a3 @ eigen__0) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))) => (~(sP30))),introduced(definition,[new_symbols(definition,[sP31])])). % 44.18/44.37 thf(sP32,plain,sP32 <=> (![X1:mu]:(![X2:mu]:(~((((likes @ X1) @ X2) @ eigen__0))))),introduced(definition,[new_symbols(definition,[sP32])])). % 44.18/44.37 thf(sP33,plain,sP33 <=> (sP25 => sP16),introduced(definition,[new_symbols(definition,[sP33])])). % 44.18/44.37 thf(sP34,plain,sP34 <=> ((a3 @ eigen__0) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP34])])). % 44.18/44.37 thf(sP35,plain,sP35 <=> (![X1:$i]:(![X2:mu]:(![X3:mu]:((~((![X4:$i]:(((a3 @ X1) @ X4) => (~((((very_much_likes @ X2) @ X3) @ X4))))))) => (((likes @ X2) @ X3) @ X1))))),introduced(definition,[new_symbols(definition,[sP35])])). % 44.18/44.37 thf(sP36,plain,sP36 <=> (![X1:mu]:((~((![X2:$i]:(((a3 @ eigen__0) @ X2) => (~((((very_much_likes @ jan) @ X1) @ X2))))))) => (((likes @ jan) @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP36])])). % 44.18/44.37 thf(sP37,plain,sP37 <=> (![X1:$i]:(![X2:mu]:(![X3:mu]:(![X4:$i]:(((a3 @ X1) @ X4) => ((~(((((likes @ X2) @ X3) @ X4) => ((((a1 @ X4) @ (@+[X5:$i]:(~((((a1 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5)))))) => (((likes @ X2) @ X3) @ (@+[X5:$i]:(~((((a1 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5))))))) => (~((((a2 @ X4) @ (@+[X5:$i]:(~((((a2 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5)))))) => (((likes @ X2) @ X3) @ (@+[X5:$i]:(~((((a2 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5))))))))))))) => (((very_much_likes @ X2) @ X3) @ X4))))))),introduced(definition,[new_symbols(definition,[sP37])])). % 44.18/44.37 thf(sP38,plain,sP38 <=> (![X1:mu]:(![X2:mu]:(![X3:$i]:(((a3 @ eigen__0) @ X3) => ((~(((((likes @ X1) @ X2) @ X3) => ((((a1 @ X3) @ (@+[X4:$i]:(~((((a1 @ X3) @ X4) => (((likes @ X1) @ X2) @ X4)))))) => (((likes @ X1) @ X2) @ (@+[X4:$i]:(~((((a1 @ X3) @ X4) => (((likes @ X1) @ X2) @ X4))))))) => (~((((a2 @ X3) @ (@+[X4:$i]:(~((((a2 @ X3) @ X4) => (((likes @ X1) @ X2) @ X4)))))) => (((likes @ X1) @ X2) @ (@+[X4:$i]:(~((((a2 @ X3) @ X4) => (((likes @ X1) @ X2) @ X4))))))))))))) => (((very_much_likes @ X1) @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP38])])). % 44.18/44.37 thf(sP39,plain,sP39 <=> (sP4 => (~(sP24))),introduced(definition,[new_symbols(definition,[sP39])])). % 44.18/44.37 thf(sP40,plain,sP40 <=> (sP34 => (~((((likes @ piotr) @ pepsi) @ (@+[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP40])])). % 44.18/44.37 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 44.18/44.37 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 44.18/44.37 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 44.18/44.37 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 44.18/44.37 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 44.18/44.37 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 44.18/44.37 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 44.18/44.37 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 44.18/44.37 thf(def_mvalid,definition,(mvalid = (!!))). % 44.18/44.37 thf(def_cond4s,definition,(cond4s = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X1 @ X3) @ X4) => (~(((X2 @ X4) @ X5)))))) => ((X2 @ X3) @ X5))))))))). % 44.18/44.37 thf(conj,conjecture,(![X1:$i]:(~((![X2:mu]:(~((~((![X3:mu]:(~((((likes @ X2) @ X3) @ X1))))))))))))). % 44.18/44.37 thf(h0,negated_conjecture,(~((![X1:$i]:(~((![X2:mu]:(![X3:mu]:(~((((likes @ X2) @ X3) @ X1)))))))))),inference(assume_negation,[status(cth)],[conj])). % 44.18/44.37 thf(h1,assumption,sP32,introduced(assumption,[])). % 44.18/44.37 thf(1,plain,(~(sP7) | sP4),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(2,plain,(~(sP22) | sP33),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(3,plain,((~(sP33) | ~(sP25)) | sP16),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(4,plain,((~(sP16) | ~(sP27)) | sP8),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(5,plain,(~(sP3) | sP26),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(6,plain,((~(sP26) | ~(sP25)) | sP27),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(7,plain,(~(sP18) | sP15),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(8,plain,(~(sP15) | sP22),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(9,plain,(sP24 | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(10,plain,(sP24 | sP25),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(11,plain,(~(sP10) | sP3),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(12,plain,(~(sP23) | sP7),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(13,plain,(~(sP6) | sP11),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(14,plain,((~(sP11) | ~(sP34)) | sP19),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(15,plain,((~(sP19) | sP2) | sP30),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(16,plain,((~(sP2) | ~(sP14)) | sP39),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(17,plain,((~(sP39) | ~(sP4)) | ~(sP24)),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(18,plain,(~(sP36) | sP1),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(19,plain,((~(sP1) | sP21) | sP5),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(20,plain,(~(sP21) | sP31),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(21,plain,((~(sP31) | ~(sP34)) | ~(sP30)),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(22,plain,(~(sP28) | sP6),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(23,plain,(~(sP20) | sP13),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(24,plain,((~(sP13) | ~(sP34)) | sP14),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(25,plain,(sP40 | sP34),inference(prop_rule,[status(thm)],[])). % 44.18/44.37 thf(26,plain,(~(sP9) | sP36),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(27,plain,(~(sP12) | ~(sP5)),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(28,plain,(~(sP38) | sP28),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(29,plain,(~(sP17) | sP20),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(30,plain,(~(sP29) | ~(sP40)),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(31,plain,(~(sP35) | sP9),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(32,plain,(~(sP32) | sP12),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(33,plain,(~(sP37) | sP38),inference(all_rule,[status(thm)],[])). % 44.18/44.37 thf(axiom_a1_1,axiom,(mvalid @ ((mbox @ a1) @ ((likes @ jan) @ cola)))). % 44.18/44.37 thf(34,plain,sP23,inference(preprocess,[status(thm)],[axiom_a1_1]). % 44.18/44.37 thf(axiom_a2_1,axiom,(mvalid @ ((mbox @ a2) @ ((likes @ jan) @ pepsi)))). % 44.18/44.37 thf(35,plain,sP10,inference(preprocess,[status(thm)],[axiom_a2_1]). % 44.18/44.37 thf(axiom_a2_4,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mbox @ a2) @ ((mimplies @ ((likes @ X1) @ pepsi)) @ ((likes @ X1) @ cola))))))). % 44.18/44.37 thf(36,plain,sP18,inference(preprocess,[status(thm)],[axiom_a2_4]). % 44.18/44.37 thf(axiom_a3_1,axiom,(mvalid @ ((mbox @ a3) @ ((likes @ jan) @ cola)))). % 44.18/44.37 thf(37,plain,sP17,inference(preprocess,[status(thm)],[axiom_a3_1]). % 44.18/44.37 thf(axiom_a3_2,axiom,(mvalid @ ((mdia @ a3) @ ((likes @ piotr) @ pepsi)))). % 44.18/44.37 thf(38,plain,(![X1:$i]:(~((![X2:$i]:(((a3 @ X1) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))),inference(preprocess,[status(thm)],[axiom_a3_2]). % 44.18/44.37 thf(39,plain,sP29,inference(normalize,[status(thm)],[38]). % 44.18/44.37 thf(axiom_a3_4,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mbox @ a3) @ ((mimplies @ ((mand @ ((likes @ X1) @ X2)) @ ((mand @ ((mbox @ a1) @ ((likes @ X1) @ X2))) @ ((mbox @ a2) @ ((likes @ X1) @ X2))))) @ ((very_much_likes @ X1) @ X2))))))))). % 44.18/44.37 thf(40,plain,(![X1:$i]:(![X2:mu]:(![X3:mu]:(![X4:$i]:(((a3 @ X1) @ X4) => ((~(((((likes @ X2) @ X3) @ X4) => ((![X5:$i]:(((a1 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5))) => (~((![X5:$i]:(((a2 @ X4) @ X5) => (((likes @ X2) @ X3) @ X5))))))))) => (((very_much_likes @ X2) @ X3) @ X4))))))),inference(preprocess,[status(thm)],[axiom_a3_4]). % 44.18/44.37 thf(41,plain,sP37,inference(normalize,[status(thm)],[40]). % 44.18/44.37 thf(axiom_user_communication_2,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mimplies @ ((mdia @ a3) @ ((very_much_likes @ X1) @ X2))) @ ((likes @ X1) @ X2)))))))). % 44.18/44.37 thf(42,plain,sP35,inference(preprocess,[status(thm)],[axiom_user_communication_2]). % 44.18/44.37 thf(43,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,39,41,42,h1])). % 44.18/44.37 thf(44,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,43,h1])). % 44.18/44.37 thf(0,theorem,(![X1:$i]:(~((![X2:mu]:(~((~((![X3:mu]:(~((((likes @ X2) @ X3) @ X1)))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[44,h0])). % 44.18/44.37 % SZS output end Proof %------------------------------------------------------------------------------