%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT039^1 : 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 : 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 01:09:00 PM UTC 2025 % Result : Theorem 21.33s 21.52s % Output : Proof 21.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.14 % Problem : AGT039^1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.05/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Wed Oct 8 12:27:53 EDT 2025 % 0.14/0.36 % CPUTime : % 21.33/21.52 % SZS status Theorem % 21.33/21.52 % Mode: mode86:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 21.33/21.52 % Inferences: 13903 % 21.33/21.52 % SZS output start Proof % 21.33/21.52 thf(ty_mu, type, mu : $tType). % 21.33/21.52 thf(ty_jan, type, jan : mu). % 21.33/21.52 thf(ty_a1, type, a1 : ($i>$i>$o)). % 21.33/21.52 thf(ty_cola, type, cola : mu). % 21.33/21.52 thf(ty_eigen__0, type, eigen__0 : $i). % 21.33/21.52 thf(ty_possibly_likes, type, possibly_likes : (mu>mu>$i>$o)). % 21.33/21.52 thf(ty_eigen__4, type, eigen__4 : $i). % 21.33/21.52 thf(ty_beer, type, beer : mu). % 21.33/21.52 thf(ty_eigen__5, type, eigen__5 : $i). % 21.33/21.52 thf(ty_likes, type, likes : (mu>mu>$i>$o)). % 21.33/21.52 thf(ty_piotr, type, piotr : mu). % 21.33/21.52 thf(ty_pepsi, type, pepsi : mu). % 21.33/21.52 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 21.33/21.52 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((a1 @ eigen__0) @ X1) => (~((((likes @ piotr) @ beer) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 21.33/21.52 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((a1 @ eigen__4) @ X1) => (~((((likes @ piotr) @ beer) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 21.33/21.52 thf(sP1,plain,sP1 <=> (((likes @ jan) @ cola) @ eigen__5),introduced(definition,[new_symbols(definition,[sP1])])). % 21.33/21.52 thf(sP2,plain,sP2 <=> (((a1 @ eigen__0) @ eigen__4) => ((~((![X1:$i]:(((a1 @ eigen__4) @ X1) => (~((((likes @ jan) @ cola) @ X1))))))) => (((likes @ jan) @ pepsi) @ eigen__4))),introduced(definition,[new_symbols(definition,[sP2])])). % 21.33/21.52 thf(sP3,plain,sP3 <=> (((a1 @ eigen__4) @ eigen__5) => sP1),introduced(definition,[new_symbols(definition,[sP3])])). % 21.33/21.52 thf(sP4,plain,sP4 <=> (![X1:$i]:(((a1 @ eigen__4) @ X1) => (~((((likes @ piotr) @ beer) @ X1))))),introduced(definition,[new_symbols(definition,[sP4])])). % 21.33/21.52 thf(sP5,plain,sP5 <=> ((~((![X1:$i]:(((a1 @ eigen__4) @ X1) => (~((((likes @ jan) @ cola) @ X1))))))) => (((likes @ jan) @ pepsi) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP5])])). % 21.33/21.52 thf(sP6,plain,sP6 <=> (((a1 @ eigen__4) @ eigen__5) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP6])])). % 21.33/21.52 thf(sP7,plain,sP7 <=> (![X1:$i]:(((a1 @ eigen__0) @ X1) => (~((((likes @ jan) @ pepsi) @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 21.33/21.52 thf(sP8,plain,sP8 <=> ((a1 @ eigen__4) @ eigen__5),introduced(definition,[new_symbols(definition,[sP8])])). % 21.33/21.52 thf(sP9,plain,sP9 <=> (((a1 @ eigen__0) @ eigen__4) => (~((((likes @ jan) @ pepsi) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP9])])). % 21.33/21.52 thf(sP10,plain,sP10 <=> (![X1:mu]:(![X2:$i]:(((a1 @ eigen__0) @ X2) => ((~((![X3:$i]:(((a1 @ X2) @ X3) => (~((((likes @ X1) @ cola) @ X3))))))) => (((likes @ X1) @ pepsi) @ X2))))),introduced(definition,[new_symbols(definition,[sP10])])). % 21.33/21.52 thf(sP11,plain,sP11 <=> (![X1:$i]:(((a1 @ eigen__4) @ X1) => (~((((likes @ jan) @ cola) @ X1))))),introduced(definition,[new_symbols(definition,[sP11])])). % 21.33/21.52 thf(sP12,plain,sP12 <=> (![X1:$i]:(((a1 @ eigen__4) @ X1) => (((likes @ jan) @ cola) @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 21.33/21.52 thf(sP13,plain,sP13 <=> (![X1:mu]:((~((![X2:$i]:(((a1 @ eigen__0) @ X2) => (~((((likes @ jan) @ X1) @ X2))))))) => (((possibly_likes @ jan) @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP13])])). % 21.33/21.52 thf(sP14,plain,sP14 <=> (![X1:$i]:(((a1 @ eigen__0) @ X1) => (~((((likes @ piotr) @ beer) @ X1))))),introduced(definition,[new_symbols(definition,[sP14])])). % 21.33/21.52 thf(sP15,plain,sP15 <=> (![X1:$i]:(((a1 @ eigen__0) @ X1) => ((~((![X2:$i]:(((a1 @ X1) @ X2) => (~((((likes @ jan) @ cola) @ X2))))))) => (((likes @ jan) @ pepsi) @ X1)))),introduced(definition,[new_symbols(definition,[sP15])])). % 21.33/21.52 thf(sP16,plain,sP16 <=> (((possibly_likes @ jan) @ pepsi) @ eigen__0),introduced(definition,[new_symbols(definition,[sP16])])). % 21.33/21.52 thf(sP17,plain,sP17 <=> (![X1:mu]:(![X2:mu]:((~((![X3:$i]:(((a1 @ eigen__0) @ X3) => (~((((likes @ X1) @ X2) @ X3))))))) => (((possibly_likes @ X1) @ X2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP17])])). % 21.33/21.52 thf(sP18,plain,sP18 <=> (sP8 => (~((((likes @ piotr) @ beer) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP18])])). % 21.33/21.52 thf(sP19,plain,sP19 <=> (![X1:$i]:(![X2:mu]:(![X3:mu]:((~((![X4:$i]:(((a1 @ X1) @ X4) => (~((((likes @ X2) @ X3) @ X4))))))) => (((possibly_likes @ X2) @ X3) @ X1))))),introduced(definition,[new_symbols(definition,[sP19])])). % 21.33/21.52 thf(sP20,plain,sP20 <=> (((likes @ jan) @ pepsi) @ eigen__4),introduced(definition,[new_symbols(definition,[sP20])])). % 21.33/21.52 thf(sP21,plain,sP21 <=> (![X1:$i]:(![X2:$i]:(((a1 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))),introduced(definition,[new_symbols(definition,[sP21])])). % 21.33/21.52 thf(sP22,plain,sP22 <=> ((~(sP7)) => sP16),introduced(definition,[new_symbols(definition,[sP22])])). % 21.33/21.52 thf(sP23,plain,sP23 <=> (![X1:$i]:(~((![X2:$i]:(((a1 @ X1) @ X2) => (~((((likes @ piotr) @ beer) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 21.33/21.52 thf(sP24,plain,sP24 <=> ((a1 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP24])])). % 21.33/21.52 thf(sP25,plain,sP25 <=> (![X1:$i]:(![X2:mu]:(![X3:$i]:(((a1 @ X1) @ X3) => ((~((![X4:$i]:(((a1 @ X3) @ X4) => (~((((likes @ X2) @ cola) @ X4))))))) => (((likes @ X2) @ pepsi) @ X3)))))),introduced(definition,[new_symbols(definition,[sP25])])). % 21.33/21.52 thf(sP26,plain,sP26 <=> (sP24 => (~((((likes @ piotr) @ beer) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP26])])). % 21.33/21.52 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 21.33/21.52 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 21.33/21.52 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 21.33/21.52 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 21.33/21.52 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 21.33/21.52 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 21.33/21.52 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 21.33/21.52 thf(def_mvalid,definition,(mvalid = (!!))). % 21.33/21.52 thf(def_cond4s,definition,(cond4s = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X1 @ X3) @ X4) => (~(((X2 @ X4) @ X5)))))) => ((X2 @ X3) @ X5))))))))). % 21.33/21.52 thf(conj,conjecture,((!!) @ ((possibly_likes @ jan) @ pepsi))). % 21.33/21.52 thf(h1,negated_conjecture,(~(((!!) @ ((possibly_likes @ jan) @ pepsi)))),inference(assume_negation,[status(cth)],[conj])). % 21.33/21.52 thf(h2,assumption,(~(sP16)),introduced(assumption,[])). % 21.33/21.52 thf(1,plain,((~(sP6) | ~(sP8)) | ~(sP1)),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(2,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(3,plain,((~(sP22) | sP7) | sP16),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(4,plain,((~(sP3) | ~(sP8)) | sP1),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(5,plain,((~(sP5) | sP11) | sP20),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(6,plain,((~(sP2) | ~(sP24)) | sP5),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(7,plain,((~(sP9) | ~(sP24)) | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(8,plain,(~(sP12) | sP3),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(9,plain,(sP18 | sP8),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(10,plain,(sP4 | ~(sP18)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 21.33/21.52 thf(11,plain,(~(sP13) | sP22),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(12,plain,(~(sP17) | sP13),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(13,plain,(~(sP23) | ~(sP4)),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(14,plain,(~(sP21) | sP12),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(15,plain,(~(sP7) | sP9),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(16,plain,(~(sP15) | sP2),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(17,plain,(sP26 | sP24),inference(prop_rule,[status(thm)],[])). % 21.33/21.52 thf(18,plain,(sP14 | ~(sP26)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 21.33/21.52 thf(19,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(20,plain,(~(sP25) | sP10),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(21,plain,(~(sP23) | ~(sP14)),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(22,plain,(~(sP19) | sP17),inference(all_rule,[status(thm)],[])). % 21.33/21.52 thf(axiom_user_communication_3,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mimplies @ ((mdia @ a1) @ ((likes @ X1) @ X2))) @ ((possibly_likes @ X1) @ X2)))))))). % 21.33/21.52 thf(23,plain,sP19,inference(preprocess,[status(thm)],[axiom_user_communication_3]). % 21.33/21.52 thf(axiom_a3_3,axiom,(mvalid @ ((mdia @ a1) @ ((likes @ piotr) @ beer)))). % 21.33/21.52 thf(24,plain,sP23,inference(preprocess,[status(thm)],[axiom_a3_3]). % 21.33/21.52 thf(axiom_a1_4,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mbox @ a1) @ ((mimplies @ ((mdia @ a1) @ ((likes @ X1) @ cola))) @ ((likes @ X1) @ pepsi))))))). % 21.33/21.52 thf(25,plain,sP25,inference(preprocess,[status(thm)],[axiom_a1_4]). % 21.33/21.52 thf(axiom_a1_1,axiom,(mvalid @ ((mbox @ a1) @ ((likes @ jan) @ cola)))). % 21.33/21.52 thf(26,plain,sP21,inference(preprocess,[status(thm)],[axiom_a1_1]). % 21.33/21.52 thf(27,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h2,23,24,25,26])). % 21.33/21.52 thf(28,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,27,h2])). % 21.33/21.52 thf(29,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[28,h0])). % 21.33/21.52 thf(0,theorem,((!!) @ ((possibly_likes @ jan) @ pepsi)),inference(contra,[status(thm),contra(discharge,[h1])],[28,h1])). % 21.33/21.52 % SZS output end Proof %------------------------------------------------------------------------------