%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT037^1 : 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 : n027.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 01:08:59 PM UTC 2025 % Result : Theorem 3.08s 3.32s % Output : Proof 3.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : AGT037^1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.03/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n027.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 : % 3.08/3.32 % SZS status Theorem % 3.08/3.32 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 3.08/3.32 % Inferences: 119 % 3.08/3.32 % SZS output start Proof % 3.08/3.32 thf(ty_mu, type, mu : $tType). % 3.08/3.32 thf(ty_jan, type, jan : mu). % 3.08/3.32 thf(ty_a3, type, a3 : ($i>$i>$o)). % 3.08/3.32 thf(ty_cola, type, cola : mu). % 3.08/3.32 thf(ty_eigen__1, type, eigen__1 : $i). % 3.08/3.32 thf(ty_eigen__0, type, eigen__0 : $i). % 3.08/3.32 thf(ty_possibly_likes, type, possibly_likes : (mu>mu>$i>$o)). % 3.08/3.32 thf(ty_likes, type, likes : (mu>mu>$i>$o)). % 3.08/3.32 thf(ty_piotr, type, piotr : mu). % 3.08/3.32 thf(ty_pepsi, type, pepsi : mu). % 3.08/3.32 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 3.08/3.32 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 3.08/3.32 thf(sP1,plain,sP1 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((likes @ jan) @ cola) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])). % 3.08/3.32 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(((a3 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))),introduced(definition,[new_symbols(definition,[sP2])])). % 3.08/3.32 thf(sP3,plain,sP3 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (((likes @ jan) @ cola) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 3.08/3.32 thf(sP4,plain,sP4 <=> (![X1:mu]:((~((![X2:$i]:(((a3 @ eigen__0) @ X2) => (~((((likes @ jan) @ X1) @ X2))))))) => (((possibly_likes @ jan) @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP4])])). % 3.08/3.32 thf(sP5,plain,sP5 <=> (((a3 @ eigen__0) @ eigen__1) => (((likes @ jan) @ cola) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP5])])). % 3.08/3.32 thf(sP6,plain,sP6 <=> (((possibly_likes @ jan) @ cola) @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 3.08/3.32 thf(sP7,plain,sP7 <=> ((a3 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP7])])). % 3.08/3.32 thf(sP8,plain,sP8 <=> (![X1:$i]:(~((![X2:$i]:(((a3 @ X1) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 3.08/3.32 thf(sP9,plain,sP9 <=> (((likes @ jan) @ cola) @ eigen__1),introduced(definition,[new_symbols(definition,[sP9])])). % 3.08/3.32 thf(sP10,plain,sP10 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))),introduced(definition,[new_symbols(definition,[sP10])])). % 3.08/3.32 thf(sP11,plain,sP11 <=> ((~(sP1)) => sP6),introduced(definition,[new_symbols(definition,[sP11])])). % 3.08/3.32 thf(sP12,plain,sP12 <=> (![X1:mu]:(![X2:mu]:((~((![X3:$i]:(((a3 @ eigen__0) @ X3) => (~((((likes @ X1) @ X2) @ X3))))))) => (((possibly_likes @ X1) @ X2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP12])])). % 3.08/3.32 thf(sP13,plain,sP13 <=> (sP7 => (~((((likes @ piotr) @ pepsi) @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 3.08/3.32 thf(sP14,plain,sP14 <=> (sP7 => (~(sP9))),introduced(definition,[new_symbols(definition,[sP14])])). % 3.08/3.32 thf(sP15,plain,sP15 <=> (![X1:$i]:(![X2:mu]:(![X3:mu]:((~((![X4:$i]:(((a3 @ X1) @ X4) => (~((((likes @ X2) @ X3) @ X4))))))) => (((possibly_likes @ X2) @ X3) @ X1))))),introduced(definition,[new_symbols(definition,[sP15])])). % 3.08/3.32 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 3.08/3.32 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 3.08/3.32 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 3.08/3.32 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 3.08/3.32 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 3.08/3.32 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 3.08/3.32 thf(def_mvalid,definition,(mvalid = (!!))). % 3.08/3.32 thf(conj,conjecture,((!!) @ ((possibly_likes @ jan) @ cola))). % 3.08/3.32 thf(h1,negated_conjecture,(~(((!!) @ ((possibly_likes @ jan) @ cola)))),inference(assume_negation,[status(cth)],[conj])). % 3.08/3.32 thf(h2,assumption,(~(sP6)),introduced(assumption,[])). % 3.08/3.32 thf(1,plain,(~(sP1) | sP14),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(2,plain,((~(sP14) | ~(sP7)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 3.08/3.32 thf(3,plain,(~(sP3) | sP5),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(4,plain,((~(sP5) | ~(sP7)) | sP9),inference(prop_rule,[status(thm)],[])). % 3.08/3.32 thf(5,plain,(sP13 | sP7),inference(prop_rule,[status(thm)],[])). % 3.08/3.32 thf(6,plain,(sP10 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 3.08/3.32 thf(7,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(8,plain,(~(sP8) | ~(sP10)),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(9,plain,(~(sP15) | sP12),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(10,plain,(~(sP12) | sP4),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(11,plain,(~(sP4) | sP11),inference(all_rule,[status(thm)],[])). % 3.08/3.32 thf(12,plain,((~(sP11) | sP1) | sP6),inference(prop_rule,[status(thm)],[])). % 3.08/3.32 thf(axiom_user_communication_5,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:(mforall_ind @ (^[X2:mu]:((mimplies @ ((mdia @ a3) @ ((likes @ X1) @ X2))) @ ((possibly_likes @ X1) @ X2)))))))). % 3.08/3.32 thf(13,plain,sP15,inference(preprocess,[status(thm)],[axiom_user_communication_5]). % 3.08/3.32 thf(axiom_a3_2,axiom,(mvalid @ ((mdia @ a3) @ ((likes @ piotr) @ pepsi)))). % 3.08/3.32 thf(14,plain,sP8,inference(preprocess,[status(thm)],[axiom_a3_2]). % 3.08/3.32 thf(axiom_a3_1,axiom,(mvalid @ ((mbox @ a3) @ ((likes @ jan) @ cola)))). % 3.08/3.32 thf(15,plain,sP2,inference(preprocess,[status(thm)],[axiom_a3_1]). % 3.08/3.32 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,13,14,15])). % 3.08/3.32 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,16,h2])). % 3.08/3.32 thf(18,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0])). % 3.08/3.32 thf(0,theorem,((!!) @ ((possibly_likes @ jan) @ cola)),inference(contra,[status(thm),contra(discharge,[h1])],[17,h1])). % 3.08/3.32 % SZS output end Proof %------------------------------------------------------------------------------