%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT038^1 : 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 : n014.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 2.55s 2.79s % Output : Proof 2.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : AGT038^1 : TPTP v9.2.0. Bugfixed v5.4.0. % 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Oct 8 12:28:08 EDT 2025 % 0.13/0.35 % CPUTime : % 2.55/2.79 % SZS status Theorem % 2.55/2.79 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0 % 2.55/2.79 % Inferences: 5733 % 2.55/2.79 % SZS output start Proof % 2.55/2.79 thf(ty_mu, type, mu : $tType). % 2.55/2.79 thf(ty_a3, type, a3 : ($i>$i>$o)). % 2.55/2.79 thf(ty_eigen__0, type, eigen__0 : $i). % 2.55/2.79 thf(ty_possibly_likes, type, possibly_likes : (mu>mu>$i>$o)). % 2.55/2.79 thf(ty_likes, type, likes : (mu>mu>$i>$o)). % 2.55/2.79 thf(ty_piotr, type, piotr : mu). % 2.55/2.79 thf(ty_pepsi, type, pepsi : mu). % 2.55/2.79 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 2.55/2.79 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((((possibly_likes @ piotr) @ pepsi) @ X1))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 2.55/2.79 thf(sP1,plain,sP1 <=> ((~((![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))))) => (((possibly_likes @ piotr) @ pepsi) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])). % 2.55/2.79 thf(sP2,plain,sP2 <=> (![X1:mu]:(![X2:mu]:((~((![X3:$i]:(((a3 @ eigen__0) @ X3) => (~((((likes @ X1) @ X2) @ X3))))))) => (((possibly_likes @ X1) @ X2) @ eigen__0)))),introduced(definition,[new_symbols(definition,[sP2])])). % 2.55/2.79 thf(sP3,plain,sP3 <=> (![X1:mu]:((~((![X2:$i]:(((a3 @ eigen__0) @ X2) => (~((((likes @ piotr) @ X1) @ X2))))))) => (((possibly_likes @ piotr) @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP3])])). % 2.55/2.79 thf(sP4,plain,sP4 <=> (![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,[sP4])])). % 2.55/2.79 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((![X2:$i]:(((a3 @ X1) @ X2) => (~((((likes @ piotr) @ pepsi) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 2.55/2.79 thf(sP6,plain,sP6 <=> ((!!) @ ((possibly_likes @ piotr) @ pepsi)),introduced(definition,[new_symbols(definition,[sP6])])). % 2.55/2.79 thf(sP7,plain,sP7 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => (~((((likes @ piotr) @ pepsi) @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 2.55/2.79 thf(sP8,plain,sP8 <=> (((possibly_likes @ piotr) @ pepsi) @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])). % 2.55/2.79 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 2.55/2.79 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 2.55/2.79 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 2.55/2.79 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 2.55/2.79 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 2.55/2.79 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 2.55/2.79 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 2.55/2.79 thf(def_mvalid,definition,(mvalid = (!!))). % 2.55/2.79 thf(conj,conjecture,sP6). % 2.55/2.79 thf(h1,negated_conjecture,(~(sP6)),inference(assume_negation,[status(cth)],[conj])). % 2.55/2.79 thf(1,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])). % 2.55/2.79 thf(2,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). % 2.55/2.79 thf(3,plain,(~(sP3) | sP1),inference(all_rule,[status(thm)],[])). % 2.55/2.79 thf(4,plain,((~(sP1) | sP7) | sP8),inference(prop_rule,[status(thm)],[])). % 2.55/2.79 thf(5,plain,(~(sP5) | ~(sP7)),inference(all_rule,[status(thm)],[])). % 2.55/2.79 thf(6,plain,(sP6 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 2.55/2.79 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)))))))). % 2.55/2.79 thf(7,plain,sP4,inference(preprocess,[status(thm)],[axiom_user_communication_5]). % 2.55/2.79 thf(axiom_a3_2,axiom,(mvalid @ ((mdia @ a3) @ ((likes @ piotr) @ pepsi)))). % 2.55/2.79 thf(8,plain,sP5,inference(preprocess,[status(thm)],[axiom_a3_2]). % 2.55/2.79 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,h1])). % 2.55/2.79 thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0])). % 2.55/2.79 thf(0,theorem,sP6,inference(contra,[status(thm),contra(discharge,[h1])],[9,h1])). % 2.55/2.79 % SZS output end Proof %------------------------------------------------------------------------------