%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : AGT035^1 : 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 : n019.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 3.76s 4.17s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : AGT035^1 : 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 % 0.12/0.35 % Computer : n019.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Wed Oct 8 12:28:08 EDT 2025 % 0.12/0.35 % CPUTime : % 3.76/4.17 % SZS status Theorem % 3.76/4.17 % Mode: mode8a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 3.76/4.17 % Inferences: 3345 % 3.76/4.17 % SZS output start Proof % 3.76/4.17 thf(ty_mu, type, mu : $tType). % 3.76/4.17 thf(ty_jan, type, jan : mu). % 3.76/4.17 thf(ty_a3, type, a3 : ($i>$i>$o)). % 3.76/4.17 thf(ty_eigen__2, type, eigen__2 : $i). % 3.76/4.17 thf(ty_cola, type, cola : mu). % 3.76/4.17 thf(ty_eigen__0, type, eigen__0 : $i). % 3.76/4.17 thf(ty_likes, type, likes : (mu>mu>$i>$o)). % 3.76/4.17 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 3.76/4.17 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((~(((a3 @ eigen__0) @ X1))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 3.76/4.17 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((a3 @ X1) @ X2) => (((likes @ jan) @ cola) @ X2)))),introduced(definition,[new_symbols(definition,[sP1])])). % 3.76/4.17 thf(sP2,plain,sP2 <=> (![X1:$i]:(((a3 @ eigen__2) @ X1) => (((likes @ jan) @ cola) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])). % 3.76/4.17 thf(sP3,plain,sP3 <=> ((a3 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP3])])). % 3.76/4.17 thf(sP4,plain,sP4 <=> (((a3 @ eigen__2) @ eigen__0) => (((likes @ jan) @ cola) @ eigen__0)),introduced(definition,[new_symbols(definition,[sP4])])). % 3.76/4.17 thf(sP5,plain,sP5 <=> ((a3 @ eigen__2) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])). % 3.76/4.17 thf(sP6,plain,sP6 <=> (![X1:$i]:(~(((a3 @ eigen__0) @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 3.76/4.17 thf(sP7,plain,sP7 <=> (((likes @ jan) @ cola) @ eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 3.76/4.17 thf(sP8,plain,sP8 <=> (![X1:$i]:(![X2:$i]:(((a3 @ X1) @ X2) => ((a3 @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP8])])). % 3.76/4.17 thf(sP9,plain,sP9 <=> (![X1:$i]:(((a3 @ eigen__0) @ X1) => ((a3 @ X1) @ eigen__0))),introduced(definition,[new_symbols(definition,[sP9])])). % 3.76/4.17 thf(sP10,plain,sP10 <=> (![X1:$i]:(~((![X2:$i]:(~(((a3 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 3.76/4.17 thf(sP11,plain,sP11 <=> (sP3 => sP5),introduced(definition,[new_symbols(definition,[sP11])])). % 3.76/4.17 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 3.76/4.17 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 3.76/4.17 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 3.76/4.17 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 3.76/4.17 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 3.76/4.17 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 3.76/4.17 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 3.76/4.17 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 3.76/4.17 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 3.76/4.17 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 3.76/4.17 thf(def_mvalid,definition,(mvalid = (!!))). % 3.76/4.17 thf(def_subrel,definition,(subrel = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(![X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => ((X2 @ X3) @ X4)))))))). % 3.76/4.17 thf(def_cond4s,definition,(cond4s = (^[X1:$i>$i>$o]:(^[X2:$i>$i>$o]:(![X3:$i]:(![X4:$i]:(![X5:$i]:((~((((X1 @ X3) @ X4) => (~(((X2 @ X4) @ X5)))))) => ((X2 @ X3) @ X5))))))))). % 3.76/4.17 thf(conjecture,conjecture,((!!) @ ((likes @ jan) @ cola))). % 3.76/4.17 thf(h1,negated_conjecture,(~(((!!) @ ((likes @ jan) @ cola)))),inference(assume_negation,[status(cth)],[conjecture])). % 3.76/4.17 thf(h2,assumption,(~(sP7)),introduced(assumption,[])). % 3.76/4.17 thf(1,plain,((~(sP11) | ~(sP3)) | sP5),inference(prop_rule,[status(thm)],[])). % 3.76/4.17 thf(2,plain,((~(sP4) | ~(sP5)) | sP7),inference(prop_rule,[status(thm)],[])). % 3.76/4.17 thf(3,plain,(~(sP9) | sP11),inference(all_rule,[status(thm)],[])). % 3.76/4.17 thf(4,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])). % 3.76/4.17 thf(5,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 3.76/4.17 thf(6,plain,(sP6 | sP3),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 3.76/4.17 thf(7,plain,(~(sP10) | ~(sP6)),inference(all_rule,[status(thm)],[])). % 3.76/4.17 thf(8,plain,(~(sP8) | sP9),inference(all_rule,[status(thm)],[])). % 3.76/4.17 thf(axioms_D_a3,axiom,(mserial @ a3)). % 3.76/4.17 thf(9,plain,sP10,inference(preprocess,[status(thm)],[axioms_D_a3]). % 3.76/4.17 thf(axioms_B_a3,axiom,(msymmetric @ a3)). % 3.76/4.17 thf(10,plain,sP8,inference(preprocess,[status(thm)],[axioms_B_a3]). % 3.76/4.17 thf(axiom_a3_1,axiom,(mvalid @ ((mbox @ a3) @ ((likes @ jan) @ cola)))). % 3.76/4.17 thf(11,plain,sP1,inference(preprocess,[status(thm)],[axiom_a3_1]). % 3.76/4.17 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,h2,9,10,11])). % 3.76/4.17 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,12,h2])). % 3.76/4.17 thf(14,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0])). % 3.76/4.17 thf(0,theorem,((!!) @ ((likes @ jan) @ cola)),inference(contra,[status(thm),contra(discharge,[h1])],[13,h1])). % 3.76/4.17 % SZS output end Proof %------------------------------------------------------------------------------