%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PHI003^2 : TPTP v9.2.0. Released v6.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n003.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 02:13:37 PM UTC 2025 % Result : Theorem 1.08s 1.30s % Output : Proof 1.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : PHI003^2 : TPTP v9.2.0. Released v6.1.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n003.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 23:18:53 EDT 2025 % 0.14/0.36 % CPUTime : % 1.08/1.30 % SZS status Theorem % 1.08/1.30 % Mode: mode506 % 1.08/1.30 % Inferences: 14 % 1.08/1.30 % SZS output start Proof % 1.08/1.30 thf(ty_mu, type, mu : $tType). % 1.08/1.30 thf(ty_eigen__0, type, eigen__0 : $i). % 1.08/1.30 thf(ty_positive, type, positive : ((mu>$i>$o)>$i>$o)). % 1.08/1.30 thf(ty_rel, type, rel : ($i>$i>$o)). % 1.08/1.30 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.08/1.30 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((![X2:$i]:(((rel @ X1) @ X2) => (![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.08/1.30 thf(sP1,plain,sP1 <=> ((!!) @ (positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.08/1.30 thf(sP2,plain,sP2 <=> ((positive @ (^[X1:mu]:(^[X2:$i]:(![X3:mu>$i>$o]:(((positive @ X3) @ X2) => ((X3 @ X1) @ X2)))))) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])). % 1.08/1.30 thf(sP3,plain,sP3 <=> (![X1:mu>$i>$o]:(((positive @ X1) @ eigen__0) => (~((![X2:$i]:(((rel @ eigen__0) @ X2) => (![X3:mu]:(~(((X1 @ X3) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.08/1.30 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:mu>$i>$o]:(((positive @ X2) @ X1) => (~((![X3:$i]:(((rel @ X1) @ X3) => (![X4:mu]:(~(((X2 @ X4) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.08/1.30 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.08/1.30 thf(sP6,plain,sP6 <=> (sP2 => (~((![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.08/1.30 thf(sP7,plain,sP7 <=> (![X1:$i]:(((rel @ eigen__0) @ X1) => (![X2:mu]:(~((![X3:mu>$i>$o]:(((positive @ X3) @ X1) => ((X3 @ X2) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.08/1.30 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 1.08/1.30 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 1.08/1.30 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 1.08/1.30 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 1.08/1.30 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.08/1.30 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.08/1.30 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) => (X2 @ X3))))))). % 1.08/1.30 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X2 @ X3) => (X1 @ X3))))))). % 1.08/1.30 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 1.08/1.30 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) => (X2 @ X3)) => (~(((~((X1 @ X3))) => (~((X2 @ X3)))))))))))). % 1.08/1.30 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 1.08/1.30 thf(def_mforall_indset,definition,(mforall_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(![X3:mu>$i>$o]:((X1 @ X3) @ X2)))))). % 1.08/1.30 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 1.08/1.30 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(~((![X3:mu]:(~(((X1 @ X3) @ X2)))))))))). % 1.08/1.30 thf(def_mexists_indset,definition,(mexists_indset = (^[X1:(mu>$i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:mu>$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 1.08/1.30 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(~((![X3:$i>$o]:(~(((X1 @ X3) @ X2)))))))))). % 1.08/1.30 thf(def_mbox_generic,definition,(mbox_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 1.08/1.30 thf(def_mdia_generic,definition,(mdia_generic = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 1.08/1.30 thf(def_mbox,definition,(mbox = (mbox_generic @ rel))). % 1.08/1.30 thf(def_mdia,definition,(mdia = (mdia_generic @ rel))). % 1.08/1.30 thf(def_mvalid,definition,(mvalid = (!!))). % 1.08/1.30 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 1.08/1.30 thf(def_god,definition,(god = (^[X1:mu]:(mforall_indset @ (^[X2:mu>$i>$o]:((mimplies @ (positive @ X2)) @ (X2 @ X1))))))). % 1.08/1.30 thf(corC,conjecture,(![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (~((~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2)))))))))))))))). % 1.08/1.30 thf(h1,negated_conjecture,(~(sP5)),inference(assume_negation,[status(cth)],[corC])). % 1.08/1.30 thf(1,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])). % 1.08/1.30 thf(2,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])). % 1.08/1.30 thf(3,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])). % 1.08/1.30 thf(4,plain,((~(sP6) | ~(sP2)) | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 1.08/1.30 thf(5,plain,(sP5 | sP7),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.08/1.30 thf(thmT1,axiom,(mvalid @ (mforall_indset @ (^[X1:mu>$i>$o]:((mimplies @ (positive @ X1)) @ (mdia @ (mexists_ind @ X1))))))). % 1.08/1.30 thf(6,plain,sP4,inference(preprocess,[status(thm)],[thmT1]). % 1.08/1.30 thf(axA3,axiom,(mvalid @ (positive @ god))). % 1.08/1.30 thf(7,plain,sP1,inference(preprocess,[status(thm)],[axA3]). % 1.08/1.30 thf(8,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h1])). % 1.08/1.30 thf(9,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0])). % 1.08/1.30 thf(0,theorem,(![X1:$i]:(~((![X2:$i]:(((rel @ X1) @ X2) => (~((~((![X3:mu]:(~((![X4:mu>$i>$o]:(((positive @ X4) @ X2) => ((X4 @ X3) @ X2))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[8,h1])). % 1.08/1.30 % SZS output end Proof 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