%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SET002^3 : TPTP v9.2.0. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n024.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 02:24:59 PM UTC 2025 % Result : Theorem 0.14s 0.40s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET002^3 : TPTP v9.2.0. Released v8.1.0. % 0.08/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.37 % Computer : n024.cluster.edu % 0.14/0.37 % Model : x86_64 x86_64 % 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.37 % Memory : 8042.1875MB % 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.37 % CPULimit : 300 % 0.14/0.37 % WCLimit : 300 % 0.14/0.37 % DateTime : Wed Oct 8 14:37:53 EDT 2025 % 0.14/0.37 % CPUTime : % 0.14/0.40 % SZS status Theorem % 0.14/0.40 % Mode: mode213 % 0.14/0.40 % Inferences: 34 % 0.14/0.40 % SZS output start Proof % 0.14/0.40 thf(ty_mworld, type, mworld : $tType). % 0.14/0.40 thf(ty_subset, type, subset : ($i>$i>mworld>$o)). % 0.14/0.40 thf(ty_union, type, union : ($i>$i>$i)). % 0.14/0.40 thf(ty_eigen__0, type, eigen__0 : $i). % 0.14/0.40 thf(ty_mactual, type, mactual : mworld). % 0.14/0.40 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)). % 0.14/0.40 thf(sP1,plain,sP1 <=> (![X1:$i]:((((subset @ eigen__0) @ X1) @ mactual) => (((qmltpeq @ ((union @ eigen__0) @ X1)) @ X1) @ mactual))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.14/0.40 thf(sP2,plain,sP2 <=> (((subset @ eigen__0) @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP2])])). % 0.14/0.40 thf(sP3,plain,sP3 <=> (![X1:$i]:(((subset @ X1) @ X1) @ mactual)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.14/0.40 thf(sP4,plain,sP4 <=> (((qmltpeq @ ((union @ eigen__0) @ eigen__0)) @ eigen__0) @ mactual),introduced(definition,[new_symbols(definition,[sP4])])). % 0.14/0.40 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:((((subset @ X1) @ X2) @ mactual) => (((qmltpeq @ ((union @ X1) @ X2)) @ X2) @ mactual)))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.14/0.40 thf(sP6,plain,sP6 <=> (sP2 => sP4),introduced(definition,[new_symbols(definition,[sP6])])). % 0.14/0.40 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 0.14/0.40 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 0.14/0.40 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.14/0.40 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.14/0.40 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 0.14/0.40 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 0.14/0.40 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 0.14/0.40 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 0.14/0.40 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:((X1 @ X3) @ X2)))))). % 0.14/0.40 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(~(((X1 @ X3) @ X2)))))))))). % 0.14/0.40 thf(prove_idempotency_of_union,conjecture,(![X1:$i]:(((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ mactual))). % 0.14/0.40 thf(h0,negated_conjecture,(~((![X1:$i]:(((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ mactual)))),inference(assume_negation,[status(cth)],[prove_idempotency_of_union])). % 0.14/0.40 thf(h1,assumption,(~(sP4)),introduced(assumption,[])). % 0.14/0.40 thf(1,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])). % 0.14/0.40 thf(2,plain,(~(sP5) | sP1),inference(all_rule,[status(thm)],[])). % 0.14/0.40 thf(3,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])). % 0.14/0.40 thf(4,plain,((~(sP6) | ~(sP2)) | sP4),inference(prop_rule,[status(thm)],[])). % 0.14/0.40 thf(subset_union,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:(mforall_di @ (^[X2:$i]:((mimplies @ ((subset @ X1) @ X2)) @ ((qmltpeq @ ((union @ X1) @ X2)) @ X2)))))))). % 0.14/0.40 thf(5,plain,sP5,inference(preprocess,[status(thm)],[subset_union]). % 0.14/0.40 thf(reflexivity_of_subset,axiom,(mlocal @ (mforall_di @ (^[X1:$i]:((subset @ X1) @ X1))))). % 0.14/0.40 thf(6,plain,sP3,inference(preprocess,[status(thm)],[reflexivity_of_subset]). % 0.14/0.40 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1])). % 0.14/0.40 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1])). % 0.14/0.40 thf(0,theorem,(![X1:$i]:(((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ mactual)),inference(contra,[status(thm),contra(discharge,[h0])],[8,h0])). % 0.14/0.40 % SZS output end Proof %------------------------------------------------------------------------------