%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:55 PM UTC 2026 % Result : Theorem 1.03s 1.80s % Output : Proof 1.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL947^10 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.35 % Computer : n011.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 21:22:14 UTC 2026 % 0.10/0.36 % CPUTime : % 1.03/1.80 % SZS status Theorem % 1.03/1.80 % Mode: mode506 % 1.03/1.80 % Inferences: 19973 % 1.03/1.80 % SZS output start Proof % 1.03/1.80 thf(ty_mworld, type, mworld : $tType). % 1.03/1.80 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)). % 1.03/1.80 thf(ty_subset, type, subset : ($i>$i>mworld>$o)). % 1.03/1.80 thf(ty_union, type, union : ($i>$i>$i)). % 1.03/1.80 thf(ty_eigen__1, type, eigen__1 : $i). % 1.03/1.80 thf(ty_eigen__0, type, eigen__0 : mworld). % 1.03/1.80 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 1.03/1.80 thf(ty_mactual, type, mactual : mworld). % 1.03/1.80 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)). % 1.03/1.80 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.03/1.80 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ X2)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 1.03/1.80 thf(h1, assumption, (![X1:mworld>$o]:(![X2:mworld]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 1.03/1.80 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:mworld]:(~((((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (((qmltpeq @ ((union @ X2) @ X2)) @ X2) @ X3)))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.03/1.80 thf(sP1,plain,sP1 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 1.03/1.80 thf(sP2,plain,sP2 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (((subset @ eigen__1) @ eigen__1) @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (((qmltpeq @ ((union @ eigen__1) @ eigen__1)) @ eigen__1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 1.03/1.80 thf(sP3,plain,sP3 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((subset @ eigen__1) @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.03/1.80 thf(sP4,plain,sP4 <=> (((eiw_di @ eigen__1) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP4])])). % 1.03/1.80 thf(sP5,plain,sP5 <=> (((mrel @ eigen__0) @ eigen__0) => (sP3 => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((qmltpeq @ ((union @ eigen__1) @ eigen__1)) @ eigen__1) @ X1))))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.03/1.80 thf(sP6,plain,sP6 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (((subset @ X1) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])). % 1.03/1.80 thf(sP7,plain,sP7 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP7])])). % 1.03/1.80 thf(sP8,plain,sP8 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (((subset @ eigen__1) @ X1) @ X3))) => (![X3:mworld]:(((mrel @ X2) @ X3) => (((qmltpeq @ ((union @ eigen__1) @ X1)) @ X1) @ X3)))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 1.03/1.80 thf(sP9,plain,sP9 <=> (((eiw_di @ eigen__1) @ eigen__0) => sP2),introduced(definition,[new_symbols(definition,[sP9])])). % 1.03/1.80 thf(sP10,plain,sP10 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (((subset @ X2) @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.03/1.80 thf(sP11,plain,sP11 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (((qmltpeq @ ((union @ eigen__1) @ eigen__1)) @ eigen__1) @ X1))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.03/1.80 thf(sP12,plain,sP12 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((subset @ X1) @ X3) @ X5))) => (![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ ((union @ X1) @ X3)) @ X3) @ X5)))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.03/1.80 thf(sP13,plain,sP13 <=> (sP7 => (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.03/1.80 thf(sP14,plain,sP14 <=> (((eiw_di @ eigen__1) @ eigen__0) => sP11),introduced(definition,[new_symbols(definition,[sP14])])). % 1.03/1.80 thf(sP15,plain,sP15 <=> (((mrel @ eigen__0) @ eigen__0) => sP8),introduced(definition,[new_symbols(definition,[sP15])])). % 1.03/1.80 thf(sP16,plain,sP16 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (((qmltpeq @ ((union @ X1) @ X1)) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP16])])). % 1.03/1.80 thf(sP17,plain,sP17 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (((qmltpeq @ ((union @ X2) @ X2)) @ X2) @ X3))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 1.03/1.80 thf(sP18,plain,sP18 <=> (((eiw_di @ eigen__1) @ eigen__0) => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((subset @ eigen__1) @ X2) @ X4))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ ((union @ eigen__1) @ X2)) @ X2) @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 1.03/1.80 thf(sP19,plain,sP19 <=> (sP3 => sP11),introduced(definition,[new_symbols(definition,[sP19])])). % 1.03/1.80 thf(sP20,plain,sP20 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((subset @ eigen__1) @ X2) @ X4))) => (![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ ((union @ eigen__1) @ X2)) @ X2) @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP20])])). % 1.03/1.80 thf(sP21,plain,sP21 <=> (sP7 => sP6),introduced(definition,[new_symbols(definition,[sP21])])). % 1.03/1.80 thf(sP22,plain,sP22 <=> (sP7 => sP12),introduced(definition,[new_symbols(definition,[sP22])])). % 1.03/1.80 thf(sP23,plain,sP23 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (((subset @ X2) @ X4) @ X6))) => (![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ ((union @ X2) @ X4)) @ X4) @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP23])])). % 1.03/1.80 thf(sP24,plain,sP24 <=> ((mrel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP24])])). % 1.03/1.80 thf(sP25,plain,sP25 <=> ((eiw_di @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP25])])). % 1.03/1.80 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 1.03/1.80 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 1.03/1.80 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 1.03/1.80 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 1.03/1.80 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 1.03/1.80 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 1.03/1.80 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 1.03/1.80 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 1.03/1.80 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 1.03/1.80 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))). % 1.03/1.80 thf(prove_idempotency_of_union,conjecture,sP17). % 1.03/1.80 thf(h2,negated_conjecture,(~(sP17)),inference(assume_negation,[status(cth)],[prove_idempotency_of_union])). % 1.03/1.80 thf(1,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(2,plain,((~(sP5) | ~(sP24)) | sP19),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(3,plain,((~(sP19) | ~(sP3)) | sP11),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(4,plain,(~(sP20) | sP15),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(5,plain,((~(sP15) | ~(sP24)) | sP8),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(6,plain,(~(sP8) | sP9),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(7,plain,((~(sP9) | ~(sP25)) | sP2),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(8,plain,((~(sP22) | ~(sP7)) | sP12),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(9,plain,(~(sP12) | sP18),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(10,plain,((~(sP18) | ~(sP25)) | sP20),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(11,plain,((~(sP21) | ~(sP7)) | sP6),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(12,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(13,plain,((~(sP4) | ~(sP25)) | sP3),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(14,plain,(~(sP23) | sP22),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(15,plain,(~(sP1) | sP24),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(16,plain,(~(sP10) | sP21),inference(all_rule,[status(thm)],[])). % 1.03/1.80 thf(17,plain,(sP14 | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(18,plain,(sP14 | sP25),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(19,plain,(sP16 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 1.03/1.80 thf(20,plain,(sP13 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(21,plain,(sP13 | sP7),inference(prop_rule,[status(thm)],[])). % 1.03/1.80 thf(22,plain,(sP17 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 1.03/1.80 thf(reflexivity_of_subset,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ ((subset @ X1) @ X1))))))). % 1.03/1.80 thf(23,plain,sP10,inference(preprocess,[status(thm)],[reflexivity_of_subset]). % 1.03/1.80 thf(subset_union,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ ((mimplies @ (mbox @ ((subset @ X1) @ X2))) @ (mbox @ ((qmltpeq @ ((union @ X1) @ X2)) @ X2)))))))))))). % 1.03/1.80 thf(24,plain,sP23,inference(preprocess,[status(thm)],[subset_union]). % 1.03/1.80 thf(mrel_reflexive,axiom,sP1). % 1.03/1.80 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,mrel_reflexive,h2])). % 1.03/1.80 thf(26,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[25,h1])). % 1.03/1.80 thf(27,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[26,h0])). % 1.03/1.80 thf(0,theorem,sP17,inference(contra,[status(thm),contra(discharge,[h2])],[25,h2])). % 1.03/1.80 % SZS output end Proof %------------------------------------------------------------------------------