%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO560^1 : TPTP v9.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : lash -P picomus -M modes -p tstp -t %d %s % Computer : n026.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 03:23:52 PM UTC 2025 % Result : Theorem 0.50s 0.68s % Output : Proof 0.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO560^1 : TPTP v9.2.0. Released v5.2.0. % 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 9 00:47:08 EDT 2025 % 0.13/0.34 % CPUTime : % 0.50/0.68 % SZS status Theorem % 0.50/0.68 % Mode: cade22grackle2xfee4 % 0.50/0.68 % Steps: 7728 % 0.50/0.68 % SZS output start Proof % 0.50/0.68 thf(ty_epsoo, type, epsoo : ((($o>$o)>$o)>$o>$o)). % 0.50/0.68 thf(ty_eigen__2, type, eigen__2 : $o). % 0.50/0.68 thf(ty_epso, type, epso : (($o>$o)>$o)). % 0.50/0.68 thf(ty_eigen__0, type, eigen__0 : $o). % 0.50/0.68 thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.50/0.68 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$o]:(~((X1 = ((epsoo @ epso) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 0.50/0.68 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$o]:(~(((~($false)) = ((epsoo @ epso) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 0.50/0.68 thf(sP1,plain,sP1 <=> (q @ (^[X1:$o]:$false)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.50/0.68 thf(sP2,plain,sP2 <=> ((epsoo @ epso) @ $false),introduced(definition,[new_symbols(definition,[sP2])])). % 0.50/0.68 thf(sP3,plain,sP3 <=> ((^[X1:$o]:(~($false))) = (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.50/0.68 thf(sP4,plain,sP4 <=> (![X1:$o]:((~($false)) = ((epsoo @ epso) @ X1))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.50/0.68 thf(sP5,plain,sP5 <=> ((^[X1:$o]:X1) = (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.50/0.68 thf(sP6,plain,sP6 <=> ((epsoo @ epso) @ eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 0.50/0.68 thf(sP7,plain,sP7 <=> ((^[X1:$o]:$false) = (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP7])])). % 0.50/0.68 thf(sP8,plain,sP8 <=> eigen__0,introduced(definition,[new_symbols(definition,[sP8])])). % 0.50/0.68 thf(sP9,plain,sP9 <=> ((epso @ (epsoo @ epso)) = eigen__2),introduced(definition,[new_symbols(definition,[sP9])])). % 0.50/0.68 thf(sP10,plain,sP10 <=> (![X1:$o]:(~(X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.50/0.68 thf(sP11,plain,sP11 <=> (![X1:$o>$o]:(~((epso @ X1)))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.50/0.68 thf(sP12,plain,sP12 <=> (![X1:$o]:(~(((epsoo @ epso) @ X1)))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.50/0.68 thf(sP13,plain,sP13 <=> (sP8 = ((epsoo @ epso) @ sP8)),introduced(definition,[new_symbols(definition,[sP13])])). % 0.50/0.68 thf(sP14,plain,sP14 <=> eigen__2,introduced(definition,[new_symbols(definition,[sP14])])). % 0.50/0.68 thf(sP15,plain,sP15 <=> $false,introduced(definition,[new_symbols(definition,[sP15])])). % 0.50/0.68 thf(sP16,plain,sP16 <=> ((~(sP15)) = sP6),introduced(definition,[new_symbols(definition,[sP16])])). % 0.50/0.68 thf(sP17,plain,sP17 <=> ((epso @ (epsoo @ epso)) = sP8),introduced(definition,[new_symbols(definition,[sP17])])). % 0.50/0.68 thf(sP18,plain,sP18 <=> (q @ (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP18])])). % 0.50/0.68 thf(sP19,plain,sP19 <=> (q @ (^[X1:$o]:(~(sP15)))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.50/0.68 thf(sP20,plain,sP20 <=> (![X1:$o]:(X1 = ((epsoo @ epso) @ X1))),introduced(definition,[new_symbols(definition,[sP20])])). % 0.50/0.68 thf(sP21,plain,sP21 <=> ((epsoo @ epso) @ (epso @ (epsoo @ epso))),introduced(definition,[new_symbols(definition,[sP21])])). % 0.50/0.68 thf(sP22,plain,sP22 <=> (epso @ (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP22])])). % 0.50/0.68 thf(sP23,plain,sP23 <=> (q @ (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP23])])). % 0.50/0.68 thf(sP24,plain,sP24 <=> (epso @ (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP24])])). % 0.50/0.68 thf(sP25,plain,sP25 <=> ((epsoo @ epso) @ sP8),introduced(definition,[new_symbols(definition,[sP25])])). % 0.50/0.68 thf(c,conjecture,sP23). % 0.50/0.68 thf(h1,negated_conjecture,(~(sP23)),inference(assume_negation,[status(cth)],[c])). % 0.50/0.68 thf(1,plain,(((~(sP2) | sP6) | sP14) | sP15),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(2,plain,(~(sP10) | sP15),inference(all_rule,[status(thm)],[])). % 0.50/0.68 thf(choiceaxo,axiom,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1))))). % 0.50/0.68 thf(3,plain,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1)))),inference(preprocess,[status(thm)],[3]). % 0.50/0.68 thf(4,plain,(sP24 | sP10),inference(choice_rule,[status(thm)],[3])). % 0.50/0.68 thf(5,plain,(~(sP11) | ~(sP24)),inference(all_rule,[status(thm)],[])). % 0.50/0.68 thf(6,plain,((sP9 | ~(sP22)) | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(7,plain,(((~(sP21) | sP6) | ~(sP9)) | sP15),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(8,plain,(((~(sP25) | sP2) | sP8) | sP15),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(9,plain,((sP17 | ~(sP22)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(10,plain,(((~(sP21) | sP25) | ~(sP17)) | sP15),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(11,plain,~(sP15),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(12,plain,((sP16 | sP15) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(13,plain,((sP13 | ~(sP8)) | ~(sP25)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(14,plain,((sP13 | sP8) | sP25),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(15,plain,(sP4 | ~(sP16)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 0.50/0.68 thf(16,plain,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1)))),inference(preprocess,[status(thm)],[16]). % 0.50/0.68 thf(17,plain,(sP21 | sP12),inference(choice_rule,[status(thm)],[16])). % 0.50/0.68 thf(choiceaxoo,axiom,(![X1:($o>$o)>$o]:((~((![X2:$o>$o]:(~((X1 @ X2)))))) => (X1 @ (epsoo @ X1))))). % 0.50/0.68 thf(18,plain,(![X1:($o>$o)>$o]:((~((![X2:$o>$o]:(~((X1 @ X2)))))) => (X1 @ (epsoo @ X1)))),inference(preprocess,[status(thm)],[18]). % 0.50/0.68 thf(19,plain,(sP22 | sP11),inference(choice_rule,[status(thm)],[18])). % 0.50/0.68 thf(20,plain,(sP20 | ~(sP13)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 0.50/0.68 thf(21,plain,(sP3 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(22,plain,(sP7 | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(23,plain,(sP5 | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 0.50/0.68 thf(24,plain,((~(sP19) | sP23) | ~(sP3)),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(25,plain,((~(sP1) | sP23) | ~(sP7)),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(26,plain,((~(sP18) | sP23) | ~(sP5)),inference(mating_rule,[status(thm)],[])). % 0.50/0.68 thf(qid,axiom,sP18). % 0.50/0.68 thf(qkf,axiom,sP1). % 0.50/0.68 thf(qkt,axiom,sP19). % 0.50/0.68 thf(27,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,4,5,6,7,8,9,10,11,12,13,14,15,17,19,20,21,22,23,24,25,26,h1,qid,qkf,qkt])). % 0.50/0.68 thf(28,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[27,h0])). % 0.50/0.68 thf(0,theorem,sP23,inference(contra,[status(thm),contra(discharge,[h1])],[27,h1])). % 0.50/0.68 % SZS output end Proof %------------------------------------------------------------------------------