%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO559^1 : 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 : n031.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 0.13s 0.40s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.01/0.12 % Problem : SYO559^1 : TPTP v9.2.0. Released v5.2.0. % 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n031.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 01:37:08 EDT 2025 % 0.13/0.35 % CPUTime : % 0.13/0.40 % SZS status Theorem % 0.13/0.40 % Mode: cade22grackle2xfee4 % 0.13/0.40 % Steps: 64 % 0.13/0.40 % SZS output start Proof % 0.13/0.40 thf(ty_epsoo, type, epsoo : ((($o>$o)>$o)>$o>$o)). % 0.13/0.40 thf(ty_epso, type, epso : (($o>$o)>$o)). % 0.13/0.40 thf(sP1,plain,sP1 <=> ((epsoo @ epso) @ $false),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.40 thf(sP2,plain,sP2 <=> $false,introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.40 thf(sP3,plain,sP3 <=> (![X1:$o]:(~(((epsoo @ epso) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.40 thf(sP4,plain,sP4 <=> ((epsoo @ epso) @ (epso @ (epsoo @ epso))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.40 thf(sP5,plain,sP5 <=> (![X1:$o]:(~(X1))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.40 thf(sP6,plain,sP6 <=> (![X1:$o>$o]:(~((epso @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.40 thf(sP7,plain,sP7 <=> (epso @ (^[X1:$o]:X1)),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.40 thf(sP8,plain,sP8 <=> ((epsoo @ epso) @ (~(sP2))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.13/0.40 thf(sP9,plain,sP9 <=> ((epso @ (epsoo @ epso)) = (~(sP2))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.13/0.40 thf(sP10,plain,sP10 <=> (epso @ (epsoo @ epso)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.13/0.40 thf(c,conjecture,(sP1 => sP8)). % 0.13/0.40 thf(h0,negated_conjecture,(~((sP1 => sP8))),inference(assume_negation,[status(cth)],[c])). % 0.13/0.40 thf(h1,assumption,sP1,introduced(assumption,[])). % 0.13/0.40 thf(h2,assumption,(~(sP8)),introduced(assumption,[])). % 0.13/0.40 thf(1,plain,(~(sP5) | sP2),inference(all_rule,[status(thm)],[])). % 0.13/0.40 thf(choiceaxo,axiom,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1))))). % 0.13/0.40 thf(2,plain,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1)))),inference(preprocess,[status(thm)],[2]). % 0.13/0.40 thf(3,plain,(sP7 | sP5),inference(choice_rule,[status(thm)],[2])). % 0.13/0.40 thf(4,plain,(~(sP6) | ~(sP7)),inference(all_rule,[status(thm)],[])). % 0.13/0.40 thf(5,plain,((sP9 | ~(sP10)) | sP2),inference(prop_rule,[status(thm)],[])). % 0.13/0.40 thf(6,plain,(((~(sP4) | sP8) | ~(sP9)) | sP2),inference(mating_rule,[status(thm)],[])). % 0.13/0.40 thf(7,plain,~(sP2),inference(prop_rule,[status(thm)],[])). % 0.13/0.40 thf(8,plain,(~(sP3) | ~(sP1)),inference(all_rule,[status(thm)],[])). % 0.13/0.40 thf(9,plain,(![X1:$o>$o]:((~((![X2:$o]:(~((X1 @ X2)))))) => (X1 @ (epso @ X1)))),inference(preprocess,[status(thm)],[9]). % 0.13/0.40 thf(10,plain,(sP4 | sP3),inference(choice_rule,[status(thm)],[9])). % 0.13/0.40 thf(choiceaxoo,axiom,(![X1:($o>$o)>$o]:((~((![X2:$o>$o]:(~((X1 @ X2)))))) => (X1 @ (epsoo @ X1))))). % 0.13/0.40 thf(11,plain,(![X1:($o>$o)>$o]:((~((![X2:$o>$o]:(~((X1 @ X2)))))) => (X1 @ (epsoo @ X1)))),inference(preprocess,[status(thm)],[11]). % 0.13/0.40 thf(12,plain,(sP10 | sP6),inference(choice_rule,[status(thm)],[11])). % 0.13/0.40 thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,3,4,5,6,7,8,10,12,h1,h2])). % 0.13/0.40 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2])). % 0.13/0.40 thf(0,theorem,(sP1 => sP8),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])). % 0.13/0.40 % SZS output end Proof %------------------------------------------------------------------------------