%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO541^1 : 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 : n014.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 03:23:50 PM UTC 2025 % Result : Theorem 0.12s 0.40s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO541^1 : TPTP v9.2.0. Released v5.2.0. % 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n014.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 9 00:49:23 EDT 2025 % 0.12/0.33 % CPUTime : % 0.12/0.40 % SZS status Theorem % 0.12/0.40 % Mode: cade22grackle2xfee4 % 0.12/0.40 % Steps: 19 % 0.12/0.40 % SZS output start Proof % 0.12/0.40 thf(ty_eigen__0, type, eigen__0 : ($i>$i)). % 0.12/0.40 thf(ty_epsii, type, epsii : ((($i>$i)>$o)>$i>$i)). % 0.12/0.40 thf(ty_eigen__1, type, eigen__1 : ($i>$i)). % 0.12/0.40 thf(sP1,plain,sP1 <=> ((epsii @ (^[X1:$i>$i]:(X1 = eigen__0))) = eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.12/0.40 thf(sP2,plain,sP2 <=> (![X1:$i>$i]:(~((X1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.12/0.40 thf(sP3,plain,sP3 <=> $false,introduced(definition,[new_symbols(definition,[sP3])])). % 0.12/0.40 thf(sP4,plain,sP4 <=> ((epsii @ (^[X1:$i>$i]:(X1 = eigen__1))) = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])). % 0.12/0.40 thf(sP5,plain,sP5 <=> (sP1 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.12/0.40 thf(sP6,plain,sP6 <=> (![X1:$i>$i]:(~((X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.12/0.40 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i>$i]:(^[X3:$i>$i]:(epsii @ (^[X4:$i>$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))). % 0.12/0.40 thf(conj,conjecture,(![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2))))))))). % 0.12/0.40 thf(h0,negated_conjecture,(~((![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2)))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.12/0.40 thf(h1,assumption,(~((![X1:$i>$i]:(~((sP1 => (~(((epsii @ (^[X2:$i>$i]:(X2 = X1))) = X1))))))))),introduced(assumption,[])). % 0.12/0.40 thf(h2,assumption,sP5,introduced(assumption,[])). % 0.12/0.40 thf(1,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). % 0.12/0.40 thf(2,plain,~(sP3),inference(prop_rule,[status(thm)],[])). % 0.12/0.40 thf(3,plain,(~(sP6) | sP3),inference(all_rule,[status(thm)],[])). % 0.12/0.40 thf(choiceaxii,axiom,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1))))). % 0.12/0.40 thf(4,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[4]). % 0.12/0.40 thf(5,plain,(sP4 | sP2),inference(choice_rule,[status(thm)],[4])). % 0.12/0.40 thf(6,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[6]). % 0.12/0.40 thf(7,plain,(sP1 | sP6),inference(choice_rule,[status(thm)],[6])). % 0.12/0.40 thf(8,plain,((~(sP5) | ~(sP1)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.12/0.40 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,5,7,8,h2])). % 0.12/0.40 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,9,h2])). % 0.12/0.40 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])). % 0.12/0.40 thf(0,theorem,(![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])). % 0.12/0.40 % SZS output end Proof %------------------------------------------------------------------------------