%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO543^1 : 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 : n013.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 0.11s 0.38s % Output : Proof 0.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.11 % Problem : SYO543^1 : TPTP v9.2.0. Released v5.2.0. % 0.05/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.11/0.32 % Computer : n013.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 9 00:49:08 EDT 2025 % 0.11/0.32 % CPUTime : % 0.11/0.38 % SZS status Theorem % 0.11/0.38 % Mode: cade22grackle2xfee4 % 0.11/0.38 % Steps: 16 % 0.11/0.38 % SZS output start Proof % 0.11/0.38 thf(ty_eigen__2, type, eigen__2 : $i). % 0.11/0.38 thf(ty_eigen__0, type, eigen__0 : $o). % 0.11/0.38 thf(ty_epsii, type, epsii : ((($i>$i)>$o)>$i>$i)). % 0.11/0.38 thf(ty_eigen__1, type, eigen__1 : ($i>$i)). % 0.11/0.38 thf(sP1,plain,sP1 <=> (![X1:$i>$i]:(~(((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__1)))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.11/0.38 thf(sP2,plain,sP2 <=> ((epsii @ (^[X1:$i>$i]:((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__1))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP2])])). % 0.11/0.38 thf(sP3,plain,sP3 <=> ((~(eigen__0)) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.11/0.38 thf(sP4,plain,sP4 <=> $false,introduced(definition,[new_symbols(definition,[sP4])])). % 0.11/0.38 thf(sP5,plain,sP5 <=> ((eigen__0 => (~(sP2))) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.11/0.38 thf(sP6,plain,sP6 <=> (((epsii @ (^[X1:$i>$i]:((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__1))))))))) @ eigen__2) = (eigen__1 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.11/0.38 thf(sP7,plain,sP7 <=> (![X1:$i]:(((epsii @ (^[X2:$i>$i]:((eigen__0 => (~((X2 = eigen__1)))) => (~(((~(eigen__0)) => (~((X2 = eigen__1))))))))) @ X1) = (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.11/0.38 thf(sP8,plain,sP8 <=> (eigen__0 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.11/0.38 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i>$i]:(^[X3:$i>$i]:(epsii @ (^[X4:$i>$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))). % 0.11/0.38 thf(conj,conjecture,(![X1:$o]:(![X2:$i>$i]:((epsii @ (^[X3:$i>$i]:((X1 => (~((X3 = X2)))) => (~(((~(X1)) => (~((X3 = X2))))))))) = X2)))). % 0.11/0.38 thf(h0,negated_conjecture,(~((![X1:$o]:(![X2:$i>$i]:((epsii @ (^[X3:$i>$i]:((X1 => (~((X3 = X2)))) => (~(((~(X1)) => (~((X3 = X2))))))))) = X2))))),inference(assume_negation,[status(cth)],[conj])). % 0.11/0.38 thf(h1,assumption,(~((![X1:$i>$i]:((epsii @ (^[X2:$i>$i]:((eigen__0 => (~((X2 = X1)))) => (~(((~(eigen__0)) => (~((X2 = X1))))))))) = X1)))),introduced(assumption,[])). % 0.11/0.38 thf(h2,assumption,(~(sP2)),introduced(assumption,[])). % 0.11/0.38 thf(h3,assumption,(~(sP7)),introduced(assumption,[])). % 0.11/0.38 thf(h4,assumption,(~(sP6)),introduced(assumption,[])). % 0.11/0.38 thf(1,plain,~(sP4),inference(prop_rule,[status(thm)],[])). % 0.11/0.38 thf(2,plain,(~(sP1) | sP4),inference(all_rule,[status(thm)],[])). % 0.11/0.38 thf(3,plain,(~(sP7) | sP6),inference(all_rule,[status(thm)],[])). % 0.11/0.38 thf(4,plain,(~(sP2) | sP7),inference(prop_rule,[status(thm)],[])). % 0.11/0.38 thf(5,plain,(sP3 | sP2),inference(prop_rule,[status(thm)],[])). % 0.11/0.38 thf(6,plain,(sP8 | sP2),inference(prop_rule,[status(thm)],[])). % 0.11/0.38 thf(7,plain,((~(sP5) | ~(sP8)) | ~(sP3)),inference(prop_rule,[status(thm)],[])). % 0.11/0.38 thf(choiceaxii,axiom,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1))))). % 0.11/0.38 thf(8,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[8]). % 0.11/0.38 thf(9,plain,(sP5 | sP1),inference(choice_rule,[status(thm)],[8])). % 0.11/0.38 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,9,h4])). % 0.11/0.38 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,10,h4])). % 0.11/0.38 thf(12,plain,$false,inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,11,h3])). % 0.11/0.38 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])). % 0.11/0.38 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])). % 0.11/0.38 thf(0,theorem,(![X1:$o]:(![X2:$i>$i]:((epsii @ (^[X3:$i>$i]:((X1 => (~((X3 = X2)))) => (~(((~(X1)) => (~((X3 = X2))))))))) = X2))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])). % 0.11/0.38 % SZS output end Proof %------------------------------------------------------------------------------