%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO539^1 : 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 : n027.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 03:23:49 PM UTC 2025 % Result : Theorem 0.21s 0.41s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO539^1 : TPTP v9.2.0. Released v5.2.0. % 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n027.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 01:02:08 EDT 2025 % 0.13/0.34 % CPUTime : % 0.21/0.41 % SZS status Theorem % 0.21/0.41 % Mode: cade22grackle2xfee4 % 0.21/0.41 % Steps: 19 % 0.21/0.41 % SZS output start Proof % 0.21/0.41 thf(ty_eigen__2, type, eigen__2 : $i). % 0.21/0.41 thf(ty_eigen__0, type, eigen__0 : $o). % 0.21/0.41 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.21/0.41 thf(ty_eigen__1, type, eigen__1 : $i). % 0.21/0.41 thf(sP1,plain,sP1 <=> ((eps @ (^[X1:$i]:((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__2))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.21/0.41 thf(sP2,plain,sP2 <=> eigen__0,introduced(definition,[new_symbols(definition,[sP2])])). % 0.21/0.41 thf(sP3,plain,sP3 <=> (sP2 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.21/0.41 thf(sP4,plain,sP4 <=> ((~(sP2)) => (~(((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.21/0.41 thf(sP5,plain,sP5 <=> ((sP2 => (~((eigen__2 = eigen__1)))) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.21/0.41 thf(sP6,plain,sP6 <=> (![X1:$i]:(~(((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.21/0.42 thf(sP7,plain,sP7 <=> ((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP7])])). % 0.21/0.42 thf(sP8,plain,sP8 <=> ((~(sP2)) => (~(((~(sP2)) => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.21/0.42 thf(sP9,plain,sP9 <=> (sP3 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.21/0.42 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(eps @ (^[X4:$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))). % 0.21/0.42 thf(conj,conjecture,(![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3)))))). % 0.21/0.42 thf(h0,negated_conjecture,(~((![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))))),inference(assume_negation,[status(cth)],[conj])). % 0.21/0.42 thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:((~(((eps @ (^[X3:$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X1))) => ((eps @ (^[X3:$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X2)))))),introduced(assumption,[])). % 0.21/0.42 thf(h2,assumption,(~((![X1:$i]:((~(((eps @ (^[X2:$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = eigen__1))) => ((eps @ (^[X2:$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = X1))))),introduced(assumption,[])). % 0.21/0.42 thf(h3,assumption,(~(((~(sP1)) => sP7))),introduced(assumption,[])). % 0.21/0.42 thf(h4,assumption,(~(sP1)),introduced(assumption,[])). % 0.21/0.42 thf(h5,assumption,(~(sP7)),introduced(assumption,[])). % 0.21/0.42 thf(1,plain,(sP5 | sP2),inference(prop_rule,[status(thm)],[])). % 0.21/0.42 thf(2,plain,(~(sP6) | ~(sP5)),inference(all_rule,[status(thm)],[])). % 0.21/0.42 thf(3,plain,(sP8 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.21/0.42 thf(4,plain,(~(sP6) | ~(sP8)),inference(all_rule,[status(thm)],[])). % 0.21/0.42 thf(5,plain,(sP4 | sP7),inference(prop_rule,[status(thm)],[])). % 0.21/0.42 thf(6,plain,(sP3 | sP1),inference(prop_rule,[status(thm)],[])). % 0.21/0.42 thf(7,plain,((~(sP9) | ~(sP3)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 0.21/0.42 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.21/0.42 thf(8,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[8]). % 0.21/0.42 thf(9,plain,(sP9 | sP6),inference(choice_rule,[status(thm)],[8])). % 0.21/0.42 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,9,h4,h5])). % 0.21/0.42 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])). % 0.21/0.42 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])). % 0.21/0.42 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])). % 0.21/0.42 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])). % 0.21/0.42 thf(0,theorem,(![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])). % 0.21/0.42 % SZS output end Proof %------------------------------------------------------------------------------