%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO534^1 : 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 : n019.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 0.20s 0.41s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO534^1 : TPTP v9.2.0. Released v5.2.0. % 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 9 01:21:53 EDT 2025 % 0.12/0.34 % CPUTime : % 0.20/0.41 % SZS status Theorem % 0.20/0.41 % Mode: cade22grackle2xfee4 % 0.20/0.41 % Steps: 78 % 0.20/0.41 % SZS output start Proof % 0.20/0.41 thf(ty_eigen__2, type, eigen__2 : $i). % 0.20/0.41 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$i>$o)). % 0.20/0.41 thf(ty_eigen__1, type, eigen__1 : $i). % 0.20/0.41 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.20/0.41 thf(ty_eigen__3, type, eigen__3 : $i). % 0.20/0.41 thf(sP1,plain,sP1 <=> (((eigen__0 @ eigen__1) @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.41 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.20/0.41 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.20/0.41 thf(sP4,plain,sP4 <=> (((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))) @ (eps @ ((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.41 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((((eigen__0 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((eigen__0 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((eigen__0 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((eigen__0 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.20/0.41 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ eigen__1) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.41 thf(sP7,plain,sP7 <=> (![X1:$i]:(~((((eigen__0 @ eigen__1) @ eigen__2) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.41 thf(def_epsa,definition,(epsa = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(?[X3:$i]:(?[X4:$i]:(((X1 @ X2) @ X3) @ X4)))))))). % 0.20/0.41 thf(def_epsb,definition,(epsb = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(?[X3:$i]:(((X1 @ (epsa @ X1)) @ X2) @ X3))))))). % 0.20/0.41 thf(def_epsc,definition,(epsc = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(((X1 @ (epsa @ X1)) @ (epsb @ X1)) @ X2)))))). % 0.20/0.41 thf(conj,conjecture,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3)))))))))))))). % 0.20/0.41 thf(h0,negated_conjecture,(~((![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.20/0.41 thf(h1,assumption,(~(((~(sP3)) => sP4))),introduced(assumption,[])). % 0.20/0.41 thf(h2,assumption,(~(sP3)),introduced(assumption,[])). % 0.20/0.41 thf(h3,assumption,(~(sP4)),introduced(assumption,[])). % 0.20/0.41 thf(h4,assumption,(~(sP6)),introduced(assumption,[])). % 0.20/0.41 thf(h5,assumption,(~(sP7)),introduced(assumption,[])). % 0.20/0.41 thf(h6,assumption,sP1,introduced(assumption,[])). % 0.20/0.41 thf(1,plain,(~(sP7) | ~(sP1)),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.20/0.41 thf(2,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[2]). % 0.20/0.41 thf(3,plain,(~(sP2) | sP3),inference(choice_rule,[status(thm)],[2])). % 0.20/0.41 thf(4,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(5,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(6,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[6]). % 0.20/0.41 thf(7,plain,(sP4 | sP5),inference(choice_rule,[status(thm)],[6])). % 0.20/0.41 thf(8,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[8]). % 0.20/0.41 thf(9,plain,(~(sP5) | sP2),inference(choice_rule,[status(thm)],[8])). % 0.20/0.41 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0])],[1,3,4,5,7,9,h6,h3])). % 0.20/0.41 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,10,h6])). % 0.20/0.41 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,11,h5])). % 0.20/0.41 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,12,h4])). % 0.20/0.41 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3])). % 0.20/0.41 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1])). % 0.20/0.41 thf(0,theorem,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])). % 0.20/0.41 % SZS output end Proof %------------------------------------------------------------------------------