%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO542^1 : 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 : n010.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 0.19s 0.41s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYO542^1 : TPTP v9.2.0. Released v5.2.0. % 0.10/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n010.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 01:07:08 EDT 2025 % 0.12/0.33 % CPUTime : % 0.19/0.41 % SZS status Theorem % 0.19/0.41 % Mode: cade22grackle2xfee4 % 0.19/0.41 % Steps: 30 % 0.19/0.41 % SZS output start Proof % 0.19/0.41 thf(ty_eigen__4, type, eigen__4 : $i). % 0.19/0.41 thf(ty_eigen__2, type, eigen__2 : ($i>$i)). % 0.19/0.41 thf(ty_eigen__3, type, eigen__3 : $i). % 0.19/0.41 thf(ty_eigen__0, type, eigen__0 : $o). % 0.19/0.41 thf(ty_epsii, type, epsii : ((($i>$i)>$o)>$i>$i)). % 0.19/0.41 thf(ty_eigen__1, type, eigen__1 : ($i>$i)). % 0.19/0.41 thf(sP1,plain,sP1 <=> (((epsii @ (^[X1:$i>$i]:((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__2))))))))) @ eigen__3) = (eigen__1 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.19/0.41 thf(sP2,plain,sP2 <=> eigen__0,introduced(definition,[new_symbols(definition,[sP2])])). % 0.19/0.41 thf(sP3,plain,sP3 <=> (![X1:$i]:(((epsii @ (^[X2:$i>$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = eigen__2))))))))) @ X1) = (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.19/0.41 thf(sP4,plain,sP4 <=> (sP2 => (~(((epsii @ (^[X1:$i>$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.19/0.41 thf(sP5,plain,sP5 <=> ((~(sP2)) => (~(((epsii @ (^[X1:$i>$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.19/0.41 thf(sP6,plain,sP6 <=> ((sP2 => (~((eigen__2 = eigen__1)))) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.19/0.41 thf(sP7,plain,sP7 <=> ((epsii @ (^[X1:$i>$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP7])])). % 0.19/0.41 thf(sP8,plain,sP8 <=> (![X1:$i]:(((epsii @ (^[X2:$i>$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = eigen__2))))))))) @ X1) = (eigen__2 @ X1))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.19/0.41 thf(sP9,plain,sP9 <=> (![X1:$i>$i]:(~(((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.19/0.41 thf(sP10,plain,sP10 <=> (((epsii @ (^[X1:$i>$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) @ eigen__4) = (eigen__2 @ eigen__4)),introduced(definition,[new_symbols(definition,[sP10])])). % 0.19/0.41 thf(sP11,plain,sP11 <=> ((epsii @ (^[X1:$i>$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP11])])). % 0.19/0.41 thf(sP12,plain,sP12 <=> ((~(sP2)) => (~(((~(sP2)) => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.19/0.41 thf(sP13,plain,sP13 <=> (sP4 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.19/0.41 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i>$i]:(^[X3:$i>$i]:(epsii @ (^[X4:$i>$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))). % 0.19/0.41 thf(conj,conjecture,(![X1:$o]:(![X2:$i>$i]:(![X3:$i>$i]:((~(((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3)))))). % 0.19/0.41 thf(h0,negated_conjecture,(~((![X1:$o]:(![X2:$i>$i]:(![X3:$i>$i]:((~(((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))))),inference(assume_negation,[status(cth)],[conj])). % 0.19/0.41 thf(h1,assumption,(~((![X1:$i>$i]:(![X2:$i>$i]:((~(((epsii @ (^[X3:$i>$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X1))) => ((epsii @ (^[X3:$i>$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X2)))))),introduced(assumption,[])). % 0.19/0.41 thf(h2,assumption,(~((![X1:$i>$i]:((~(((epsii @ (^[X2:$i>$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = eigen__1))) => ((epsii @ (^[X2:$i>$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = X1))))),introduced(assumption,[])). % 0.19/0.41 thf(h3,assumption,(~(((~(sP11)) => sP7))),introduced(assumption,[])). % 0.19/0.41 thf(h4,assumption,(~(sP11)),introduced(assumption,[])). % 0.19/0.41 thf(h5,assumption,(~(sP7)),introduced(assumption,[])). % 0.19/0.41 thf(h6,assumption,(~(sP3)),introduced(assumption,[])). % 0.19/0.41 thf(h7,assumption,(~(sP1)),introduced(assumption,[])). % 0.19/0.41 thf(h8,assumption,(~(sP8)),introduced(assumption,[])). % 0.19/0.41 thf(h9,assumption,(~(sP10)),introduced(assumption,[])). % 0.19/0.41 thf(1,plain,(sP6 | sP2),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(2,plain,(~(sP9) | ~(sP6)),inference(all_rule,[status(thm)],[])). % 0.19/0.41 thf(3,plain,(sP12 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(4,plain,(~(sP9) | ~(sP12)),inference(all_rule,[status(thm)],[])). % 0.19/0.41 thf(5,plain,(~(sP3) | sP1),inference(all_rule,[status(thm)],[])). % 0.19/0.41 thf(6,plain,(~(sP8) | sP10),inference(all_rule,[status(thm)],[])). % 0.19/0.41 thf(7,plain,(~(sP7) | sP8),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(8,plain,(~(sP11) | sP3),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(9,plain,(sP5 | sP7),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(10,plain,(sP4 | sP11),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(11,plain,((~(sP13) | ~(sP4)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.19/0.41 thf(choiceaxii,axiom,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1))))). % 0.19/0.41 thf(12,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[12]). % 0.19/0.41 thf(13,plain,(sP13 | sP9),inference(choice_rule,[status(thm)],[12])). % 0.19/0.41 thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,13,h7,h9])). % 0.19/0.41 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h7,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__4)],[h8,14,h9])). % 0.19/0.41 thf(16,plain,$false,inference(tab_fe,[status(thm),assumptions([h7,h6,h4,h5,h3,h2,h1,h0]),tab_fe(discharge,[h8])],[h5,15,h8])). % 0.19/0.41 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__3)],[h6,16,h7])). % 0.19/0.41 thf(18,plain,$false,inference(tab_fe,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_fe(discharge,[h6])],[h4,17,h6])). % 0.19/0.41 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,18,h4,h5])). % 0.19/0.41 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,19,h3])). % 0.19/0.41 thf(21,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,20,h2])). % 0.19/0.41 thf(22,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1])). % 0.19/0.41 thf(0,theorem,(![X1:$o]:(![X2:$i>$i]:(![X3:$i>$i]:((~(((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((epsii @ (^[X4:$i>$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))),inference(contra,[status(thm),contra(discharge,[h0])],[22,h0])). % 0.19/0.41 % SZS output end Proof %------------------------------------------------------------------------------