%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO530^1 : 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 : n016.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 0.13s 0.42s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO530^1 : TPTP v9.2.0. Released v5.2.0. % 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n016.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 00:35:08 EDT 2025 % 0.13/0.34 % CPUTime : % 0.13/0.42 % SZS status Theorem % 0.13/0.42 % Mode: cade22grackle2xfee4 % 0.13/0.42 % Steps: 24 % 0.13/0.42 % SZS output start Proof % 0.13/0.42 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.42 thf(ty_eigen__2, type, eigen__2 : $i). % 0.13/0.42 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.13/0.42 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)). % 0.13/0.42 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.42 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(~(((eigen__0 @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.42 thf(sP3,plain,sP3 <=> (![X1:$i]:(~(((eigen__0 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((eigen__0 @ X2) @ X3))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.42 thf(sP4,plain,sP4 <=> (![X1:$i]:(~(((eigen__0 @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.42 thf(sP5,plain,sP5 <=> ((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))))) @ (eps @ (eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.42 thf(def_epsa,definition,(epsa = (^[X1:$i>$i>$o]:(eps @ (^[X2:$i]:(?[X3:$i]:((X1 @ X2) @ X3))))))). % 0.13/0.42 thf(def_epsb,definition,(epsb = (^[X1:$i>$i>$o]:(eps @ (^[X2:$i]:((X1 @ (epsa @ X1)) @ X2)))))). % 0.13/0.42 thf(conj,conjecture,(![X1:$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))))))). % 0.13/0.42 thf(h0,negated_conjecture,(~((![X1:$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.13/0.42 thf(h1,assumption,(~(((~(sP2)) => sP5))),introduced(assumption,[])). % 0.13/0.42 thf(h2,assumption,(~(sP2)),introduced(assumption,[])). % 0.13/0.42 thf(h3,assumption,(~(sP5)),introduced(assumption,[])). % 0.13/0.42 thf(h4,assumption,(~(sP4)),introduced(assumption,[])). % 0.13/0.42 thf(h5,assumption,sP1,introduced(assumption,[])). % 0.13/0.42 thf(1,plain,(~(sP4) | ~(sP1)),inference(all_rule,[status(thm)],[])). % 0.13/0.42 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.13/0.42 thf(2,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[2]). % 0.13/0.42 thf(3,plain,(~(sP3) | sP2),inference(choice_rule,[status(thm)],[2])). % 0.13/0.42 thf(4,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])). % 0.13/0.42 thf(5,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[5]). % 0.13/0.42 thf(6,plain,(sP5 | sP3),inference(choice_rule,[status(thm)],[5])). % 0.13/0.42 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[1,3,4,6,h5,h3])). % 0.13/0.42 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,7,h5])). % 0.13/0.42 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,8,h4])). % 0.13/0.42 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3])). % 0.13/0.42 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])). % 0.13/0.42 thf(0,theorem,(![X1:$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])). % 0.13/0.42 % SZS output end Proof %------------------------------------------------------------------------------