%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SEV428^1 : 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 : n001.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 02:55:53 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 : SEV428^1 : TPTP v9.2.0. Released v5.2.0. % 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.14/0.34 % Computer : n001.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Oct 8 19:34:53 EDT 2025 % 0.14/0.34 % CPUTime : % 0.20/0.41 % SZS status Theorem % 0.20/0.41 % Mode: cade22grackle2xfee4 % 0.20/0.41 % Steps: 85 % 0.20/0.41 % SZS output start Proof % 0.20/0.41 thf(ty_epsio, type, epsio : ((($i>$o)>$o)>$i>$o)). % 0.20/0.41 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 0.20/0.41 thf(ty_c, type, c : (($i>$o)>$o)). % 0.20/0.41 thf(ty_a, type, a : $i). % 0.20/0.41 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.20/0.41 thf(sP1,plain,sP1 <=> (c @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.20/0.41 thf(sP2,plain,sP2 <=> (![X1:$i]:(~(((epsio @ (^[X2:$i>$o]:(~(((c @ X2) => (~((X2 @ (eps @ X2))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.20/0.41 thf(sP3,plain,sP3 <=> ((epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))) @ (eps @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.20/0.41 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:((c @ X1) => (~((X1 @ (eps @ X1)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.20/0.41 thf(sP5,plain,sP5 <=> (eigen__0 @ (eps @ eigen__0)),introduced(definition,[new_symbols(definition,[sP5])])). % 0.20/0.41 thf(sP6,plain,sP6 <=> (![X1:$i]:(~((eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.20/0.41 thf(sP7,plain,sP7 <=> ((c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))) => sP2),introduced(definition,[new_symbols(definition,[sP7])])). % 0.20/0.41 thf(sP8,plain,sP8 <=> (eigen__0 @ a),introduced(definition,[new_symbols(definition,[sP8])])). % 0.20/0.41 thf(sP9,plain,sP9 <=> ((c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.20/0.41 thf(sP10,plain,sP10 <=> (sP1 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.20/0.41 thf(sP11,plain,sP11 <=> (c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.20/0.41 thf(def_setunion,definition,(setunion = (^[X1:($i>$o)>$o]:(^[X2:$i]:(?[X3:$i>$o]:((X1 @ X3) & (X3 @ X2))))))). % 0.20/0.41 thf(def_choosenonempty,definition,(choosenonempty = (^[X1:($i>$o)>$o]:(epsio @ (^[X2:$i>$o]:((X1 @ X2) & (X2 @ (eps @ X2)))))))). % 0.20/0.41 thf(conj,conjecture,(~(sP7))). % 0.20/0.41 thf(h0,negated_conjecture,sP7,inference(assume_negation,[status(cth)],[conj])). % 0.20/0.41 thf(h1,assumption,(~((sP1 => (~(sP8))))),introduced(assumption,[])). % 0.20/0.41 thf(h2,assumption,sP1,introduced(assumption,[])). % 0.20/0.41 thf(h3,assumption,sP8,introduced(assumption,[])). % 0.20/0.41 thf(1,plain,(~(sP2) | ~(sP3)),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(2,plain,(~(sP6) | ~(sP8)),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.20/0.41 thf(3,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[3]). % 0.20/0.41 thf(4,plain,(sP5 | sP6),inference(choice_rule,[status(thm)],[3])). % 0.20/0.41 thf(5,plain,((~(sP10) | ~(sP1)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(6,plain,(~(sP4) | sP10),inference(all_rule,[status(thm)],[])). % 0.20/0.41 thf(7,plain,(sP9 | sP3),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(8,plain,(sP9 | sP11),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(choiceaxio,axiom,(![X1:($i>$o)>$o]:((~((![X2:$i>$o]:(~((X1 @ X2)))))) => (X1 @ (epsio @ X1))))). % 0.20/0.41 thf(9,plain,(![X1:($i>$o)>$o]:((~((![X2:$i>$o]:(~((X1 @ X2)))))) => (X1 @ (epsio @ X1)))),inference(preprocess,[status(thm)],[9]). % 0.20/0.41 thf(10,plain,(~(sP9) | sP4),inference(choice_rule,[status(thm)],[9])). % 0.20/0.41 thf(11,plain,((~(sP7) | ~(sP11)) | sP2),inference(prop_rule,[status(thm)],[])). % 0.20/0.41 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,4,5,6,7,8,10,11,h0,h2,h3])). % 0.20/0.41 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3])). % 0.20/0.41 thf(ca,axiom,(~((![X1:$i>$o]:((c @ X1) => (~((X1 @ a)))))))). % 0.20/0.41 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[ca,13,h1])). % 0.20/0.41 thf(0,theorem,(~(sP7)),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])). % 0.20/0.41 % SZS output end Proof 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