%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO547^1 : 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 : n013.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 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYO547^1 : TPTP v9.2.0. Released v5.2.0. % 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.10/0.32 % Computer : n013.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Thu Oct 9 00:39:53 EDT 2025 % 0.10/0.32 % CPUTime : % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % Mode: cade22grackle2xfee4 % 0.16/0.37 % Steps: 8 % 0.16/0.37 % SZS output start Proof % 0.16/0.37 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 0.16/0.37 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.16/0.37 thf(ty_eigen__1, type, eigen__1 : $i). % 0.16/0.37 thf(sP1,plain,sP1 <=> (eigen__0 @ eigen__1),introduced(definition,[new_symbols(definition,[sP1])])). % 0.16/0.37 thf(sP2,plain,sP2 <=> (eigen__0 @ (eps @ (^[X1:$i]:(~((eigen__0 @ X1)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.16/0.37 thf(sP3,plain,sP3 <=> (![X1:$i]:(eigen__0 @ X1)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.16/0.37 thf(def_epscomp,definition,(epscomp = (^[X1:$i>$o]:(eps @ (^[X2:$i]:((~) @ (X1 @ X2))))))). % 0.16/0.37 thf(choicecomp,conjecture,(![X1:$i>$o]:((~((![X2:$i]:(X1 @ X2)))) => (~((X1 @ (eps @ (^[X2:$i]:(~((X1 @ X2))))))))))). % 0.16/0.37 thf(h0,negated_conjecture,(~((![X1:$i>$o]:((~((![X2:$i]:(X1 @ X2)))) => (~((X1 @ (eps @ (^[X2:$i]:(~((X1 @ X2)))))))))))),inference(assume_negation,[status(cth)],[choicecomp])). % 0.16/0.37 thf(h1,assumption,(~(((~(((!!) @ eigen__0))) => (~(sP2))))),introduced(assumption,[])). % 0.16/0.37 thf(h2,assumption,(~(sP3)),introduced(assumption,[])). % 0.16/0.37 thf(h3,assumption,sP2,introduced(assumption,[])). % 0.16/0.37 thf(h4,assumption,(~(sP1)),introduced(assumption,[])). % 0.16/0.37 thf(1,plain,(~(sP3) | sP1),inference(all_rule,[status(thm)],[])). % 0.16/0.37 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.16/0.37 thf(2,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[2]). % 0.16/0.37 thf(3,plain,(~(sP2) | sP3),inference(choice_rule,[status(thm)],[2])). % 0.16/0.37 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,3,h4,h3])). % 0.16/0.37 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,4,h4])). % 0.16/0.37 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,5,h2,h3])). % 0.16/0.37 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1])). % 0.16/0.37 thf(0,theorem,(![X1:$i>$o]:((~((![X2:$i]:(X1 @ X2)))) => (~((X1 @ (eps @ (^[X2:$i]:(~((X1 @ X2)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])). % 0.16/0.37 % SZS output end Proof %------------------------------------------------------------------------------