%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : SYO512^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : lash -P picomus -M modes -p tstp -t %d %s % Computer : n011.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 03:23:47 PM UTC 2025 % Result : Theorem 0.12s 0.38s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO512^1 : TPTP v9.2.0. Released v4.1.0. % 0.11/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n011.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 01:18:38 EDT 2025 % 0.12/0.34 % CPUTime : % 0.12/0.38 % SZS status Theorem % 0.12/0.38 % Mode: cade22grackle2xfee4 % 0.12/0.38 % Steps: 9 % 0.12/0.38 % SZS output start Proof % 0.12/0.38 thf(ty_r, type, r : ($i>$i>$o)). % 0.12/0.38 thf(ty_eigen__0, type, eigen__0 : $i). % 0.12/0.38 thf(ty_eps, type, eps : (($i>$o)>$i)). % 0.12/0.38 thf(sP1,plain,sP1 <=> ((r @ eigen__0) @ (eps @ (r @ eigen__0))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.12/0.38 thf(sP2,plain,sP2 <=> (![X1:$i]:(~(((r @ eigen__0) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.12/0.38 thf(sP3,plain,sP3 <=> (![X1:$i]:(~((![X2:$i]:(~(((r @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.12/0.38 thf(claim,conjecture,(![X1:$i]:((r @ X1) @ (eps @ (r @ X1))))). % 0.12/0.38 thf(h0,negated_conjecture,(~((![X1:$i]:((r @ X1) @ (eps @ (r @ X1)))))),inference(assume_negation,[status(cth)],[claim])). % 0.12/0.38 thf(h1,assumption,(~(sP1)),introduced(assumption,[])). % 0.12/0.38 thf(epschoice,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 0.12/0.38 thf(1,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[1]). % 0.12/0.38 thf(2,plain,(sP1 | sP2),inference(choice_rule,[status(thm)],[1])). % 0.12/0.38 thf(3,plain,(~(sP3) | ~(sP2)),inference(all_rule,[status(thm)],[])). % 0.12/0.38 thf(rtotal,axiom,sP3). % 0.12/0.38 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[2,3,h1,rtotal])). % 0.12/0.38 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1])). % 0.12/0.38 thf(0,theorem,(![X1:$i]:((r @ X1) @ (eps @ (r @ X1)))),inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])). % 0.12/0.38 % SZS output end Proof %------------------------------------------------------------------------------