%------------------------------------------------------------------------------ % File : Lash---1.13 % Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : lash -P picomus -M modes -p tstp -t %d %s % Computer : n029.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:27:25 PM UTC 2026 % Result : Theorem 20.11s 20.41s % Output : Proof 20.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : lash -P picomus -M modes -p tstp -t %d %s % 0.08/0.34 % Computer : n029.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sat Sep 5 00:24:10 UTC 2026 % 0.08/0.34 % CPUTime : % 20.11/20.41 % SZS status Theorem % 20.11/20.41 % Mode: cade22grackle2x798d % 20.11/20.41 % Steps: 1695 % 20.11/20.41 % SZS output start Proof % 20.11/20.41 thf(ty_a, type, a : $tType). % 20.11/20.41 thf(ty_eigen__0, type, eigen__0 : (((a>$o)>a)>a>$o)). % 20.11/20.41 thf(sP1,plain,sP1 <=> (![X1:(a>$o)>a]:(~((![X2:a]:(~(((eigen__0 @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 20.11/20.41 thf(sP2,plain,sP2 <=> ((eigen__0 @ (@+)) @ (@+[X1:a]:((eigen__0 @ (@+)) @ X1))),introduced(definition,[new_symbols(definition,[sP2])])). % 20.11/20.41 thf(sP3,plain,sP3 <=> (![X1:(a>$o)>a]:(~(((eigen__0 @ X1) @ (X1 @ (eigen__0 @ X1)))))),introduced(definition,[new_symbols(definition,[sP3])])). % 20.11/20.41 thf(sP4,plain,sP4 <=> (![X1:a]:(~(((eigen__0 @ (@+)) @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])). % 20.11/20.41 thf(cTHM534,conjecture,((![X1:(a>$o)>$o]:((![X2:a>$o]:((X1 @ X2) => (~((![X3:a]:(~((X2 @ X3)))))))) => (~((![X2:(a>$o)>a]:(~((![X3:a>$o]:((X1 @ X3) => (X3 @ (X2 @ X3))))))))))) => (![X1:((a>$o)>a)>a>$o]:((![X2:(a>$o)>a]:(~((![X3:a]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:(a>$o)>a]:(~(((X1 @ X2) @ (X2 @ (X1 @ X2)))))))))))). % 20.11/20.41 thf(h0,negated_conjecture,(~(((![X1:(a>$o)>$o]:((![X2:a>$o]:((X1 @ X2) => (~((![X3:a]:(~((X2 @ X3)))))))) => (~((![X2:(a>$o)>a]:(~((![X3:a>$o]:((X1 @ X3) => (X3 @ (X2 @ X3))))))))))) => (![X1:((a>$o)>a)>a>$o]:((![X2:(a>$o)>a]:(~((![X3:a]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:(a>$o)>a]:(~(((X1 @ X2) @ (X2 @ (X1 @ X2))))))))))))),inference(assume_negation,[status(cth)],[cTHM534])). % 20.11/20.41 thf(h1,assumption,(![X1:(a>$o)>$o]:((![X2:a>$o]:((X1 @ X2) => (~((![X3:a]:(~((X2 @ X3)))))))) => (~((![X2:(a>$o)>a]:(~((![X3:a>$o]:((X1 @ X3) => (X3 @ (X2 @ X3))))))))))),introduced(assumption,[])). % 20.11/20.41 thf(h2,assumption,(~((![X1:((a>$o)>a)>a>$o]:((![X2:(a>$o)>a]:(~((![X3:a]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:(a>$o)>a]:(~(((X1 @ X2) @ (X2 @ (X1 @ X2)))))))))))),introduced(assumption,[])). % 20.11/20.41 thf(h3,assumption,(~((sP1 => (~(sP3))))),introduced(assumption,[])). % 20.11/20.41 thf(h4,assumption,sP1,introduced(assumption,[])). % 20.11/20.41 thf(h5,assumption,sP3,introduced(assumption,[])). % 20.11/20.41 thf(1,plain,(sP2 | sP4),inference(choice_rule,[status(thm)],[])). % 20.11/20.41 thf(2,plain,(~(sP3) | ~(sP2)),inference(all_rule,[status(thm)],[])). % 20.11/20.41 thf(3,plain,(~(sP1) | ~(sP4)),inference(all_rule,[status(thm)],[])). % 20.11/20.41 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,3,h4,h5])). % 20.11/20.41 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,4,h4,h5])). % 20.11/20.41 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,5,h3])). % 20.11/20.41 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,6,h1,h2])). % 20.11/20.41 thf(0,theorem,((![X1:(a>$o)>$o]:((![X2:a>$o]:((X1 @ X2) => (~((![X3:a]:(~((X2 @ X3)))))))) => (~((![X2:(a>$o)>a]:(~((![X3:a>$o]:((X1 @ X3) => (X3 @ (X2 @ X3))))))))))) => (![X1:((a>$o)>a)>a>$o]:((![X2:(a>$o)>a]:(~((![X3:a]:(~(((X1 @ X2) @ X3))))))) => (~((![X2:(a>$o)>a]:(~(((X1 @ X2) @ (X2 @ (X1 @ X2))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])). % 20.11/20.41 % SZS output end Proof %------------------------------------------------------------------------------