%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO209^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n022.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 03:25:08 PM UTC 2025 % Result : Theorem 33.69s 33.86s % Output : Proof 33.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYO209^5 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n022.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 9 01:24:38 EDT 2025 % 0.14/0.36 % CPUTime : % 33.69/33.86 % SZS status Theorem % 33.69/33.86 % Mode: mode482 % 33.69/33.86 % Inferences: 148 % 33.69/33.86 % SZS output start Proof % 33.69/33.86 thf(ty_a, type, a : $tType). % 33.69/33.86 thf(ty_eigen__0, type, eigen__0 : (a>a>$o)). % 33.69/33.86 thf(ty_eigen__3, type, eigen__3 : a). % 33.69/33.86 thf(h0, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 33.69/33.86 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:a]:(~((~(((eigen__0 @ X1) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 33.69/33.86 thf(h1, assumption, (![X1:(a>a>$o)>$o]:(![X2:a>a>$o]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 33.69/33.86 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:a>a>$o]:(~((~((![X2:a>$o]:(~((![X3:a]:(~(((X1 @ X3) = X2))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 33.69/33.86 thf(sP1,plain,sP1 <=> (![X1:a>$o]:(~((![X2:a]:(~(((eigen__0 @ X2) = X1))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 33.69/33.86 thf(sP2,plain,sP2 <=> (![X1:a]:(((eigen__0 @ eigen__3) @ X1) = (~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])). % 33.69/33.86 thf(sP3,plain,sP3 <=> ((eigen__0 @ eigen__3) = (^[X1:a]:(~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP3])])). % 33.69/33.86 thf(sP4,plain,sP4 <=> ((eigen__0 @ eigen__3) @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])). % 33.69/33.86 thf(sP5,plain,sP5 <=> (sP4 = (~(sP4))),introduced(definition,[new_symbols(definition,[sP5])])). % 33.69/33.86 thf(sP6,plain,sP6 <=> (![X1:a]:(~(((eigen__0 @ X1) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 33.69/33.86 thf(sP7,plain,sP7 <=> (![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~(((X1 @ X3) = X2)))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 33.69/33.86 thf(cCT29,conjecture,(![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:(a>$o)>$o]:((X4 @ (X1 @ X3)) => (X4 @ X2))))))))))))). % 33.69/33.86 thf(h2,negated_conjecture,(~((![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:(a>$o)>$o]:((X4 @ (X1 @ X3)) => (X4 @ X2)))))))))))))),inference(assume_negation,[status(cth)],[cCT29])). % 33.69/33.86 thf(1,plain,((~(sP5) | ~(sP4)) | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 33.69/33.86 thf(2,plain,((~(sP5) | sP4) | sP4),inference(prop_rule,[status(thm)],[])). % 33.69/33.86 thf(3,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])). % 33.69/33.86 thf(4,plain,(~(sP3) | sP2),inference(prop_rule,[status(thm)],[])). % 33.69/33.86 thf(5,plain,(sP6 | sP3),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 33.69/33.86 thf(6,plain,(~(sP1) | ~(sP6)),inference(all_rule,[status(thm)],[])). % 33.69/33.86 thf(7,plain,(sP7 | sP1),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 33.69/33.86 thf(8,plain,(~(sP7)),inference(normalize,[status(thm)],[h2]). % 33.69/33.86 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8])). % 33.69/33.86 thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[9,h1])). % 33.69/33.86 thf(11,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[10,h0])). % 33.69/33.86 thf(0,theorem,(![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:(a>$o)>$o]:((X4 @ (X1 @ X3)) => (X4 @ X2)))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[9,h2])). % 33.69/33.86 % SZS output end Proof %------------------------------------------------------------------------------