%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO213^5 : 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 : n020.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 03:25:09 PM UTC 2025 % Result : Theorem 33.49s 33.87s % Output : Proof 33.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SYO213^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.14/0.36 % Computer : n020.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 00:47:38 EDT 2025 % 0.14/0.36 % CPUTime : % 33.49/33.87 % SZS status Theorem % 33.49/33.87 % Mode: mode482 % 33.49/33.87 % Inferences: 518 % 33.49/33.87 % SZS output start Proof % 33.49/33.87 thf(ty_a, type, a : $tType). % 33.49/33.87 thf(ty_eigen__0, type, eigen__0 : (a>a>$o)). % 33.49/33.87 thf(ty_eigen__4, type, eigen__4 : a). % 33.49/33.87 thf(ty_eigen__5, type, eigen__5 : a). % 33.49/33.87 thf(h0, assumption, (![X1:(a>a>$o)>$o]:(![X2:a>a>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 33.49/33.87 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:a>a>$o]:(~((~((![X2:a>$o]:(~((![X3:a]:(~((((X1 @ X3) = X2) = (X2 = X2)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 33.49/33.87 thf(h1, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 33.49/33.87 thf(eigendef_eigen__4, definition, eigen__4 = (eps__1 @ (^[X1:a]:(~((~((((eigen__0 @ X1) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2))))) = ((^[X2:a]:(~(((eigen__0 @ X2) @ X2)))) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 33.49/33.87 thf(eigendef_eigen__5, definition, eigen__5 = (eps__1 @ (^[X1:a]:(~(((~(((eigen__0 @ X1) @ X1))) = (~(((eigen__0 @ X1) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 33.49/33.87 thf(sP1,plain,sP1 <=> (![X1:a>$o]:(~((![X2:a]:(~((((eigen__0 @ X2) = X1) = (X1 = X1)))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 33.49/33.87 thf(sP2,plain,sP2 <=> (![X1:a]:(((eigen__0 @ eigen__4) @ X1) = (~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])). % 33.49/33.87 thf(sP3,plain,sP3 <=> (((eigen__0 @ eigen__4) @ eigen__4) = (~(((eigen__0 @ eigen__4) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP3])])). % 33.49/33.87 thf(sP4,plain,sP4 <=> (((eigen__0 @ eigen__4) = (^[X1:a]:(~(((eigen__0 @ X1) @ X1))))) = ((^[X1:a]:(~(((eigen__0 @ X1) @ X1)))) = (^[X1:a]:(~(((eigen__0 @ X1) @ X1)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 33.49/33.87 thf(sP5,plain,sP5 <=> (![X1:a]:(~((((eigen__0 @ X1) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2))))) = ((^[X2:a]:(~(((eigen__0 @ X2) @ X2)))) = (^[X2:a]:(~(((eigen__0 @ X2) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 33.49/33.87 thf(sP6,plain,sP6 <=> ((eigen__0 @ eigen__4) = (^[X1:a]:(~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP6])])). % 33.49/33.87 thf(sP7,plain,sP7 <=> ((^[X1:a]:(~(((eigen__0 @ X1) @ X1)))) = (^[X1:a]:(~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])). % 33.49/33.87 thf(sP8,plain,sP8 <=> ((~(((eigen__0 @ eigen__5) @ eigen__5))) = (~(((eigen__0 @ eigen__5) @ eigen__5)))),introduced(definition,[new_symbols(definition,[sP8])])). % 33.49/33.87 thf(sP9,plain,sP9 <=> (![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((((X1 @ X3) = X2) = (X2 = X2))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 33.49/33.87 thf(sP10,plain,sP10 <=> (![X1:a]:((~(((eigen__0 @ X1) @ X1))) = (~(((eigen__0 @ X1) @ X1))))),introduced(definition,[new_symbols(definition,[sP10])])). % 33.49/33.87 thf(sP11,plain,sP11 <=> ((eigen__0 @ eigen__4) @ eigen__4),introduced(definition,[new_symbols(definition,[sP11])])). % 33.49/33.87 thf(cCT30,conjecture,(![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:$o>$o]:((X4 @ ((X1 @ X3) = X2)) => (X4 @ (X2 = X2)))))))))))))). % 33.49/33.87 thf(h2,negated_conjecture,(~((![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:$o>$o]:((X4 @ ((X1 @ X3) = X2)) => (X4 @ (X2 = X2))))))))))))))),inference(assume_negation,[status(cth)],[cCT30])). % 33.49/33.87 thf(1,plain,((~(sP3) | ~(sP11)) | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(2,plain,((~(sP3) | sP11) | sP11),inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(3,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). % 33.49/33.87 thf(4,plain,(~(sP6) | sP2),inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(5,plain,sP8,inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(6,plain,(sP10 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5])). % 33.49/33.87 thf(7,plain,(sP7 | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(8,plain,((~(sP4) | sP6) | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 33.49/33.87 thf(9,plain,(sP5 | sP4),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4])). % 33.49/33.87 thf(10,plain,(~(sP1) | ~(sP5)),inference(all_rule,[status(thm)],[])). % 33.49/33.87 thf(11,plain,(sP9 | sP1),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 33.49/33.87 thf(12,plain,(~(sP9)),inference(normalize,[status(thm)],[h2]). % 33.49/33.87 thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12])). % 33.49/33.87 thf(14,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1])). % 33.49/33.87 thf(15,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0])). % 33.49/33.87 thf(0,theorem,(![X1:a>a>$o]:(~((![X2:a>$o]:(~((![X3:a]:(~((![X4:$o>$o]:((X4 @ ((X1 @ X3) = X2)) => (X4 @ (X2 = X2))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[13,h2])). % 33.49/33.87 % SZS output end Proof %------------------------------------------------------------------------------