0.04/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.35 Computer : n004.cluster.edu 0.12/0.35 Model : x86_64 x86_64 0.12/0.35 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.35 RAMPerCPU : 8042.1875MB 0.12/0.35 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.35 % CPULimit : 1440 0.12/0.35 % DateTime : Mon Jul 3 05:32:15 EDT 2023 0.12/0.35 % CPUTime : 151.66/151.82 % SZS status Theorem 151.66/151.82 % Mode: mode510 151.66/151.82 % Inferences: 3636 151.66/151.82 % SZS output start Proof 151.66/151.82 thf(ty_eigen__436, type, eigen__436 : ($i>$o)). 151.66/151.82 thf(ty_eigen__35, type, eigen__35 : ($i>$o)). 151.66/151.82 thf(ty_eigen__437, type, eigen__437 : $i). 151.66/151.82 thf(ty_eigen__438, type, eigen__438 : $i). 151.66/151.82 thf(h0, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). 151.66/151.82 thf(eigendef_eigen__436, definition, eigen__436 = (eps__0 @ (^[X1:$i>$o]:(~((![X2:$i]:(![X3:$i]:((~(((X1 @ X3) => (~((eigen__35 @ X2)))))) = (~(((eigen__35 @ X2) => (~((X1 @ X3))))))))))))), introduced(definition,[new_symbols(definition,[eigen__436])])). 151.66/151.82 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). 151.66/151.82 thf(eigendef_eigen__438, definition, eigen__438 = (eps__1 @ (^[X1:$i]:(~(((~(((eigen__436 @ X1) => (~((eigen__35 @ eigen__437)))))) = (~(((eigen__35 @ eigen__437) => (~((eigen__436 @ X1))))))))))), introduced(definition,[new_symbols(definition,[eigen__438])])). 151.66/151.82 thf(eigendef_eigen__437, definition, eigen__437 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:((~(((eigen__436 @ X2) => (~((eigen__35 @ X1)))))) = (~(((eigen__35 @ X1) => (~((eigen__436 @ X2)))))))))))), introduced(definition,[new_symbols(definition,[eigen__437])])). 151.66/151.82 thf(eigendef_eigen__35, definition, eigen__35 = (eps__0 @ (^[X1:$i>$o]:(~((![X2:$i>$o]:(![X3:$i]:(![X4:$i]:((~(((X2 @ X4) => (~((X1 @ X3)))))) = (~(((X1 @ X3) => (~((X2 @ X4)))))))))))))), introduced(definition,[new_symbols(definition,[eigen__35])])). 151.66/151.82 thf(sP1,plain,sP1 <=> ((eigen__436 @ eigen__438) => (~((eigen__35 @ eigen__437)))),introduced(definition,[new_symbols(definition,[sP1])])). 151.66/151.82 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:((~(((eigen__436 @ X2) => (~((eigen__35 @ X1)))))) = (~(((eigen__35 @ X1) => (~((eigen__436 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP2])])). 151.66/151.82 thf(sP3,plain,sP3 <=> (![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i]:(![X4:$i]:((~(((X2 @ X4) => (~((X1 @ X3)))))) = (~(((X1 @ X3) => (~((X2 @ X4))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). 151.66/151.82 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:(![X2:$i]:(![X3:$i]:((~(((X1 @ X3) => (~((eigen__35 @ X2)))))) = (~(((eigen__35 @ X2) => (~((X1 @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP4])])). 151.66/151.82 thf(sP5,plain,sP5 <=> (![X1:$i]:((~(((eigen__436 @ X1) => (~((eigen__35 @ eigen__437)))))) = (~(((eigen__35 @ eigen__437) => (~((eigen__436 @ X1)))))))),introduced(definition,[new_symbols(definition,[sP5])])). 151.66/151.82 thf(sP6,plain,sP6 <=> (![X1:($i>$o)>($i>$o)>(($i>$i>$i)>$i)>$o]:(~((![X2:$i>$o]:(![X3:$i>$o]:(![X4:$i]:(![X5:$i]:((~(((X3 @ X5) => (~((X2 @ X4)))))) = (((X1 @ X2) @ X3) @ (^[X6:$i>$i>$i]:((X6 @ X4) @ X5))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). 151.66/151.82 thf(sP7,plain,sP7 <=> (eigen__35 @ eigen__437),introduced(definition,[new_symbols(definition,[sP7])])). 151.66/151.82 thf(sP8,plain,sP8 <=> ((~(sP1)) = (~((sP7 => (~((eigen__436 @ eigen__438))))))),introduced(definition,[new_symbols(definition,[sP8])])). 151.66/151.82 thf(sP9,plain,sP9 <=> (eigen__436 @ eigen__438),introduced(definition,[new_symbols(definition,[sP9])])). 151.66/151.82 thf(sP10,plain,sP10 <=> (sP7 => (~(sP9))),introduced(definition,[new_symbols(definition,[sP10])])). 151.66/151.82 thf(cEXISTS_CART_SET_PROD_pme,conjecture,(~(sP6))). 151.66/151.82 thf(h2,negated_conjecture,sP6,inference(assume_negation,[status(cth)],[cEXISTS_CART_SET_PROD_pme])). 151.66/151.82 thf(1,plain,(sP1 | sP7),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(2,plain,(sP1 | sP9),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(3,plain,(sP10 | sP9),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(4,plain,(sP10 | sP7),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(5,plain,((~(sP1) | ~(sP9)) | ~(sP7)),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(6,plain,((~(sP10) | ~(sP7)) | ~(sP9)),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(7,plain,((sP8 | sP1) | sP10),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(8,plain,((sP8 | ~(sP1)) | ~(sP10)),inference(prop_rule,[status(thm)],[])). 151.66/151.82 thf(9,plain,(sP5 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__438])). 151.66/151.82 thf(10,plain,(sP2 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__437])). 151.66/151.82 thf(11,plain,(sP4 | ~(sP2)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__436])). 151.66/151.82 thf(12,plain,(sP3 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__35])). 151.66/151.82 thf(13,plain,(~(sP6) | ~(sP3)),inference(all_rule,[status(thm)],[])). 151.66/151.82 thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h2])). 151.66/151.82 thf(15,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[14,h1])). 151.66/151.82 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[15,h0])). 151.66/151.82 thf(0,theorem,(~(sP6)),inference(contra,[status(thm),contra(discharge,[h2])],[14,h2])). 151.66/151.82 % SZS output end Proof 151.66/151.82 EOF