%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO030^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n014.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 03:24:42 PM UTC 2025 % Result : Theorem 5.02s 5.29s % Output : Proof 5.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SYO030^1 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 9 01:08:23 EDT 2025 % 0.13/0.35 % CPUTime : % 5.02/5.29 % SZS status Theorem % 5.02/5.29 % Mode: mode495 % 5.02/5.29 % Inferences: 278 % 5.02/5.29 % SZS output start Proof % 5.02/5.29 thf(ty_eigen__27, type, eigen__27 : $o). % 5.02/5.29 thf(ty_eigen__20, type, eigen__20 : $o). % 5.02/5.29 thf(h0, assumption, (![X1:$o>$o]:(![X2:$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 5.02/5.29 thf(eigendef_eigen__20, definition, eigen__20 = (eps__0 @ (^[X1:$o]:(~((~((((^[X2:$o]:X1) = ((=) @ X1)) = X1))))))), introduced(definition,[new_symbols(definition,[eigen__20])])). % 5.02/5.29 thf(eigendef_eigen__27, definition, eigen__27 = (eps__0 @ (^[X1:$o]:(~((~(((eigen__20 = X1) = X1))))))), introduced(definition,[new_symbols(definition,[eigen__27])])). % 5.02/5.29 thf(sP1,plain,sP1 <=> (![X1:$o]:(~((((^[X2:$o]:X1) = ((=) @ X1)) = X1)))),introduced(definition,[new_symbols(definition,[sP1])])). % 5.02/5.29 thf(sP2,plain,sP2 <=> ((^[X1:$o]:eigen__20) = ((=) @ eigen__20)),introduced(definition,[new_symbols(definition,[sP2])])). % 5.02/5.29 thf(sP3,plain,sP3 <=> (![X1:$o]:(eigen__20 = (eigen__20 = X1))),introduced(definition,[new_symbols(definition,[sP3])])). % 5.02/5.29 thf(sP4,plain,sP4 <=> ((eigen__20 = eigen__27) = eigen__27),introduced(definition,[new_symbols(definition,[sP4])])). % 5.02/5.29 thf(sP5,plain,sP5 <=> (eigen__20 = $false),introduced(definition,[new_symbols(definition,[sP5])])). % 5.02/5.29 thf(sP6,plain,sP6 <=> eigen__20,introduced(definition,[new_symbols(definition,[sP6])])). % 5.02/5.29 thf(sP7,plain,sP7 <=> (sP6 = eigen__27),introduced(definition,[new_symbols(definition,[sP7])])). % 5.02/5.29 thf(sP8,plain,sP8 <=> (![X1:$o]:(~(((sP6 = X1) = X1)))),introduced(definition,[new_symbols(definition,[sP8])])). % 5.02/5.29 thf(sP9,plain,sP9 <=> eigen__27,introduced(definition,[new_symbols(definition,[sP9])])). % 5.02/5.29 thf(sP10,plain,sP10 <=> (![X1:$o>$o]:(~((![X2:$o]:(~(((X1 @ X2) = X2))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 5.02/5.29 thf(sP11,plain,sP11 <=> (sP2 = sP6),introduced(definition,[new_symbols(definition,[sP11])])). % 5.02/5.29 thf(sP12,plain,sP12 <=> (sP6 = sP5),introduced(definition,[new_symbols(definition,[sP12])])). % 5.02/5.29 thf(sP13,plain,sP13 <=> $false,introduced(definition,[new_symbols(definition,[sP13])])). % 5.02/5.29 thf(def_leibeq,definition,(leibeq = (^[X1:$o]:(^[X2:$o]:(![X3:$o>$o]:((X3 @ X1) => (X3 @ X2))))))). % 5.02/5.29 thf(conj,conjecture,(~((![X1:$o>$o]:(~((![X2:$o]:(~((![X3:$o>$o]:((X3 @ (X1 @ X2)) => (X3 @ X2)))))))))))). % 5.02/5.29 thf(h1,negated_conjecture,(![X1:$o>$o]:(~((![X2:$o]:(~((![X3:$o>$o]:((X3 @ (X1 @ X2)) => (X3 @ X2))))))))),inference(assume_negation,[status(cth)],[conj])). % 5.02/5.29 thf(1,plain,((~(sP5) | ~(sP6)) | sP13),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(2,plain,((~(sP12) | ~(sP6)) | sP5),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(3,plain,(~(sP3) | sP12),inference(all_rule,[status(thm)],[])). % 5.02/5.29 thf(4,plain,(~(sP2) | sP3),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(5,plain,((~(sP7) | sP6) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(6,plain,((sP7 | sP6) | sP9),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(7,plain,((~(sP4) | ~(sP7)) | sP9),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(8,plain,((~(sP4) | sP7) | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(9,plain,(sP8 | sP4),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__27])). % 5.02/5.29 thf(10,plain,(~(sP10) | ~(sP8)),inference(all_rule,[status(thm)],[])). % 5.02/5.29 thf(11,plain,((~(sP11) | sP2) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(12,plain,(sP1 | sP11),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20])). % 5.02/5.29 thf(13,plain,(~(sP10) | ~(sP1)),inference(all_rule,[status(thm)],[])). % 5.02/5.29 thf(14,plain,~(sP13),inference(prop_rule,[status(thm)],[])). % 5.02/5.29 thf(15,plain,sP10,inference(normalize,[status(thm)],[h1]). % 5.02/5.29 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])). % 5.02/5.29 thf(17,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[16,h0])). % 5.02/5.29 thf(0,theorem,(~((![X1:$o>$o]:(~((![X2:$o]:(~((![X3:$o>$o]:((X3 @ (X1 @ X2)) => (X3 @ X2))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[16,h1])). % 5.02/5.29 % SZS output end Proof %------------------------------------------------------------------------------