%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SEV428^1 : TPTP v9.2.0. Released v5.2.0. % 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 02:56:48 PM UTC 2025 % Result : Theorem 1.09s 1.27s % Output : Proof 1.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEV428^1 : TPTP v9.2.0. Released v5.2.0. % 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.34 % Computer : n020.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Oct 8 19:34:53 EDT 2025 % 0.12/0.34 % CPUTime : % 1.09/1.27 % SZS status Theorem % 1.09/1.27 % Mode: mode506 % 1.09/1.27 % Inferences: 2037 % 1.09/1.27 % SZS output start Proof % 1.09/1.27 thf(ty_a, type, a : $i). % 1.09/1.27 thf(ty_eps, type, eps : (($i>$o)>$i)). % 1.09/1.27 thf(ty_epsio, type, epsio : ((($i>$o)>$o)>$i>$o)). % 1.09/1.27 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 1.09/1.27 thf(ty_c, type, c : (($i>$o)>$o)). % 1.09/1.27 thf(h0, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 1.09/1.27 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ a)))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 1.09/1.27 thf(sP1,plain,sP1 <=> (![X1:$i>$o]:((c @ X1) => (~((X1 @ a))))),introduced(definition,[new_symbols(definition,[sP1])])). % 1.09/1.27 thf(sP2,plain,sP2 <=> (eigen__0 @ a),introduced(definition,[new_symbols(definition,[sP2])])). % 1.09/1.27 thf(sP3,plain,sP3 <=> ((c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))) => (~(((epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))) @ (eps @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 1.09/1.27 thf(sP4,plain,sP4 <=> ((c @ eigen__0) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP4])])). % 1.09/1.27 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])). % 1.09/1.27 thf(sP6,plain,sP6 <=> (c @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])). % 1.09/1.27 thf(sP7,plain,sP7 <=> (![X1:$i>$o]:((c @ X1) => (~((X1 @ (eps @ X1)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 1.09/1.27 thf(sP8,plain,sP8 <=> (eigen__0 @ (eps @ eigen__0)),introduced(definition,[new_symbols(definition,[sP8])])). % 1.09/1.27 thf(sP9,plain,sP9 <=> ((epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))) @ (eps @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 1.09/1.27 thf(sP10,plain,sP10 <=> (c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 1.09/1.27 thf(sP11,plain,sP11 <=> (sP10 => (![X1:$i]:(~(((epsio @ (^[X2:$i>$o]:(~(((c @ X2) => (~((X2 @ (eps @ X2))))))))) @ X1))))),introduced(definition,[new_symbols(definition,[sP11])])). % 1.09/1.27 thf(sP12,plain,sP12 <=> (sP6 => (~(sP8))),introduced(definition,[new_symbols(definition,[sP12])])). % 1.09/1.27 thf(sP13,plain,sP13 <=> (![X1:$i]:(~(((epsio @ (^[X2:$i>$o]:(~(((c @ X2) => (~((X2 @ (eps @ X2))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 1.09/1.27 thf(def_setunion,definition,(setunion = (^[X1:($i>$o)>$o]:(^[X2:$i]:(~((![X3:$i>$o]:((X1 @ X3) => (~((X3 @ X2))))))))))). % 1.09/1.27 thf(def_choosenonempty,definition,(choosenonempty = (^[X1:($i>$o)>$o]:(epsio @ (^[X2:$i>$o]:(~(((X1 @ X2) => (~((X2 @ (eps @ X2)))))))))))). % 1.09/1.27 thf(conj,conjecture,(~(sP11))). % 1.09/1.27 thf(h1,negated_conjecture,sP11,inference(assume_negation,[status(cth)],[conj])). % 1.09/1.27 thf(1,plain,(~(sP5) | ~(sP2)),inference(all_rule,[status(thm)],[])). % 1.09/1.27 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))). % 1.09/1.27 thf(2,plain,(sP8 | sP5),inference(choice_rule,[status(thm)],[choiceax])). % 1.09/1.27 thf(3,plain,(~(sP13) | ~(sP9)),inference(all_rule,[status(thm)],[])). % 1.09/1.27 thf(4,plain,(sP3 | sP9),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(5,plain,(sP3 | sP10),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(6,plain,(~(sP7) | sP12),inference(all_rule,[status(thm)],[])). % 1.09/1.27 thf(7,plain,((~(sP12) | ~(sP6)) | ~(sP8)),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(choiceaxio,axiom,(![X1:($i>$o)>$o]:((~((![X2:$i>$o]:(~((X1 @ X2)))))) => (X1 @ (epsio @ X1))))). % 1.09/1.27 thf(8,plain,(~(sP3) | sP7),inference(choice_rule,[status(thm)],[choiceaxio])). % 1.09/1.27 thf(9,plain,(sP4 | sP2),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(10,plain,(sP4 | sP6),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(11,plain,(sP1 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 1.09/1.27 thf(12,plain,((~(sP11) | ~(sP10)) | sP13),inference(prop_rule,[status(thm)],[])). % 1.09/1.27 thf(ca,axiom,((setunion @ c) @ a)). % 1.09/1.27 thf(13,plain,(~(sP1)),inference(preprocess,[status(thm)],[ca]). % 1.09/1.27 thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h1])). % 1.09/1.27 thf(15,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0])). % 1.09/1.27 thf(0,theorem,(~(sP11)),inference(contra,[status(thm),contra(discharge,[h1])],[14,h1])). % 1.09/1.27 % SZS output end Proof %------------------------------------------------------------------------------