%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO010^1 : 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 : n012.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 03:24:39 PM UTC 2025 % Result : Theorem 0.12s 0.36s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SYO010^1 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.12/0.33 % Computer : n012.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 9 01:06:23 EDT 2025 % 0.12/0.34 % CPUTime : % 0.12/0.36 % SZS status Theorem % 0.12/0.36 % Mode: mode213 % 0.12/0.36 % Inferences: 10 % 0.12/0.36 % SZS output start Proof % 0.12/0.36 thf(ty_p, type, p : (($i>$i)>$o)). % 0.12/0.36 thf(ty_eigen__1, type, eigen__1 : $i). % 0.12/0.36 thf(ty_f, type, f : ($i>$i)). % 0.12/0.36 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 0.12/0.36 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((X1 = (f @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 0.12/0.36 thf(sP1,plain,sP1 <=> (p @ (^[X1:$i]:X1)),introduced(definition,[new_symbols(definition,[sP1])])). % 0.12/0.36 thf(sP2,plain,sP2 <=> ((f @ eigen__1) = eigen__1),introduced(definition,[new_symbols(definition,[sP2])])). % 0.12/0.36 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.12/0.36 thf(sP4,plain,sP4 <=> (eigen__1 = (f @ eigen__1)),introduced(definition,[new_symbols(definition,[sP4])])). % 0.12/0.36 thf(sP5,plain,sP5 <=> (sP2 => sP4),introduced(definition,[new_symbols(definition,[sP5])])). % 0.12/0.36 thf(sP6,plain,sP6 <=> (![X1:$i]:((f @ X1) = X1)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.12/0.36 thf(sP7,plain,sP7 <=> (![X1:$i]:(((f @ eigen__1) = X1) => (X1 = (f @ eigen__1)))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.12/0.36 thf(sP8,plain,sP8 <=> (p @ f),introduced(definition,[new_symbols(definition,[sP8])])). % 0.12/0.36 thf(sP9,plain,sP9 <=> ((^[X1:$i]:X1) = f),introduced(definition,[new_symbols(definition,[sP9])])). % 0.12/0.36 thf(sP10,plain,sP10 <=> (![X1:$i]:(X1 = (f @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.12/0.36 thf(def_leibeq,definition,(leibeq = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.12/0.36 thf(conj,conjecture,((~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (f @ X1)) => (X2 @ X1)))) => (~(sP1))))) => sP8)). % 0.12/0.36 thf(h1,negated_conjecture,(~(((~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (f @ X1)) => (X2 @ X1)))) => (~(sP1))))) => sP8))),inference(assume_negation,[status(cth)],[conj])). % 0.12/0.36 thf(h2,assumption,(~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (f @ X1)) => (X2 @ X1)))) => (~(sP1))))),introduced(assumption,[])). % 0.12/0.36 thf(h3,assumption,(~(sP8)),introduced(assumption,[])). % 0.12/0.36 thf(h4,assumption,(![X1:$i]:(![X2:$i>$o]:((X2 @ (f @ X1)) => (X2 @ X1)))),introduced(assumption,[])). % 0.12/0.36 thf(h5,assumption,sP1,introduced(assumption,[])). % 0.12/0.36 thf(1,plain,(~(sP6) | sP2),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(2,plain,((~(sP5) | ~(sP2)) | sP4),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(3,plain,(~(sP7) | sP5),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(4,plain,(~(sP3) | sP7),inference(all_rule,[status(thm)],[])). % 0.12/0.36 thf(5,plain,(sP10 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 0.12/0.36 thf(6,plain,(sP9 | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 0.12/0.36 thf(7,plain,sP3,inference(eq_sym,[status(thm)],[])). % 0.12/0.36 thf(8,plain,((~(sP1) | sP8) | ~(sP9)),inference(mating_rule,[status(thm)],[])). % 0.12/0.36 thf(9,plain,sP6,inference(normalize,[status(thm)],[h4]). % 0.12/0.36 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h5,h3])). % 0.12/0.36 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,10,h4,h5])). % 0.12/0.36 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3])). % 0.12/0.36 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])). % 0.12/0.36 thf(0,theorem,((~(((![X1:$i]:(![X2:$i>$o]:((X2 @ (f @ X1)) => (X2 @ X1)))) => (~(sP1))))) => sP8),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])). % 0.12/0.36 % SZS output end Proof %------------------------------------------------------------------------------