%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO364^5 : 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 : n024.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 03:25:25 PM UTC 2025 % Result : Theorem 101.47s 101.57s % Output : Proof 101.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : SYO364^5 : TPTP v9.2.0. Released v4.0.0. % 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.35 % Computer : n024.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Thu Oct 9 01:08:38 EDT 2025 % 0.15/0.36 % CPUTime : % 101.47/101.57 % SZS status Theorem % 101.47/101.57 % Mode: mode492 % 101.47/101.57 % Inferences: 1149 % 101.47/101.57 % SZS output start Proof % 101.47/101.57 thf(ty_a, type, a : $tType). % 101.47/101.57 thf(ty_h, type, h : (a>a)). % 101.47/101.57 thf(ty_eigen__2, type, eigen__2 : a). % 101.47/101.57 thf(ty_eigen__0, type, eigen__0 : ((a>a)>$o)). % 101.47/101.57 thf(ty_j, type, j : (a>a)). % 101.47/101.57 thf(ty_g, type, g : ((a>a)>a>a)). % 101.47/101.57 thf(ty_f, type, f : ((a>a)>a>a)). % 101.47/101.57 thf(h0, assumption, (![X1:a>$o]:(![X2:a]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 101.47/101.57 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:a]:(~((((f @ h) @ X1) = ((g @ j) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 101.47/101.57 thf(sP1,plain,sP1 <=> (eigen__0 @ (f @ h)),introduced(definition,[new_symbols(definition,[sP1])])). % 101.47/101.57 thf(sP2,plain,sP2 <=> (((g @ h) @ eigen__2) = ((f @ h) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP2])])). % 101.47/101.57 thf(sP3,plain,sP3 <=> (((f @ h) @ eigen__2) = ((g @ h) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP3])])). % 101.47/101.57 thf(sP4,plain,sP4 <=> ((f @ h) = (g @ j)),introduced(definition,[new_symbols(definition,[sP4])])). % 101.47/101.57 thf(sP5,plain,sP5 <=> (h = j),introduced(definition,[new_symbols(definition,[sP5])])). % 101.47/101.57 thf(sP6,plain,sP6 <=> (![X1:a]:((((f @ h) @ eigen__2) = X1) => (X1 = ((f @ h) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP6])])). % 101.47/101.57 thf(sP7,plain,sP7 <=> (sP3 => sP2),introduced(definition,[new_symbols(definition,[sP7])])). % 101.47/101.57 thf(sP8,plain,sP8 <=> (((g @ h) @ eigen__2) = ((g @ j) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP8])])). % 101.47/101.57 thf(sP9,plain,sP9 <=> (![X1:a]:(((f @ h) @ X1) = ((g @ j) @ X1))),introduced(definition,[new_symbols(definition,[sP9])])). % 101.47/101.57 thf(sP10,plain,sP10 <=> (![X1:a]:(((f @ h) @ X1) = ((g @ h) @ X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 101.47/101.57 thf(sP11,plain,sP11 <=> (![X1:a]:(![X2:a]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP11])])). % 101.47/101.57 thf(sP12,plain,sP12 <=> (![X1:a]:((h @ X1) = (j @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 101.47/101.57 thf(sP13,plain,sP13 <=> (eigen__0 @ (g @ j)),introduced(definition,[new_symbols(definition,[sP13])])). % 101.47/101.57 thf(sP14,plain,sP14 <=> (eigen__2 = eigen__2),introduced(definition,[new_symbols(definition,[sP14])])). % 101.47/101.57 thf(sP15,plain,sP15 <=> (((f @ h) @ eigen__2) = ((g @ j) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP15])])). % 101.47/101.57 thf(sP16,plain,sP16 <=> (![X1:a>a]:(![X2:a]:(((f @ X1) @ X2) = ((g @ X1) @ X2)))),introduced(definition,[new_symbols(definition,[sP16])])). % 101.47/101.57 thf(cEDEC_pme,conjecture,((~(((![X1:a>a]:(![X2:a]:(![X3:a>$o]:((X3 @ ((f @ X1) @ X2)) => (X3 @ ((g @ X1) @ X2)))))) => (~((![X1:a]:(![X2:a>$o]:((X2 @ (h @ X1)) => (X2 @ (j @ X1)))))))))) => (![X1:(a>a)>$o]:((X1 @ (f @ h)) => (X1 @ (g @ j)))))). % 101.47/101.57 thf(h1,negated_conjecture,(~(((~(((![X1:a>a]:(![X2:a]:(![X3:a>$o]:((X3 @ ((f @ X1) @ X2)) => (X3 @ ((g @ X1) @ X2)))))) => (~((![X1:a]:(![X2:a>$o]:((X2 @ (h @ X1)) => (X2 @ (j @ X1)))))))))) => (![X1:(a>a)>$o]:((X1 @ (f @ h)) => (X1 @ (g @ j))))))),inference(assume_negation,[status(cth)],[cEDEC_pme])). % 101.47/101.57 thf(h2,assumption,(~(((![X1:a>a]:(![X2:a]:(![X3:a>$o]:((X3 @ ((f @ X1) @ X2)) => (X3 @ ((g @ X1) @ X2)))))) => (~((![X1:a]:(![X2:a>$o]:((X2 @ (h @ X1)) => (X2 @ (j @ X1)))))))))),introduced(assumption,[])). % 101.47/101.57 thf(h3,assumption,(~((![X1:(a>a)>$o]:((X1 @ (f @ h)) => (X1 @ (g @ j)))))),introduced(assumption,[])). % 101.47/101.57 thf(h4,assumption,(![X1:a>a]:(![X2:a]:(![X3:a>$o]:((X3 @ ((f @ X1) @ X2)) => (X3 @ ((g @ X1) @ X2)))))),introduced(assumption,[])). % 101.47/101.57 thf(h5,assumption,(![X1:a]:(![X2:a>$o]:((X2 @ (h @ X1)) => (X2 @ (j @ X1))))),introduced(assumption,[])). % 101.47/101.57 thf(h6,assumption,(~((sP1 => sP13))),introduced(assumption,[])). % 101.47/101.57 thf(h7,assumption,sP1,introduced(assumption,[])). % 101.47/101.57 thf(h8,assumption,(~(sP13)),introduced(assumption,[])). % 101.47/101.57 thf(1,plain,((sP8 | ~(sP5)) | ~(sP14)),inference(prop_rule,[status(thm)],[])). % 101.47/101.57 thf(2,plain,(((~(sP3) | sP15) | ~(sP2)) | ~(sP8)),inference(confrontation_rule,[status(thm)],[])). % 101.47/101.57 thf(3,plain,((~(sP7) | ~(sP3)) | sP2),inference(prop_rule,[status(thm)],[])). % 101.47/101.57 thf(4,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])). % 101.47/101.57 thf(5,plain,sP14,inference(prop_rule,[status(thm)],[])). % 101.47/101.57 thf(6,plain,(sP5 | ~(sP12)),inference(prop_rule,[status(thm)],[])). % 101.47/101.57 thf(7,plain,(~(sP10) | sP3),inference(all_rule,[status(thm)],[])). % 101.47/101.57 thf(8,plain,(~(sP16) | sP10),inference(all_rule,[status(thm)],[])). % 101.47/101.57 thf(9,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])). % 101.47/101.57 thf(10,plain,sP11,inference(eq_sym,[status(thm)],[])). % 101.47/101.57 thf(11,plain,(sP9 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 101.47/101.57 thf(12,plain,(sP4 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 101.47/101.57 thf(13,plain,((~(sP1) | sP13) | ~(sP4)),inference(mating_rule,[status(thm)],[])). % 101.47/101.57 thf(14,plain,sP16,inference(normalize,[status(thm)],[h4]). % 101.47/101.57 thf(15,plain,sP12,inference(normalize,[status(thm)],[h5]). % 101.47/101.57 thf(16,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h7,h8])). % 101.47/101.57 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,16,h7,h8])). % 101.47/101.57 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,17,h6])). % 101.47/101.57 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,18,h4,h5])). % 101.47/101.57 thf(20,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,19,h2,h3])). % 101.47/101.57 thf(21,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0])). % 101.47/101.57 thf(0,theorem,((~(((![X1:a>a]:(![X2:a]:(![X3:a>$o]:((X3 @ ((f @ X1) @ X2)) => (X3 @ ((g @ X1) @ X2)))))) => (~((![X1:a]:(![X2:a>$o]:((X2 @ (h @ X1)) => (X2 @ (j @ X1)))))))))) => (![X1:(a>a)>$o]:((X1 @ (f @ h)) => (X1 @ (g @ j))))),inference(contra,[status(thm),contra(discharge,[h1])],[20,h1])). % 101.47/101.57 % SZS output end Proof %------------------------------------------------------------------------------