%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO274^5 : 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 : n025.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 03:25:16 PM UTC 2025 % Result : Theorem 0.13s 0.37s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO274^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.35 % Computer : n025.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 00:26:08 EDT 2025 % 0.13/0.35 % CPUTime : % 0.13/0.37 % SZS status Theorem % 0.13/0.37 % Mode: mode213 % 0.13/0.37 % Inferences: 9 % 0.13/0.37 % SZS output start Proof % 0.13/0.37 thf(ty_a, type, a : $tType). % 0.13/0.37 thf(ty_b, type, b : $tType). % 0.13/0.37 thf(ty_c, type, c : $tType). % 0.13/0.37 thf(ty_cG, type, cG : (c>b)). % 0.13/0.37 thf(ty_eigen__2, type, eigen__2 : (c>$o)). % 0.13/0.37 thf(ty_eigen__1, type, eigen__1 : c). % 0.13/0.37 thf(ty_eigen__0, type, eigen__0 : c). % 0.13/0.37 thf(ty_cF, type, cF : (b>a)). % 0.13/0.37 thf(sP1,plain,sP1 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.37 thf(sP2,plain,sP2 <=> (![X1:b]:(![X2:b]:(((cF @ X1) = (cF @ X2)) => (X1 = X2)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.37 thf(sP3,plain,sP3 <=> (((cG @ eigen__0) = (cG @ eigen__1)) => (eigen__0 = eigen__1)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.37 thf(sP4,plain,sP4 <=> (((cF @ (cG @ eigen__0)) = (cF @ (cG @ eigen__1))) => ((cG @ eigen__0) = (cG @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.37 thf(sP5,plain,sP5 <=> ((cF @ (cG @ eigen__0)) = (cF @ (cG @ eigen__1))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.37 thf(sP6,plain,sP6 <=> (![X1:c]:(((cG @ eigen__0) = (cG @ X1)) => (eigen__0 = X1))),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.37 thf(sP7,plain,sP7 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.37 thf(sP8,plain,sP8 <=> ((cG @ eigen__0) = (cG @ eigen__1)),introduced(definition,[new_symbols(definition,[sP8])])). % 0.13/0.37 thf(sP9,plain,sP9 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP9])])). % 0.13/0.37 thf(sP10,plain,sP10 <=> (![X1:b]:(((cF @ (cG @ eigen__0)) = (cF @ X1)) => ((cG @ eigen__0) = X1))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.13/0.37 thf(sP11,plain,sP11 <=> (![X1:c]:(![X2:c]:(((cG @ X1) = (cG @ X2)) => (X1 = X2)))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.13/0.37 thf(cTHM48_EXPD,conjecture,((~(((![X1:b]:(![X2:b]:((![X3:a>$o]:((X3 @ (cF @ X1)) => (X3 @ (cF @ X2)))) => (![X3:b>$o]:((X3 @ X1) => (X3 @ X2)))))) => (~((![X1:c]:(![X2:c]:((![X3:b>$o]:((X3 @ (cG @ X1)) => (X3 @ (cG @ X2)))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))))))) => (![X1:c]:(![X2:c]:((![X3:a>$o]:((X3 @ (cF @ (cG @ X1))) => (X3 @ (cF @ (cG @ X2))))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2)))))))). % 0.13/0.37 thf(h0,negated_conjecture,(~(((~(((![X1:b]:(![X2:b]:((![X3:a>$o]:((X3 @ (cF @ X1)) => (X3 @ (cF @ X2)))) => (![X3:b>$o]:((X3 @ X1) => (X3 @ X2)))))) => (~((![X1:c]:(![X2:c]:((![X3:b>$o]:((X3 @ (cG @ X1)) => (X3 @ (cG @ X2)))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))))))) => (![X1:c]:(![X2:c]:((![X3:a>$o]:((X3 @ (cF @ (cG @ X1))) => (X3 @ (cF @ (cG @ X2))))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))))),inference(assume_negation,[status(cth)],[cTHM48_EXPD])). % 0.13/0.37 thf(h1,assumption,(~(((![X1:b]:(![X2:b]:((![X3:a>$o]:((X3 @ (cF @ X1)) => (X3 @ (cF @ X2)))) => (![X3:b>$o]:((X3 @ X1) => (X3 @ X2)))))) => (~((![X1:c]:(![X2:c]:((![X3:b>$o]:((X3 @ (cG @ X1)) => (X3 @ (cG @ X2)))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))))))),introduced(assumption,[])). % 0.13/0.37 thf(h2,assumption,(~((![X1:c]:(![X2:c]:((![X3:a>$o]:((X3 @ (cF @ (cG @ X1))) => (X3 @ (cF @ (cG @ X2))))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2)))))))),introduced(assumption,[])). % 0.13/0.37 thf(h3,assumption,(![X1:b]:(![X2:b]:((![X3:a>$o]:((X3 @ (cF @ X1)) => (X3 @ (cF @ X2)))) => (![X3:b>$o]:((X3 @ X1) => (X3 @ X2)))))),introduced(assumption,[])). % 0.13/0.37 thf(h4,assumption,(![X1:c]:(![X2:c]:((![X3:b>$o]:((X3 @ (cG @ X1)) => (X3 @ (cG @ X2)))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2)))))),introduced(assumption,[])). % 0.13/0.37 thf(h5,assumption,(~((![X1:c]:((![X2:a>$o]:((X2 @ (cF @ (cG @ eigen__0))) => (X2 @ (cF @ (cG @ X1))))) => (![X2:c>$o]:((X2 @ eigen__0) => (X2 @ X1))))))),introduced(assumption,[])). % 0.13/0.37 thf(h6,assumption,(~(((![X1:a>$o]:((X1 @ (cF @ (cG @ eigen__0))) => (X1 @ (cF @ (cG @ eigen__1))))) => (![X1:c>$o]:((X1 @ eigen__0) => (X1 @ eigen__1)))))),introduced(assumption,[])). % 0.13/0.37 thf(h7,assumption,(![X1:a>$o]:((X1 @ (cF @ (cG @ eigen__0))) => (X1 @ (cF @ (cG @ eigen__1))))),introduced(assumption,[])). % 0.13/0.37 thf(h8,assumption,(~((![X1:c>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])). % 0.13/0.37 thf(h9,assumption,(~((sP1 => sP7))),introduced(assumption,[])). % 0.13/0.37 thf(h10,assumption,sP1,introduced(assumption,[])). % 0.13/0.37 thf(h11,assumption,(~(sP7)),introduced(assumption,[])). % 0.13/0.37 thf(1,plain,(~(sP11) | sP6),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(2,plain,(~(sP6) | sP3),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(3,plain,((~(sP3) | ~(sP8)) | sP9),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(4,plain,((~(sP1) | sP7) | ~(sP9)),inference(mating_rule,[status(thm)],[])). % 0.13/0.37 thf(5,plain,(~(sP2) | sP10),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(6,plain,(~(sP10) | sP4),inference(all_rule,[status(thm)],[])). % 0.13/0.37 thf(7,plain,((~(sP4) | ~(sP5)) | sP8),inference(prop_rule,[status(thm)],[])). % 0.13/0.37 thf(8,plain,sP2,inference(normalize,[status(thm)],[h3]). % 0.13/0.37 thf(9,plain,sP11,inference(normalize,[status(thm)],[h4]). % 0.13/0.37 thf(10,plain,sP5,inference(normalize,[status(thm)],[h7]). % 0.13/0.37 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,h10,h11])). % 0.13/0.37 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,11,h10,h11])). % 0.13/0.37 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,12,h9])). % 0.13/0.37 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,13,h7,h8])). % 0.13/0.37 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,14,h6])). % 0.13/0.37 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,15,h5])). % 0.13/0.37 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,16,h3,h4])). % 0.13/0.37 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,17,h1,h2])). % 0.13/0.37 thf(0,theorem,((~(((![X1:b]:(![X2:b]:((![X3:a>$o]:((X3 @ (cF @ X1)) => (X3 @ (cF @ X2)))) => (![X3:b>$o]:((X3 @ X1) => (X3 @ X2)))))) => (~((![X1:c]:(![X2:c]:((![X3:b>$o]:((X3 @ (cG @ X1)) => (X3 @ (cG @ X2)))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))))))) => (![X1:c]:(![X2:c]:((![X3:a>$o]:((X3 @ (cF @ (cG @ X1))) => (X3 @ (cF @ (cG @ X2))))) => (![X3:c>$o]:((X3 @ X1) => (X3 @ X2))))))),inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])). % 0.13/0.37 % SZS output end Proof %------------------------------------------------------------------------------