%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SYO001^1 : 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 : n016.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 03:24:38 PM UTC 2025 % Result : Theorem 0.13s 0.38s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYO001^1 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.35 % Computer : n016.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 01:36:23 EDT 2025 % 0.13/0.36 % CPUTime : % 0.13/0.38 % SZS status Theorem % 0.13/0.38 % Mode: mode213 % 0.13/0.38 % Inferences: 7 % 0.13/0.38 % SZS output start Proof % 0.13/0.38 thf(ty_eigen__2, type, eigen__2 : $i). % 0.13/0.38 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.38 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.38 thf(ty_eigen__3, type, eigen__3 : ($i>$o)). % 0.13/0.38 thf(sP1,plain,sP1 <=> (eigen__3 @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.38 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.38 thf(sP3,plain,sP3 <=> ((eigen__0 = eigen__1) => (eigen__1 = eigen__0)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.38 thf(sP4,plain,sP4 <=> (eigen__1 = eigen__0),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.38 thf(sP5,plain,sP5 <=> (eigen__1 = eigen__2),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.38 thf(sP6,plain,sP6 <=> (eigen__3 @ eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.38 thf(sP7,plain,sP7 <=> (![X1:$i]:((eigen__0 = X1) => (X1 = eigen__0))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.38 thf(sP8,plain,sP8 <=> (eigen__0 = eigen__2),introduced(definition,[new_symbols(definition,[sP8])])). % 0.13/0.38 thf(sP9,plain,sP9 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP9])])). % 0.13/0.38 thf(def_leibeq,definition,(leibeq = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))). % 0.13/0.38 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (~((![X4:$i>$o]:((X4 @ X2) => (X4 @ X3)))))))) => (![X4:$i>$o]:((X4 @ X1) => (X4 @ X3)))))))). % 0.13/0.38 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (~((![X4:$i>$o]:((X4 @ X2) => (X4 @ X3)))))))) => (![X4:$i>$o]:((X4 @ X1) => (X4 @ X3))))))))),inference(assume_negation,[status(cth)],[conj])). % 0.13/0.38 thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:((~(((![X3:$i>$o]:((X3 @ eigen__0) => (X3 @ X1))) => (~((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2)))))))) => (![X3:$i>$o]:((X3 @ eigen__0) => (X3 @ X2)))))))),introduced(assumption,[])). % 0.13/0.38 thf(h2,assumption,(~((![X1:$i]:((~(((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ eigen__1))) => (~((![X2:$i>$o]:((X2 @ eigen__1) => (X2 @ X1)))))))) => (![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))))))),introduced(assumption,[])). % 0.13/0.38 thf(h3,assumption,(~(((~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (~((![X1:$i>$o]:((X1 @ eigen__1) => (X1 @ eigen__2)))))))) => (![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__2)))))),introduced(assumption,[])). % 0.13/0.38 thf(h4,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (~((![X1:$i>$o]:((X1 @ eigen__1) => (X1 @ eigen__2)))))))),introduced(assumption,[])). % 0.13/0.38 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__2))))),introduced(assumption,[])). % 0.13/0.38 thf(h6,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])). % 0.13/0.38 thf(h7,assumption,(![X1:$i>$o]:((X1 @ eigen__1) => (X1 @ eigen__2))),introduced(assumption,[])). % 0.13/0.38 thf(h8,assumption,(~((sP1 => sP6))),introduced(assumption,[])). % 0.13/0.38 thf(h9,assumption,sP1,introduced(assumption,[])). % 0.13/0.38 thf(h10,assumption,(~(sP6)),introduced(assumption,[])). % 0.13/0.38 thf(1,plain,(((~(sP9) | sP8) | ~(sP4)) | ~(sP5)),inference(confrontation_rule,[status(thm)],[])). % 0.13/0.38 thf(2,plain,((~(sP1) | sP6) | ~(sP8)),inference(mating_rule,[status(thm)],[])). % 0.13/0.38 thf(3,plain,((~(sP3) | ~(sP9)) | sP4),inference(prop_rule,[status(thm)],[])). % 0.13/0.38 thf(4,plain,(~(sP7) | sP3),inference(all_rule,[status(thm)],[])). % 0.13/0.38 thf(5,plain,(~(sP2) | sP7),inference(all_rule,[status(thm)],[])). % 0.13/0.38 thf(6,plain,sP2,inference(eq_sym,[status(thm)],[])). % 0.13/0.38 thf(7,plain,sP9,inference(normalize,[status(thm)],[h6]). % 0.13/0.38 thf(8,plain,sP5,inference(normalize,[status(thm)],[h7]). % 0.13/0.38 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,h9,h10])). % 0.13/0.38 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,9,h9,h10])). % 0.13/0.38 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h5,10,h8])). % 0.13/0.38 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,11,h6,h7])). % 0.13/0.38 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,12,h4,h5])). % 0.13/0.38 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,13,h3])). % 0.13/0.38 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,14,h2])). % 0.13/0.38 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,15,h1])). % 0.13/0.38 thf(0,theorem,(![X1:$i]:(![X2:$i]:(![X3:$i]:((~(((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (~((![X4:$i>$o]:((X4 @ X2) => (X4 @ X3)))))))) => (![X4:$i>$o]:((X4 @ X1) => (X4 @ X3))))))),inference(contra,[status(thm),contra(discharge,[h0])],[16,h0])). % 0.13/0.38 % SZS output end Proof %------------------------------------------------------------------------------