%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV107^7 : TPTP v9.2.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n004.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 03:06:47 PM UTC 2025 % Result : Theorem 12.28s 11.51s % Output : Proof 12.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWV107^7 : TPTP v9.2.0. Released v5.5.0. % 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n004.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 14:18:53 EDT 2025 % 0.13/0.34 % CPUTime : % 12.28/11.51 % SZS status Theorem % 12.28/11.51 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0 % 12.28/11.51 % Inferences: 187 % 12.28/11.51 % SZS output start Proof % 12.28/11.51 thf(ty_mu, type, mu : $tType). % 12.28/11.51 thf(ty_n0, type, n0 : mu). % 12.28/11.51 thf(ty_eigen__6, type, eigen__6 : $i). % 12.28/11.51 thf(ty_n999, type, n999 : mu). % 12.28/11.51 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 12.28/11.51 thf(ty_eigen__2, type, eigen__2 : $i). % 12.28/11.51 thf(ty_eigen__7, type, eigen__7 : $i). % 12.28/11.51 thf(ty_minus, type, minus : (mu>mu>mu)). % 12.28/11.51 thf(ty_n6, type, n6 : mu). % 12.28/11.51 thf(ty_eigen__4, type, eigen__4 : $i). % 12.28/11.51 thf(ty_eigen__5, type, eigen__5 : $i). % 12.28/11.51 thf(ty_eigen__3, type, eigen__3 : $i). % 12.28/11.51 thf(ty_eigen__8, type, eigen__8 : $i). % 12.28/11.51 thf(ty_eigen__9, type, eigen__9 : $i). % 12.28/11.51 thf(ty_n1, type, n1 : mu). % 12.28/11.51 thf(ty_n2, type, n2 : mu). % 12.28/11.51 thf(ty_n3, type, n3 : mu). % 12.28/11.51 thf(ty_geq, type, geq : (mu>mu>$i>$o)). % 12.28/11.51 thf(ty_true, type, true : ($i>$o)). % 12.28/11.51 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 12.28/11.51 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ n2) @ n0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X4)))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((~(((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X8))) => (~((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X8)))))))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => (true @ X8))))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 12.28/11.51 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__5) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~(((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X5))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (true @ X5)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])). % 12.28/11.51 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__7) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 12.28/11.51 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~(((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ n2) @ n0) @ X5))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X8))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => ((~(((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X9))) => (~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X9)))))))) => (![X9:$i]:(((rel_s4 @ X8) @ X9) => (true @ X9)))))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 12.28/11.51 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ n2) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~(((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X7))) => (~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X7)))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (true @ X7)))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 12.28/11.51 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__8) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 12.28/11.51 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__6) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X4)))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__7])])). % 12.28/11.51 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__4) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ n2) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((~(((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X6))) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X6)))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (true @ X6))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 12.28/11.51 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X4)))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 12.28/11.51 thf(sP2,plain,sP2 <=> ((~(((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (((geq @ n2) @ n0) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X1)))))))) => (![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~(((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X5))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (true @ X5)))))))))))))))),introduced(definition,[new_symbols(definition,[sP2])])). % 12.28/11.51 thf(sP3,plain,sP3 <=> (((rel_s4 @ eigen__3) @ eigen__4) => ((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ n2) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((~(((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X6))) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X6)))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (true @ X6)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 12.28/11.51 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ n2) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((~(((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X6))) => (~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X6)))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => (true @ X6)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 12.28/11.51 thf(sP5,plain,sP5 <=> (((rel_s4 @ eigen__5) @ eigen__6) => ((![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => sP1)),introduced(definition,[new_symbols(definition,[sP5])])). % 12.28/11.51 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((rel_s4 @ eigen__7) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__7) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 12.28/11.51 thf(sP7,plain,sP7 <=> ((![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 12.28/11.51 thf(sP8,plain,sP8 <=> (((rel_s4 @ eigen__4) @ eigen__5) => sP2),introduced(definition,[new_symbols(definition,[sP8])])). % 12.28/11.51 thf(sP9,plain,sP9 <=> ((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => sP4),introduced(definition,[new_symbols(definition,[sP9])])). % 12.28/11.51 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s4 @ eigen__8) @ X1) => ((~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))))),introduced(definition,[new_symbols(definition,[sP10])])). % 12.28/11.51 thf(sP11,plain,sP11 <=> (![X1:$i]:(((rel_s4 @ eigen__7) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 12.28/11.51 thf(sP12,plain,sP12 <=> (((rel_s4 @ eigen__2) @ eigen__3) => ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ n2) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~(((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X7))) => (~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X7)))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (true @ X7))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 12.28/11.51 thf(sP13,plain,sP13 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))),introduced(definition,[new_symbols(definition,[sP13])])). % 12.28/11.51 thf(sP14,plain,sP14 <=> (((rel_s4 @ eigen__7) @ eigen__8) => sP7),introduced(definition,[new_symbols(definition,[sP14])])). % 12.28/11.51 thf(sP15,plain,sP15 <=> ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X1))) => (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ n2) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~(((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X7))) => (~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X7)))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (true @ X7)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 12.28/11.51 thf(sP16,plain,sP16 <=> (![X1:$i]:(((rel_s4 @ eigen__5) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~(((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X5))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => (true @ X5))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 12.28/11.51 thf(sP17,plain,sP17 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~(((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ n2) @ n0) @ X5))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X8))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => ((~(((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X9))) => (~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X9)))))))) => (![X9:$i]:(((rel_s4 @ X8) @ X9) => (true @ X9))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP17])])). % 12.28/11.51 thf(sP18,plain,sP18 <=> ((~(((![X1:$i]:(((rel_s4 @ eigen__9) @ X1) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__9) @ X1) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X1)))))))) => (![X1:$i]:(((rel_s4 @ eigen__9) @ X1) => (true @ X1)))),introduced(definition,[new_symbols(definition,[sP18])])). % 12.28/11.51 thf(sP19,plain,sP19 <=> (![X1:$i]:(((rel_s4 @ eigen__9) @ X1) => (true @ X1))),introduced(definition,[new_symbols(definition,[sP19])])). % 12.28/11.51 thf(sP20,plain,sP20 <=> ((![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X1))) => sP1),introduced(definition,[new_symbols(definition,[sP20])])). % 12.28/11.51 thf(sP21,plain,sP21 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ n2) @ n0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X4)))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((~(((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X8))) => (~((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X8)))))))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => (true @ X8)))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 12.28/11.51 thf(sP22,plain,sP22 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ n2) @ n0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X3)))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X5))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~(((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X7))) => (~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X7)))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (true @ X7))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP22])])). % 12.28/11.51 thf(sP23,plain,sP23 <=> (((rel_s4 @ eigen__6) @ eigen__7) => sP6),introduced(definition,[new_symbols(definition,[sP23])])). % 12.28/11.51 thf(sP24,plain,sP24 <=> (((rel_s4 @ eigen__8) @ eigen__9) => sP18),introduced(definition,[new_symbols(definition,[sP24])])). % 12.28/11.51 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 12.28/11.51 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 12.28/11.51 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 12.28/11.51 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 12.28/11.51 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 12.28/11.51 thf(def_mvalid,definition,(mvalid = (!!))). % 12.28/11.51 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 12.28/11.51 thf(quaternion_ds1_inuse_0019,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~((~((~(((~((~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ n2) @ n0) @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((~((~((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X8))))))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => ((~((~((~(((~((~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X9))))))) => (~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X9)))))))))))) => (![X9:$i]:(((rel_s4 @ X8) @ X9) => (true @ X9)))))))))))))))))))))))))). % 12.28/11.51 thf(h1,negated_conjecture,(~(sP17)),inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0019])). % 12.28/11.51 thf(1,plain,(~(sP13) | sP19),inference(all_rule,[status(thm)],[])). % 12.28/11.51 thf(2,plain,(sP18 | ~(sP19)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(3,plain,(sP24 | ~(sP18)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(4,plain,(sP10 | ~(sP24)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])). % 12.28/11.51 thf(5,plain,(sP7 | ~(sP10)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(6,plain,(sP14 | ~(sP7)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(7,plain,(sP11 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 12.28/11.51 thf(8,plain,(sP6 | ~(sP11)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(9,plain,(sP23 | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(10,plain,(sP1 | ~(sP23)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])). % 12.28/11.51 thf(11,plain,(sP20 | ~(sP1)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(12,plain,(sP5 | ~(sP20)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(13,plain,(sP16 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])). % 12.28/11.51 thf(14,plain,(sP2 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(15,plain,(sP8 | ~(sP2)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(16,plain,(sP4 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 12.28/11.51 thf(17,plain,(sP9 | ~(sP4)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(18,plain,(sP3 | ~(sP9)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(19,plain,(sP22 | ~(sP3)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 12.28/11.51 thf(20,plain,(sP15 | ~(sP22)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(21,plain,(sP12 | ~(sP15)),inference(prop_rule,[status(thm)],[])). % 12.28/11.51 thf(22,plain,(sP21 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 12.28/11.51 thf(23,plain,(sP17 | ~(sP21)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 12.28/11.51 thf(ttrue,axiom,(mvalid @ (mbox_s4 @ true))). % 12.28/11.51 thf(24,plain,sP13,inference(preprocess,[status(thm)],[ttrue]). % 12.28/11.51 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,h1])). % 12.28/11.51 thf(26,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[25,h0])). % 12.28/11.51 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X3))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => ((~((~((~(((~((~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ n2) @ n0) @ X5))))))) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X5)))))))))))) => (![X5:$i]:(((rel_s4 @ X4) @ X5) => ((~((~((![X6:$i]:(((rel_s4 @ X5) @ X6) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X6))))))) => (![X6:$i]:(((rel_s4 @ X5) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => ((~((~((![X8:$i]:(((rel_s4 @ X7) @ X8) => (((geq @ ((minus @ n6) @ n1)) @ n0) @ X8))))))) => (![X8:$i]:(((rel_s4 @ X7) @ X8) => ((~((~((~(((~((~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n3) @ n1)) @ n0) @ X9))))))) => (~((![X9:$i]:(((rel_s4 @ X8) @ X9) => (((geq @ ((minus @ n999) @ n1)) @ n0) @ X9)))))))))))) => (![X9:$i]:(((rel_s4 @ X8) @ X9) => (true @ X9))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[25,h1])). % 12.28/11.51 % SZS output end Proof %------------------------------------------------------------------------------