%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET776+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n028.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 : 600s % DateTime : Tue Jul 19 05:43:53 EDT 2022 % Result : Theorem 1.06s 1.22s % Output : Proof 1.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET776+4 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n028.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 08:46:43 EDT 2022 % 0.13/0.33 % CPUTime : % 1.06/1.22 % SZS status Theorem % 1.06/1.22 (* PROOF-FOUND *) % 1.06/1.22 (* BEGIN-PROOF *) % 1.06/1.22 % SZS output start Proof % 1.06/1.22 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 1.06/1.22 2. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 1.06/1.22 3. (member T_3 T_1) (-. (member T_3 T_1)) ### Axiom % 1.06/1.22 4. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 1.06/1.22 5. (member T_4 T_1) (-. (member T_4 T_1)) ### Axiom % 1.06/1.22 6. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 1.06/1.22 7. (member T_4 T_1) (-. (member T_4 T_1)) ### Axiom % 1.06/1.22 8. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 1.06/1.22 9. (apply T_5 T_4 T_0) (-. (apply T_5 T_4 T_0)) ### Axiom % 1.06/1.22 10. (-. (apply T_6 T_0 T_4)) (apply T_6 T_0 T_4) ### Axiom % 1.06/1.22 11. ((apply T_6 T_4 T_0) /\ (apply T_6 T_0 T_4)) (-. (apply T_6 T_0 T_4)) ### And 10 % 1.06/1.22 12. ((apply T_5 T_4 T_0) <=> ((apply T_6 T_4 T_0) /\ (apply T_6 T_0 T_4))) (-. (apply T_6 T_0 T_4)) (apply T_5 T_4 T_0) ### Equiv 9 11 % 1.06/1.22 13. (((member T_4 T_1) /\ (member T_0 T_1)) => ((apply T_5 T_4 T_0) <=> ((apply T_6 T_4 T_0) /\ (apply T_6 T_0 T_4)))) (apply T_5 T_4 T_0) (-. (apply T_6 T_0 T_4)) (member T_0 T_1) (member T_4 T_1) ### DisjTree 7 8 12 % 1.06/1.22 14. (All B, (((member T_4 T_1) /\ (member B T_1)) => ((apply T_5 T_4 B) <=> ((apply T_6 T_4 B) /\ (apply T_6 B T_4))))) (member T_4 T_1) (member T_0 T_1) (-. (apply T_6 T_0 T_4)) (apply T_5 T_4 T_0) ### All 13 % 1.06/1.22 15. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (apply T_5 T_4 T_0) (-. (apply T_6 T_0 T_4)) (member T_0 T_1) (member T_4 T_1) ### All 14 % 1.06/1.22 16. (apply T_6 T_4 T_2) (-. (apply T_6 T_4 T_2)) ### Axiom % 1.06/1.22 17. (-. (apply T_6 T_0 T_2)) (apply T_6 T_0 T_2) ### Axiom % 1.06/1.22 18. (((member T_0 T_1) /\ ((member T_4 T_1) /\ (member T_2 T_1))) => (((apply T_6 T_0 T_4) /\ (apply T_6 T_4 T_2)) => (apply T_6 T_0 T_2))) (-. (apply T_6 T_0 T_2)) (apply T_6 T_4 T_2) (apply T_5 T_4 T_0) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (member T_2 T_1) (member T_4 T_1) (member T_0 T_1) ### DisjTree 4 5 6 15 16 17 % 1.06/1.22 19. (All Z, (((member T_0 T_1) /\ ((member T_4 T_1) /\ (member Z T_1))) => (((apply T_6 T_0 T_4) /\ (apply T_6 T_4 Z)) => (apply T_6 T_0 Z)))) (member T_0 T_1) (member T_4 T_1) (member T_2 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (apply T_5 T_4 T_0) (apply T_6 T_4 T_2) (-. (apply T_6 T_0 T_2)) ### All 18 % 1.06/1.22 20. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 1.06/1.22 21. (member T_3 T_1) (-. (member T_3 T_1)) ### Axiom % 1.06/1.22 22. (apply T_5 T_2 T_3) (-. (apply T_5 T_2 T_3)) ### Axiom % 1.06/1.22 23. (-. (apply T_6 T_2 T_3)) (apply T_6 T_2 T_3) ### Axiom % 1.06/1.22 24. ((apply T_6 T_2 T_3) /\ (apply T_6 T_3 T_2)) (-. (apply T_6 T_2 T_3)) ### And 23 % 1.06/1.22 25. ((apply T_5 T_2 T_3) <=> ((apply T_6 T_2 T_3) /\ (apply T_6 T_3 T_2))) (-. (apply T_6 T_2 T_3)) (apply T_5 T_2 T_3) ### Equiv 22 24 % 1.06/1.22 26. (((member T_2 T_1) /\ (member T_3 T_1)) => ((apply T_5 T_2 T_3) <=> ((apply T_6 T_2 T_3) /\ (apply T_6 T_3 T_2)))) (apply T_5 T_2 T_3) (-. (apply T_6 T_2 T_3)) (member T_3 T_1) (member T_2 T_1) ### DisjTree 20 21 25 % 1.06/1.22 27. (All B, (((member T_2 T_1) /\ (member B T_1)) => ((apply T_5 T_2 B) <=> ((apply T_6 T_2 B) /\ (apply T_6 B T_2))))) (member T_2 T_1) (member T_3 T_1) (-. (apply T_6 T_2 T_3)) (apply T_5 T_2 T_3) ### All 26 % 1.06/1.22 28. (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (apply T_5 T_2 T_3) (-. (apply T_6 T_2 T_3)) (member T_3 T_1) (member T_2 T_1) ### All 27 % 1.06/1.22 29. (-. (apply T_6 T_0 T_3)) (apply T_6 T_0 T_3) ### Axiom % 1.06/1.22 30. (((member T_0 T_1) /\ ((member T_2 T_1) /\ (member T_3 T_1))) => (((apply T_6 T_0 T_2) /\ (apply T_6 T_2 T_3)) => (apply T_6 T_0 T_3))) (-. (apply T_6 T_0 T_3)) (apply T_5 T_2 T_3) (apply T_6 T_4 T_2) (apply T_5 T_4 T_0) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (member T_4 T_1) (All Z, (((member T_0 T_1) /\ ((member T_4 T_1) /\ (member Z T_1))) => (((apply T_6 T_0 T_4) /\ (apply T_6 T_4 Z)) => (apply T_6 T_0 Z)))) (member T_3 T_1) (member T_2 T_1) (member T_0 T_1) ### DisjTree 1 2 3 19 28 29 % 1.06/1.22 31. (All Z, (((member T_0 T_1) /\ ((member T_2 T_1) /\ (member Z T_1))) => (((apply T_6 T_0 T_2) /\ (apply T_6 T_2 Z)) => (apply T_6 T_0 Z)))) (member T_0 T_1) (member T_2 T_1) (member T_3 T_1) (All Z, (((member T_0 T_1) /\ ((member T_4 T_1) /\ (member Z T_1))) => (((apply T_6 T_0 T_4) /\ (apply T_6 T_4 Z)) => (apply T_6 T_0 Z)))) (member T_4 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (apply T_5 T_4 T_0) (apply T_6 T_4 T_2) (apply T_5 T_2 T_3) (-. (apply T_6 T_0 T_3)) ### All 30 % 1.06/1.22 32. (All Y, (All Z, (((member T_0 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 T_0 Y) /\ (apply T_6 Y Z)) => (apply T_6 T_0 Z))))) (-. (apply T_6 T_0 T_3)) (apply T_5 T_2 T_3) (apply T_6 T_4 T_2) (apply T_5 T_4 T_0) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (member T_4 T_1) (All Z, (((member T_0 T_1) /\ ((member T_4 T_1) /\ (member Z T_1))) => (((apply T_6 T_0 T_4) /\ (apply T_6 T_4 Z)) => (apply T_6 T_0 Z)))) (member T_3 T_1) (member T_2 T_1) (member T_0 T_1) ### All 31 % 1.06/1.22 33. (member T_0 T_1) (member T_2 T_1) (member T_3 T_1) (member T_4 T_1) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (apply T_5 T_4 T_0) (apply T_6 T_4 T_2) (apply T_5 T_2 T_3) (-. (apply T_6 T_0 T_3)) (All Y, (All Z, (((member T_0 T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 T_0 Y) /\ (apply T_6 Y Z)) => (apply T_6 T_0 Z))))) ### All 32 % 1.06/1.22 34. (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) (-. (apply T_6 T_0 T_3)) (apply T_5 T_2 T_3) (apply T_6 T_4 T_2) (apply T_5 T_4 T_0) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (member T_4 T_1) (member T_3 T_1) (member T_2 T_1) (member T_0 T_1) ### All 33 % 1.06/1.22 35. (-. (((member T_4 T_1) /\ ((member T_2 T_1) /\ ((member T_0 T_1) /\ (member T_3 T_1)))) => (((apply T_5 T_4 T_0) /\ ((apply T_5 T_2 T_3) /\ (apply T_6 T_4 T_2))) => (apply T_6 T_0 T_3)))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) ### ConjTree 34 % 1.06/1.22 36. (-. (All Y2, (((member T_4 T_1) /\ ((member T_2 T_1) /\ ((member T_0 T_1) /\ (member Y2 T_1)))) => (((apply T_5 T_4 T_0) /\ ((apply T_5 T_2 Y2) /\ (apply T_6 T_4 T_2))) => (apply T_6 T_0 Y2))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) ### NotAllEx 35 % 1.06/1.22 37. (-. (All Y1, (All Y2, (((member T_4 T_1) /\ ((member T_2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 T_4 Y1) /\ ((apply T_5 T_2 Y2) /\ (apply T_6 T_4 T_2))) => (apply T_6 Y1 Y2)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) ### NotAllEx 36 % 1.06/1.22 38. (-. (All X2, (All Y1, (All Y2, (((member T_4 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 T_4 Y1) /\ ((apply T_5 X2 Y2) /\ (apply T_6 T_4 X2))) => (apply T_6 Y1 Y2))))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) ### NotAllEx 37 % 1.06/1.22 39. (-. (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 X1 Y1) /\ ((apply T_5 X2 Y2) /\ (apply T_6 X1 X2))) => (apply T_6 Y1 Y2)))))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z)))))) ### NotAllEx 38 % 1.06/1.22 40. ((All X, ((member X T_1) => (apply T_6 X X))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_6 X Y) /\ (apply T_6 Y Z)) => (apply T_6 X Z))))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) (-. (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 X1 Y1) /\ ((apply T_5 X2 Y2) /\ (apply T_6 X1 X2))) => (apply T_6 Y1 Y2)))))))) ### And 39 % 1.06/1.22 41. (pre_order T_6 T_1) (-. (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 X1 Y1) /\ ((apply T_5 X2 Y2) /\ (apply T_6 X1 X2))) => (apply T_6 Y1 Y2)))))))) (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A)))))) ### Definition-Pseudo(pre_order) 40 % 1.06/1.22 42. (-. (((pre_order T_6 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply T_5 A B) <=> ((apply T_6 A B) /\ (apply T_6 B A))))))) => (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply T_5 X1 Y1) /\ ((apply T_5 X2 Y2) /\ (apply T_6 X1 X2))) => (apply T_6 Y1 Y2))))))))) ### ConjTree 41 % 1.06/1.22 43. (-. (All R, (((pre_order T_6 T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply T_6 A B) /\ (apply T_6 B A))))))) => (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply R X1 Y1) /\ ((apply R X2 Y2) /\ (apply T_6 X1 X2))) => (apply T_6 Y1 Y2)))))))))) ### NotAllEx 42 % 1.06/1.22 44. (-. (All P, (All R, (((pre_order P T_1) /\ (All A, (All B, (((member A T_1) /\ (member B T_1)) => ((apply R A B) <=> ((apply P A B) /\ (apply P B A))))))) => (All X1, (All X2, (All Y1, (All Y2, (((member X1 T_1) /\ ((member X2 T_1) /\ ((member Y1 T_1) /\ (member Y2 T_1)))) => (((apply R X1 Y1) /\ ((apply R X2 Y2) /\ (apply P X1 X2))) => (apply P Y1 Y2))))))))))) ### NotAllEx 43 % 1.06/1.22 45. (-. (All E, (All P, (All R, (((pre_order P E) /\ (All A, (All B, (((member A E) /\ (member B E)) => ((apply R A B) <=> ((apply P A B) /\ (apply P B A))))))) => (All X1, (All X2, (All Y1, (All Y2, (((member X1 E) /\ ((member X2 E) /\ ((member Y1 E) /\ (member Y2 E)))) => (((apply R X1 Y1) /\ ((apply R X2 Y2) /\ (apply P X1 X2))) => (apply P Y1 Y2)))))))))))) ### NotAllEx 44 % 1.06/1.22 % SZS output end Proof % 1.06/1.22 (* END-PROOF *) %------------------------------------------------------------------------------