%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n008.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 05:44:01 EDT 2022 % Result : Theorem 0.21s 0.44s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET794+4 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.35 % Computer : n008.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jul 11 10:54:53 EDT 2022 % 0.14/0.35 % CPUTime : % 0.21/0.44 % SZS status Theorem % 0.21/0.44 (* PROOF-FOUND *) % 0.21/0.44 (* BEGIN-PROOF *) % 0.21/0.44 % SZS output start Proof % 0.21/0.44 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.21/0.44 2. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 0.21/0.44 3. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 0.21/0.44 4. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom % 0.21/0.44 5. (-. (apply T_3 T_2 T_0)) (apply T_3 T_2 T_0) ### Axiom % 0.21/0.44 6. (-. (apply T_3 T_0 T_2)) (apply T_3 T_0 T_2) ### Axiom % 0.21/0.44 7. (((member T_2 T_1) /\ (member T_0 T_1)) => ((apply T_3 T_2 T_0) \/ (apply T_3 T_0 T_2))) (-. (apply T_3 T_0 T_2)) (-. (apply T_3 T_2 T_0)) (member T_0 T_1) (member T_2 T_1) ### DisjTree 3 4 5 6 % 0.21/0.44 8. (All Y, (((member T_2 T_1) /\ (member Y T_1)) => ((apply T_3 T_2 Y) \/ (apply T_3 Y T_2)))) (member T_2 T_1) (member T_0 T_1) (-. (apply T_3 T_2 T_0)) (-. (apply T_3 T_0 T_2)) ### All 7 % 0.21/0.44 9. (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (-. (apply T_3 T_0 T_2)) (-. (apply T_3 T_2 T_0)) (member T_0 T_1) (member T_2 T_1) ### All 8 % 0.21/0.44 10. (member T_2 T_1) (-. (member T_2 T_1)) ### Axiom % 0.21/0.44 11. (T_3 != T_3) ### Refl(=) % 0.21/0.44 12. (T_0 = T_2) (T_2 != T_0) ### Sym(=) % 0.21/0.44 13. (T_2 != T_2) ### Refl(=) % 0.21/0.44 14. (-. (apply T_3 T_0 T_2)) (apply T_3 T_2 T_2) (T_0 = T_2) ### P-NotP 11 12 13 % 0.21/0.44 15. ((member T_2 T_1) => (apply T_3 T_2 T_2)) (T_0 = T_2) (-. (apply T_3 T_0 T_2)) (member T_2 T_1) ### Imply 10 14 % 0.21/0.44 16. (All X, ((member X T_1) => (apply T_3 X X))) (member T_2 T_1) (-. (apply T_3 T_0 T_2)) (T_0 = T_2) ### All 15 % 0.21/0.44 17. (((member T_2 T_1) /\ (apply T_3 T_2 T_0)) => (T_0 = T_2)) (All X, ((member X T_1) => (apply T_3 X X))) (member T_0 T_1) (-. (apply T_3 T_0 T_2)) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (member T_2 T_1) ### DisjTree 2 9 16 % 0.21/0.44 18. (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X))) (member T_2 T_1) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (-. (apply T_3 T_0 T_2)) (member T_0 T_1) (All X, ((member X T_1) => (apply T_3 X X))) ### All 17 % 0.21/0.44 19. (-. ((member T_2 T_1) => (apply T_3 T_0 T_2))) (All X, ((member X T_1) => (apply T_3 X X))) (member T_0 T_1) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X))) ### NotImply 18 % 0.21/0.44 20. (-. (All X, ((member X T_1) => (apply T_3 T_0 X)))) (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_3 X X))) ### NotAllEx 19 % 0.21/0.44 21. (-. ((member T_0 T_1) /\ (All X, ((member X T_1) => (apply T_3 T_0 X))))) (All X, ((member X T_1) => (apply T_3 X X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X))) (member T_0 T_1) ### NotAnd 1 20 % 0.21/0.44 22. (-. (least T_0 T_3 T_1)) (member T_0 T_1) (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (All X, ((member X T_1) => (apply T_3 X X))) ### Definition-Pseudo(least) 21 % 0.21/0.44 23. ((member T_0 T_1) /\ (All X, (((member X T_1) /\ (apply T_3 X T_0)) => (T_0 = X)))) (All X, ((member X T_1) => (apply T_3 X X))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (-. (least T_0 T_3 T_1)) ### And 22 % 0.21/0.44 24. (min T_0 T_3 T_1) (-. (least T_0 T_3 T_1)) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (All X, ((member X T_1) => (apply T_3 X X))) ### Definition-Pseudo(min) 23 % 0.21/0.44 25. ((All X, ((member X T_1) => (apply T_3 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => (((apply T_3 X Y) /\ (apply T_3 Y X)) => (X = Y))))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_3 X Y) /\ (apply T_3 Y Z)) => (apply T_3 X Z)))))))) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) (-. (least T_0 T_3 T_1)) (min T_0 T_3 T_1) ### ConjTree 24 % 0.21/0.44 26. (order T_3 T_1) (min T_0 T_3 T_1) (-. (least T_0 T_3 T_1)) (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X))))) ### Definition-Pseudo(order) 25 % 0.21/0.44 27. ((order T_3 T_1) /\ (All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_3 X Y) \/ (apply T_3 Y X)))))) (-. (least T_0 T_3 T_1)) (min T_0 T_3 T_1) ### And 26 % 0.21/0.44 28. (total_order T_3 T_1) (min T_0 T_3 T_1) (-. (least T_0 T_3 T_1)) ### Definition-Pseudo(total_order) 27 % 0.21/0.44 29. (-. (((total_order T_3 T_1) /\ (min T_0 T_3 T_1)) => (least T_0 T_3 T_1))) ### ConjTree 28 % 0.21/0.44 30. (-. (All M, (((total_order T_3 T_1) /\ (min M T_3 T_1)) => (least M T_3 T_1)))) ### NotAllEx 29 % 0.21/0.44 31. (-. (All E, (All M, (((total_order T_3 E) /\ (min M T_3 E)) => (least M T_3 E))))) ### NotAllEx 30 % 0.21/0.44 32. (-. (All R, (All E, (All M, (((total_order R E) /\ (min M R E)) => (least M R E)))))) ### NotAllEx 31 % 0.21/0.44 % SZS output end Proof % 0.21/0.44 (* END-PROOF *) %------------------------------------------------------------------------------