%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET617+3 : 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 : n007.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 05:42:49 EDT 2022 % Result : Theorem 283.53s 284.27s % Output : Proof 283.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 07:43:31 EDT 2022 % 0.12/0.33 % CPUTime : % 283.53/284.27 % SZS status Theorem % 283.53/284.27 (* PROOF-FOUND *) % 283.53/284.27 (* BEGIN-PROOF *) % 283.53/284.27 % SZS output start Proof % 283.53/284.27 1. ((difference T_0 (empty_set)) != T_0) ((difference T_0 (empty_set)) = T_0) ### Axiom % 283.53/284.27 2. (All B, ((difference B (empty_set)) = B)) ((difference T_0 (empty_set)) != T_0) ### All 1 % 283.53/284.27 3. ((difference (empty_set) T_0) != (empty_set)) ((difference (empty_set) T_0) = (empty_set)) ### Axiom % 283.53/284.27 4. (All B, ((difference (empty_set) B) = (empty_set))) ((difference (empty_set) T_0) != (empty_set)) ### All 3 % 283.53/284.27 5. ((union (difference T_0 (empty_set)) (difference (empty_set) T_0)) != (union T_0 (empty_set))) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((difference B (empty_set)) = B)) ### NotEqual 2 4 % 283.53/284.27 6. (T_0 != T_0) ### Refl(=) % 283.53/284.27 7. (T_0 != T_0) ### Refl(=) % 283.53/284.27 8. ((union (difference T_0 (empty_set)) (difference (empty_set) T_0)) != T_0) ((union T_0 (empty_set)) = T_0) (All B, ((difference B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) ### TransEq 5 6 7 % 283.53/284.27 9. (All B, ((union B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((difference B (empty_set)) = B)) ((union (difference T_0 (empty_set)) (difference (empty_set) T_0)) != T_0) ### All 8 % 283.53/284.27 10. ((symmetric_difference T_0 (empty_set)) != T_0) (All B, ((difference B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((union B (empty_set)) = B)) ### Definition-Pseudo(symmetric_difference) 9 % 283.53/284.27 11. ((difference T_0 (empty_set)) = T_0) (T_0 != (difference T_0 (empty_set))) ### Sym(=) % 283.53/284.27 12. ((empty_set) != (difference (empty_set) T_0)) ((difference (empty_set) T_0) = (empty_set)) ### Sym(=) % 283.53/284.27 13. (All B, ((difference (empty_set) B) = (empty_set))) ((empty_set) != (difference (empty_set) T_0)) ### All 12 % 283.53/284.27 14. ((union T_0 (empty_set)) != (union (difference T_0 (empty_set)) (difference (empty_set) T_0))) (All B, ((difference (empty_set) B) = (empty_set))) ((difference T_0 (empty_set)) = T_0) ### NotEqual 11 13 % 283.53/284.27 15. ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union (difference (empty_set) T_0) (difference T_0 (empty_set)))) ### Refl(=) % 283.53/284.27 16. ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union (difference (empty_set) T_0) (difference T_0 (empty_set)))) ### Refl(=) % 283.53/284.27 17. ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union T_0 (empty_set))) ((union (difference T_0 (empty_set)) (difference (empty_set) T_0)) = (union (difference (empty_set) T_0) (difference T_0 (empty_set)))) ((difference T_0 (empty_set)) = T_0) (All B, ((difference (empty_set) B) = (empty_set))) ### TransEq-sym 14 15 16 % 283.53/284.27 18. ((union (difference T_0 (empty_set)) (difference (empty_set) T_0)) = (symmetric_difference (empty_set) T_0)) (All B, ((difference (empty_set) B) = (empty_set))) ((difference T_0 (empty_set)) = T_0) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union T_0 (empty_set))) ### Definition-Pseudo(symmetric_difference) 17 % 283.53/284.27 19. ((symmetric_difference T_0 (empty_set)) = (symmetric_difference (empty_set) T_0)) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union T_0 (empty_set))) ((difference T_0 (empty_set)) = T_0) (All B, ((difference (empty_set) B) = (empty_set))) ### Definition-Pseudo(symmetric_difference) 18 % 283.53/284.27 20. (All C, ((symmetric_difference T_0 C) = (symmetric_difference C T_0))) (All B, ((difference (empty_set) B) = (empty_set))) ((difference T_0 (empty_set)) = T_0) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != (union T_0 (empty_set))) ### All 19 % 283.53/284.27 21. (T_0 != T_0) ### Refl(=) % 283.53/284.27 22. (T_0 != T_0) ### Refl(=) % 283.53/284.27 23. ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != T_0) ((union T_0 (empty_set)) = T_0) ((difference T_0 (empty_set)) = T_0) (All B, ((difference (empty_set) B) = (empty_set))) (All C, ((symmetric_difference T_0 C) = (symmetric_difference C T_0))) ### TransEq 20 21 22 % 283.53/284.27 24. (All B, ((difference B (empty_set)) = B)) (All C, ((symmetric_difference T_0 C) = (symmetric_difference C T_0))) (All B, ((difference (empty_set) B) = (empty_set))) ((union T_0 (empty_set)) = T_0) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != T_0) ### All 23 % 283.53/284.27 25. (All B, (All C, ((symmetric_difference B C) = (symmetric_difference C B)))) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != T_0) ((union T_0 (empty_set)) = T_0) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((difference B (empty_set)) = B)) ### All 24 % 283.53/284.27 26. (All B, ((union B (empty_set)) = B)) (All B, ((difference B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) ((union (difference (empty_set) T_0) (difference T_0 (empty_set))) != T_0) (All B, (All C, ((symmetric_difference B C) = (symmetric_difference C B)))) ### All 25 % 283.53/284.27 27. ((symmetric_difference (empty_set) T_0) != T_0) (All B, (All C, ((symmetric_difference B C) = (symmetric_difference C B)))) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((difference B (empty_set)) = B)) (All B, ((union B (empty_set)) = B)) ### Definition-Pseudo(symmetric_difference) 26 % 283.53/284.27 28. (-. (((symmetric_difference T_0 (empty_set)) = T_0) /\ ((symmetric_difference (empty_set) T_0) = T_0))) (All B, (All C, ((symmetric_difference B C) = (symmetric_difference C B)))) (All B, ((union B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((difference B (empty_set)) = B)) ### NotAnd 10 27 % 283.53/284.27 29. (-. (All B, (((symmetric_difference B (empty_set)) = B) /\ ((symmetric_difference (empty_set) B) = B)))) (All B, ((difference B (empty_set)) = B)) (All B, ((difference (empty_set) B) = (empty_set))) (All B, ((union B (empty_set)) = B)) (All B, (All C, ((symmetric_difference B C) = (symmetric_difference C B)))) ### NotAllEx 28 % 283.53/284.27 % SZS output end Proof % 283.53/284.27 (* END-PROOF *) %------------------------------------------------------------------------------