%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n021.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 14:49:35 EDT 2022 % Result : Theorem 29.24s 29.48s % Output : Proof 29.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n021.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 Jun 19 21:41:48 EDT 2022 % 0.12/0.34 % CPUTime : % 29.24/29.48 % SZS status Theorem % 29.24/29.48 (* PROOF-FOUND *) % 29.24/29.48 (* BEGIN-PROOF *) % 29.24/29.48 % SZS output start Proof % 29.24/29.48 1. (relation T_0) (-. (relation T_0)) ### Axiom % 29.24/29.48 2. (relation T_0) (-. (relation T_0)) ### Axiom % 29.24/29.48 3. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) ### Axiom % 29.24/29.48 4. (-. (is_connected_in T_0 (relation_field T_0))) (is_connected_in T_0 (relation_field T_0)) ### Axiom % 29.24/29.48 5. ((is_connected_in T_0 (relation_field T_0)) <=> (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) (-. (is_connected_in T_0 (relation_field T_0))) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) ### Equiv 3 4 % 29.24/29.48 6. (All B, ((is_connected_in T_0 B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) T_0)) /\ (-. (in (ordered_pair D C) T_0))))))))))) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (-. (is_connected_in T_0 (relation_field T_0))) ### All 5 % 29.24/29.48 7. ((relation T_0) => (All B, ((is_connected_in T_0 B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) T_0)) /\ (-. (in (ordered_pair D C) T_0)))))))))))) (-. (is_connected_in T_0 (relation_field T_0))) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (relation T_0) ### Imply 2 6 % 29.24/29.48 8. (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) (relation T_0) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (-. (is_connected_in T_0 (relation_field T_0))) ### All 7 % 29.24/29.48 9. (-. (connected T_0)) (connected T_0) ### Axiom % 29.24/29.48 10. ((connected T_0) <=> (is_connected_in T_0 (relation_field T_0))) (-. (connected T_0)) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (relation T_0) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) ### Equiv 8 9 % 29.24/29.48 11. ((relation T_0) => ((connected T_0) <=> (is_connected_in T_0 (relation_field T_0)))) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (-. (connected T_0)) (relation T_0) ### Imply 1 10 % 29.24/29.48 12. (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (relation T_0) (-. (connected T_0)) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) ### All 11 % 29.24/29.48 13. (relation T_0) (-. (relation T_0)) ### Axiom % 29.24/29.48 14. (relation T_0) (-. (relation T_0)) ### Axiom % 29.24/29.48 15. (connected T_0) (-. (connected T_0)) ### Axiom % 29.24/29.48 16. (-. (is_connected_in T_0 (relation_field T_0))) (is_connected_in T_0 (relation_field T_0)) ### Axiom % 29.24/29.48 17. ((connected T_0) <=> (is_connected_in T_0 (relation_field T_0))) (-. (is_connected_in T_0 (relation_field T_0))) (connected T_0) ### Equiv 15 16 % 29.24/29.48 18. ((relation T_0) => ((connected T_0) <=> (is_connected_in T_0 (relation_field T_0)))) (connected T_0) (-. (is_connected_in T_0 (relation_field T_0))) (relation T_0) ### Imply 14 17 % 29.24/29.48 19. (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (relation T_0) (-. (is_connected_in T_0 (relation_field T_0))) (connected T_0) ### All 18 % 29.24/29.48 20. (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))) ### Axiom % 29.24/29.48 21. ((is_connected_in T_0 (relation_field T_0)) <=> (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) (connected T_0) (relation T_0) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) ### Equiv 19 20 % 29.24/29.48 22. (All B, ((is_connected_in T_0 B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) T_0)) /\ (-. (in (ordered_pair D C) T_0))))))))))) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (relation T_0) (connected T_0) (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) ### All 21 % 29.24/29.48 23. ((relation T_0) => (All B, ((is_connected_in T_0 B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) T_0)) /\ (-. (in (ordered_pair D C) T_0)))))))))))) (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) (connected T_0) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (relation T_0) ### Imply 13 22 % 29.24/29.48 24. (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) (relation T_0) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (connected T_0) (-. (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))) ### All 23 % 29.24/29.48 25. (-. ((connected T_0) <=> (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0))))))))))) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) (relation T_0) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) ### NotEquiv 12 24 % 29.24/29.48 26. (-. ((relation T_0) => ((connected T_0) <=> (All B, (All C, (-. ((in B (relation_field T_0)) /\ ((in C (relation_field T_0)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) T_0)) /\ (-. (in (ordered_pair C B) T_0)))))))))))) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) ### NotImply 25 % 29.24/29.49 27. (-. (All A, ((relation A) => ((connected A) <=> (All B, (All C, (-. ((in B (relation_field A)) /\ ((in C (relation_field A)) /\ ((B != C) /\ ((-. (in (ordered_pair B C) A)) /\ (-. (in (ordered_pair C B) A))))))))))))) (All A, ((relation A) => (All B, ((is_connected_in A B) <=> (All C, (All D, (-. ((in C B) /\ ((in D B) /\ ((C != D) /\ ((-. (in (ordered_pair C D) A)) /\ (-. (in (ordered_pair D C) A))))))))))))) (All A, ((relation A) => ((connected A) <=> (is_connected_in A (relation_field A))))) ### NotAllEx 26 % 29.24/29.49 % SZS output end Proof % 29.24/29.49 (* END-PROOF *) %------------------------------------------------------------------------------