%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM414+1 : 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 : n020.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 : Mon Jul 18 14:42:14 EDT 2022 % Result : Theorem 0.19s 0.42s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n020.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 : 600 % 0.13/0.34 % DateTime : Tue Jul 5 18:44:29 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.42 % SZS status Theorem % 0.19/0.42 (* PROOF-FOUND *) % 0.19/0.42 (* BEGIN-PROOF *) % 0.19/0.42 % SZS output start Proof % 0.19/0.42 1. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.19/0.42 2. (ordinal T_1) (-. (ordinal T_1)) ### Axiom % 0.19/0.42 3. (ordinal T_1) (-. (ordinal T_1)) ### Axiom % 0.19/0.42 4. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.19/0.42 5. (ordinal T_1) (-. (ordinal T_1)) ### Axiom % 0.19/0.42 6. (ordinal T_0) (-. (ordinal T_0)) ### Axiom % 0.19/0.42 7. (-. (ordinal_subset T_1 T_0)) (ordinal_subset T_1 T_0) ### Axiom % 0.19/0.42 8. (-. (ordinal_subset T_0 T_1)) (ordinal_subset T_0 T_1) ### Axiom % 0.19/0.42 9. (((ordinal T_1) /\ (ordinal T_0)) => ((ordinal_subset T_1 T_0) \/ (ordinal_subset T_0 T_1))) (-. (ordinal_subset T_0 T_1)) (-. (ordinal_subset T_1 T_0)) (ordinal T_0) (ordinal T_1) ### DisjTree 5 6 7 8 % 0.19/0.42 10. (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (ordinal T_1) (ordinal T_0) (-. (ordinal_subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) ### All 9 % 0.19/0.42 11. (-. (subset T_1 T_0)) (subset T_1 T_0) ### Axiom % 0.19/0.42 12. ((ordinal_subset T_1 T_0) <=> (subset T_1 T_0)) (-. (subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) (ordinal T_0) (ordinal T_1) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) ### Equiv 10 11 % 0.19/0.42 13. (((ordinal T_1) /\ (ordinal T_0)) => ((ordinal_subset T_1 T_0) <=> (subset T_1 T_0))) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (ordinal_subset T_0 T_1)) (-. (subset T_1 T_0)) (ordinal T_0) (ordinal T_1) ### DisjTree 3 4 12 % 0.19/0.42 14. (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) (ordinal T_1) (ordinal T_0) (-. (subset T_1 T_0)) (-. (ordinal_subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) ### All 13 % 0.19/0.42 15. (-. (subset T_0 T_1)) (subset T_0 T_1) ### Axiom % 0.19/0.42 16. ((ordinal_subset T_0 T_1) <=> (subset T_0 T_1)) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (ordinal T_0) (ordinal T_1) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) ### Equiv 14 15 % 0.19/0.42 17. (((ordinal T_0) /\ (ordinal T_1)) => ((ordinal_subset T_0 T_1) <=> (subset T_0 T_1))) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) ### DisjTree 1 2 16 % 0.19/0.42 18. (All B, (((ordinal T_0) /\ (ordinal B)) => ((ordinal_subset T_0 B) <=> (subset T_0 B)))) (ordinal T_0) (ordinal T_1) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) <=> (subset T_1 B)))) ### All 17 % 0.19/0.42 19. (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (-. (subset T_1 T_0)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) (All B, (((ordinal T_0) /\ (ordinal B)) => ((ordinal_subset T_0 B) <=> (subset T_0 B)))) ### All 18 % 0.19/0.42 20. (ordinal T_0) (ordinal T_1) (-. (subset T_0 T_1)) (All B, (((ordinal T_1) /\ (ordinal B)) => ((ordinal_subset T_1 B) \/ (ordinal_subset B T_1)))) (-. (subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) ### All 19 % 0.19/0.42 21. (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (-. (subset T_1 T_0)) (-. (subset T_0 T_1)) (ordinal T_1) (ordinal T_0) ### All 20 % 0.19/0.42 22. (T_1 != T_0) (T_0 = T_1) ### Sym(=) % 0.19/0.42 23. (-. (proper_subset T_0 T_1)) (T_1 != T_0) (ordinal T_0) (ordinal T_1) (-. (subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### Extension/test/not_d8_xboole_0 21 22 % 0.19/0.42 24. (T_1 != T_0) (T_1 = T_0) ### Axiom % 0.19/0.42 25. (-. (proper_subset T_1 T_0)) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (ordinal T_1) (ordinal T_0) (T_1 != T_0) (-. (proper_subset T_0 T_1)) ### Extension/test/not_d8_xboole_0 23 24 % 0.19/0.42 26. (-. ((ordinal T_0) => (-. ((-. (proper_subset T_1 T_0)) /\ ((T_1 != T_0) /\ (-. (proper_subset T_0 T_1))))))) (ordinal T_1) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### ConjTree 25 % 0.19/0.42 27. (-. (All B, ((ordinal B) => (-. ((-. (proper_subset T_1 B)) /\ ((T_1 != B) /\ (-. (proper_subset B T_1)))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (ordinal T_1) ### NotAllEx 26 % 0.19/0.42 28. (-. ((ordinal T_1) => (All B, ((ordinal B) => (-. ((-. (proper_subset T_1 B)) /\ ((T_1 != B) /\ (-. (proper_subset B T_1))))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) ### NotImply 27 % 0.19/0.42 29. (-. (All A, ((ordinal A) => (All B, ((ordinal B) => (-. ((-. (proper_subset A B)) /\ ((A != B) /\ (-. (proper_subset B A)))))))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) \/ (ordinal_subset B A))))) (All A, (All B, (((ordinal A) /\ (ordinal B)) => ((ordinal_subset A B) <=> (subset A B))))) ### NotAllEx 28 % 0.19/0.42 % SZS output end Proof % 0.19/0.42 (* END-PROOF *) %------------------------------------------------------------------------------