%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SEU355+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 : n024.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 14:50:30 EDT 2022 % Result : Theorem 0.20s 0.41s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n024.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 : Sun Jun 19 10:36:47 EDT 2022 % 0.13/0.33 % CPUTime : % 0.20/0.41 % SZS status Theorem % 0.20/0.41 (* PROOF-FOUND *) % 0.20/0.41 (* BEGIN-PROOF *) % 0.20/0.41 % SZS output start Proof % 0.20/0.41 1. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.20/0.41 2. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.20/0.41 3. (in T_2 (empty_set)) (-. (in T_2 (empty_set))) ### Axiom % 0.20/0.41 4. (empty (empty_set)) (-. (empty (empty_set))) ### Axiom % 0.20/0.41 5. (-. ((in T_2 (empty_set)) /\ (empty (empty_set)))) (empty (empty_set)) (in T_2 (empty_set)) ### NotAnd 3 4 % 0.20/0.41 6. (All B, (-. ((in T_2 B) /\ (empty B)))) (in T_2 (empty_set)) (empty (empty_set)) ### All 5 % 0.20/0.41 7. (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (in T_2 (empty_set)) ### All 6 % 0.20/0.41 8. (-. ((element T_2 (the_carrier T_0)) => ((in T_2 (empty_set)) => (related T_0 T_2 T_1)))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### ConjTree 7 % 0.20/0.41 9. (-. (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) ### NotAllEx 8 % 0.20/0.41 10. (-. (relstr_set_smaller T_0 (empty_set) T_1)) (relstr_set_smaller T_0 (empty_set) T_1) ### Axiom % 0.20/0.41 11. ((relstr_set_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1))))) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### Equiv 9 10 % 0.20/0.41 12. ((element T_1 (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1)))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### Imply 2 11 % 0.20/0.41 13. (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) C) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D C))))))) (element T_1 (the_carrier T_0)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### All 12 % 0.20/0.41 14. (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 D C)))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 13 % 0.20/0.41 15. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 D C))))))))) (element T_1 (the_carrier T_0)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) ### Imply 1 14 % 0.20/0.41 16. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 15 % 0.20/0.41 17. (rel_str T_0) (-. (rel_str T_0)) ### Axiom % 0.20/0.41 18. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom % 0.20/0.41 19. (in T_3 (empty_set)) (-. (in T_3 (empty_set))) ### Axiom % 0.20/0.41 20. (empty (empty_set)) (-. (empty (empty_set))) ### Axiom % 0.20/0.41 21. (-. ((in T_3 (empty_set)) /\ (empty (empty_set)))) (empty (empty_set)) (in T_3 (empty_set)) ### NotAnd 19 20 % 0.20/0.41 22. (All B, (-. ((in T_3 B) /\ (empty B)))) (in T_3 (empty_set)) (empty (empty_set)) ### All 21 % 0.20/0.41 23. (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (in T_3 (empty_set)) ### All 22 % 0.20/0.41 24. (-. ((element T_3 (the_carrier T_0)) => ((in T_3 (empty_set)) => (related T_0 T_1 T_3)))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### ConjTree 23 % 0.20/0.41 25. (-. (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) ### NotAllEx 24 % 0.20/0.41 26. (-. (relstr_element_smaller T_0 (empty_set) T_1)) (relstr_element_smaller T_0 (empty_set) T_1) ### Axiom % 0.20/0.41 27. ((relstr_element_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D))))) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### Equiv 25 26 % 0.20/0.41 28. ((element T_1 (the_carrier T_0)) => ((relstr_element_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D)))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### Imply 18 27 % 0.20/0.41 29. (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 (empty_set) C) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 C D))))))) (element T_1 (the_carrier T_0)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### All 28 % 0.20/0.41 30. (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 C D)))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 29 % 0.20/0.41 31. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) ### Imply 17 30 % 0.20/0.41 32. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 31 % 0.20/0.41 33. (-. ((relstr_set_smaller T_0 (empty_set) T_1) /\ (relstr_element_smaller T_0 (empty_set) T_1))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (element T_1 (the_carrier T_0)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAnd 16 32 % 0.20/0.41 34. (-. ((element T_1 (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) T_1) /\ (relstr_element_smaller T_0 (empty_set) T_1)))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) ### NotImply 33 % 0.20/0.41 35. (-. (All B, ((element B (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) B) /\ (relstr_element_smaller T_0 (empty_set) B))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAllEx 34 % 0.20/0.41 36. (-. ((rel_str T_0) => (All B, ((element B (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) B) /\ (relstr_element_smaller T_0 (empty_set) B)))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) ### NotImply 35 % 0.20/0.42 37. (-. (All A, ((rel_str A) => (All B, ((element B (the_carrier A)) => ((relstr_set_smaller A (empty_set) B) /\ (relstr_element_smaller A (empty_set) B))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAllEx 36 % 0.20/0.42 % SZS output end Proof % 0.20/0.42 (* END-PROOF *) %------------------------------------------------------------------------------