TSTP Solution File: SEU321+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU321+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 : n014.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 14:50:14 EDT 2022
% Result : Theorem 2.30s 2.58s
% Output : Proof 2.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n014.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 : Mon Jun 20 06:30:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.30/2.58 % SZS status Theorem
% 2.30/2.58 (* PROOF-FOUND *)
% 2.30/2.58 (* BEGIN-PROOF *)
% 2.30/2.58 % SZS output start Proof
% 2.30/2.58 1. (-. (empty_carrier T_0)) (empty_carrier T_0) ### Axiom
% 2.30/2.58 2. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 2.30/2.58 3. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 2.30/2.58 4. (-. (empty (the_carrier T_0))) (empty (the_carrier T_0)) ### Axiom
% 2.30/2.58 5. (in T_1 (the_carrier T_0)) (-. (in T_1 (the_carrier T_0))) ### Axiom
% 2.30/2.58 6. ((the_carrier T_0) = (empty_set)) ((the_carrier T_0) != (empty_set)) ### Axiom
% 2.30/2.58 7. (-. (subset (the_carrier T_0) (empty_set))) ((the_carrier T_0) = (empty_set)) ### Refl(subset) 6
% 2.30/2.58 8. (-. (element (the_carrier T_0) (powerset (empty_set)))) (element (the_carrier T_0) (powerset (empty_set))) ### Axiom
% 2.30/2.58 9. ((element (the_carrier T_0) (powerset (empty_set))) <=> (subset (the_carrier T_0) (empty_set))) (-. (element (the_carrier T_0) (powerset (empty_set)))) ((the_carrier T_0) = (empty_set)) ### Equiv 7 8
% 2.30/2.58 10. (All B, ((element (the_carrier T_0) (powerset B)) <=> (subset (the_carrier T_0) B))) ((the_carrier T_0) = (empty_set)) (-. (element (the_carrier T_0) (powerset (empty_set)))) ### All 9
% 2.30/2.58 11. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (element (the_carrier T_0) (powerset (empty_set)))) ((the_carrier T_0) = (empty_set)) ### All 10
% 2.30/2.58 12. (empty (empty_set)) (-. (empty (empty_set))) ### Axiom
% 2.30/2.58 13. (-. ((in T_1 (the_carrier T_0)) /\ ((element (the_carrier T_0) (powerset (empty_set))) /\ (empty (empty_set))))) (empty (empty_set)) ((the_carrier T_0) = (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_1 (the_carrier T_0)) ### DisjTree 5 11 12
% 2.30/2.58 14. (All C, (-. ((in T_1 (the_carrier T_0)) /\ ((element (the_carrier T_0) (powerset C)) /\ (empty C))))) (in T_1 (the_carrier T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ((the_carrier T_0) = (empty_set)) (empty (empty_set)) ### All 13
% 2.30/2.58 15. (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty (empty_set)) ((the_carrier T_0) = (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_1 (the_carrier T_0)) ### All 14
% 2.30/2.58 16. ((element T_1 (the_carrier T_0)) => ((empty (the_carrier T_0)) \/ (in T_1 (the_carrier T_0)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ((the_carrier T_0) = (empty_set)) (empty (empty_set)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (-. (empty (the_carrier T_0))) (element T_1 (the_carrier T_0)) ### DisjTree 3 4 15
% 2.30/2.58 17. (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (element T_1 (the_carrier T_0)) (-. (empty (the_carrier T_0))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty (empty_set)) ((the_carrier T_0) = (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### All 16
% 2.30/2.58 18. (((-. (empty_carrier T_0)) /\ (one_sorted_str T_0)) => (-. (empty (the_carrier T_0)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ((the_carrier T_0) = (empty_set)) (empty (empty_set)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (element T_1 (the_carrier T_0)) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (one_sorted_str T_0) (-. (empty_carrier T_0)) ### DisjTree 1 2 17
% 2.30/2.58 19. (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (element T_1 (the_carrier T_0)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty (empty_set)) ((the_carrier T_0) = (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### All 18
% 2.30/2.58 20. (-. ((the_carrier T_0) != (empty_set))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty (empty_set)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (element T_1 (the_carrier T_0)) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) ### NotNot 19
% 2.30/2.58 21. (element T_2 (powerset (the_carrier T_0))) (-. (element T_2 (powerset (the_carrier T_0)))) ### Axiom
% 2.30/2.58 22. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 2.30/2.58 23. (-. (in T_1 T_2)) (in T_1 T_2) ### Axiom
% 2.30/2.58 24. (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (in T_1 (subset_complement (the_carrier T_0) T_2)) ### Axiom
% 2.30/2.58 25. ((element T_1 (the_carrier T_0)) => ((-. (in T_1 T_2)) => (in T_1 (subset_complement (the_carrier T_0) T_2)))) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (-. (in T_1 T_2)) (element T_1 (the_carrier T_0)) ### DisjTree 22 23 24
% 2.30/2.58 26. (All C, ((element C (the_carrier T_0)) => ((-. (in C T_2)) => (in C (subset_complement (the_carrier T_0) T_2))))) (element T_1 (the_carrier T_0)) (-. (in T_1 T_2)) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) ### All 25
% 2.30/2.58 27. ((element T_2 (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((-. (in C T_2)) => (in C (subset_complement (the_carrier T_0) T_2)))))) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (-. (in T_1 T_2)) (element T_1 (the_carrier T_0)) (element T_2 (powerset (the_carrier T_0))) ### Imply 21 26
% 2.30/2.58 28. (All B, ((element B (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((-. (in C B)) => (in C (subset_complement (the_carrier T_0) B))))))) (element T_2 (powerset (the_carrier T_0))) (element T_1 (the_carrier T_0)) (-. (in T_1 T_2)) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) ### All 27
% 2.30/2.58 29. (((the_carrier T_0) != (empty_set)) => (All B, ((element B (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((-. (in C B)) => (in C (subset_complement (the_carrier T_0) B)))))))) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (-. (in T_1 T_2)) (element T_2 (powerset (the_carrier T_0))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (element T_1 (the_carrier T_0)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) ### Imply 20 28
% 2.30/2.58 30. (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty (empty_set)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (element T_1 (the_carrier T_0)) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (element T_2 (powerset (the_carrier T_0))) (-. (in T_1 T_2)) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) ### All 29
% 2.30/2.58 31. (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (-. (in T_1 T_2)) (element T_2 (powerset (the_carrier T_0))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (element T_1 (the_carrier T_0)) (empty (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) ### All 30
% 2.30/2.58 32. (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty (empty_set)) (element T_1 (the_carrier T_0)) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (element T_2 (powerset (the_carrier T_0))) (-. (in T_1 T_2)) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) ### All 31
% 2.37/2.61 33. (element T_2 (powerset (the_carrier T_0))) (-. (element T_2 (powerset (the_carrier T_0)))) ### Axiom
% 2.37/2.61 34. (in T_1 (subset_complement (the_carrier T_0) T_2)) (-. (in T_1 (subset_complement (the_carrier T_0) T_2))) ### Axiom
% 2.37/2.61 35. (in T_1 T_2) (-. (in T_1 T_2)) ### Axiom
% 2.37/2.61 36. ((element T_2 (powerset (the_carrier T_0))) => (-. ((in T_1 (subset_complement (the_carrier T_0) T_2)) /\ (in T_1 T_2)))) (in T_1 T_2) (in T_1 (subset_complement (the_carrier T_0) T_2)) (element T_2 (powerset (the_carrier T_0))) ### DisjTree 33 34 35
% 2.37/2.61 37. (All C, ((element C (powerset (the_carrier T_0))) => (-. ((in T_1 (subset_complement (the_carrier T_0) C)) /\ (in T_1 C))))) (element T_2 (powerset (the_carrier T_0))) (in T_1 (subset_complement (the_carrier T_0) T_2)) (in T_1 T_2) ### All 36
% 2.37/2.61 38. (All B, (All C, ((element C (powerset (the_carrier T_0))) => (-. ((in B (subset_complement (the_carrier T_0) C)) /\ (in B C)))))) (in T_1 T_2) (in T_1 (subset_complement (the_carrier T_0) T_2)) (element T_2 (powerset (the_carrier T_0))) ### All 37
% 2.37/2.61 39. (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (element T_2 (powerset (the_carrier T_0))) (in T_1 (subset_complement (the_carrier T_0) T_2)) (in T_1 T_2) ### All 38
% 2.37/2.61 40. (-. (-. (in T_1 T_2))) (in T_1 (subset_complement (the_carrier T_0) T_2)) (element T_2 (powerset (the_carrier T_0))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) ### NotNot 39
% 2.37/2.61 41. (-. ((in T_1 (subset_complement (the_carrier T_0) T_2)) <=> (-. (in T_1 T_2)))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (element T_2 (powerset (the_carrier T_0))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (element T_1 (the_carrier T_0)) (empty (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ### NotEquiv 32 40
% 2.37/2.61 42. ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (element T_1 (the_carrier T_0)) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (element T_2 (powerset (the_carrier T_0))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (-. ((in T_1 (subset_complement (the_carrier T_0) T_2)) <=> (-. (in T_1 T_2)))) ### ConjTree 41
% 2.37/2.61 43. (-. ((element T_1 (the_carrier T_0)) => ((in T_1 (subset_complement (the_carrier T_0) T_2)) <=> (-. (in T_1 T_2))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (element T_2 (powerset (the_carrier T_0))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) ### NotImply 42
% 2.37/2.61 44. (-. (All C, ((element C (the_carrier T_0)) => ((in C (subset_complement (the_carrier T_0) T_2)) <=> (-. (in C T_2)))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (element T_2 (powerset (the_carrier T_0))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) ### NotAllEx 43
% 2.37/2.61 45. (-. ((element T_2 (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((in C (subset_complement (the_carrier T_0) T_2)) <=> (-. (in C T_2))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_0)) (one_sorted_str T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) ### NotImply 44
% 2.37/2.61 46. (-. (All B, ((element B (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((in C (subset_complement (the_carrier T_0) B)) <=> (-. (in C B)))))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (one_sorted_str T_0) (-. (empty_carrier T_0)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) ### NotAllEx 45
% 2.37/2.61 47. (-. (((-. (empty_carrier T_0)) /\ (one_sorted_str T_0)) => (All B, ((element B (powerset (the_carrier T_0))) => (All C, ((element C (the_carrier T_0)) => ((in C (subset_complement (the_carrier T_0) B)) <=> (-. (in C B))))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) ### ConjTree 46
% 2.37/2.62 48. (-. (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (All B, ((element B (powerset (the_carrier A))) => (All C, ((element C (the_carrier A)) => ((in C (subset_complement (the_carrier A) B)) <=> (-. (in C B)))))))))) ((empty (empty_set)) /\ ((v1_membered (empty_set)) /\ ((v2_membered (empty_set)) /\ ((v3_membered (empty_set)) /\ ((v4_membered (empty_set)) /\ (v5_membered (empty_set))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((A != (empty_set)) => (All B, ((element B (powerset A)) => (All C, ((element C A) => ((-. (in C B)) => (in C (subset_complement A B))))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, ((element C (powerset A)) => (-. ((in B (subset_complement A C)) /\ (in B C))))))) ### NotAllEx 47
% 2.37/2.62 % SZS output end Proof
% 2.37/2.62 (* END-PROOF *)
%------------------------------------------------------------------------------