TSTP Solution File: SEU375+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU375+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 : n005.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 14:50:40 EDT 2022
% Result : Theorem 0.87s 1.02s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU375+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 11:56:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.87/1.02 % SZS status Theorem
% 0.87/1.02 (* PROOF-FOUND *)
% 0.87/1.02 (* BEGIN-PROOF *)
% 0.87/1.02 % SZS output start Proof
% 0.87/1.02 1. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 0.87/1.02 2. (net_str T_1 T_0) (-. (net_str T_1 T_0)) ### Axiom
% 0.87/1.02 3. (-. (rel_str T_1)) (rel_str T_1) ### Axiom
% 0.87/1.02 4. ((net_str T_1 T_0) => (rel_str T_1)) (-. (rel_str T_1)) (net_str T_1 T_0) ### Imply 2 3
% 0.87/1.02 5. (All B, ((net_str B T_0) => (rel_str B))) (net_str T_1 T_0) (-. (rel_str T_1)) ### All 4
% 0.87/1.02 6. ((one_sorted_str T_0) => (All B, ((net_str B T_0) => (rel_str B)))) (-. (rel_str T_1)) (net_str T_1 T_0) (one_sorted_str T_0) ### Imply 1 5
% 0.87/1.02 7. (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (-. (rel_str T_1)) ### All 6
% 0.87/1.02 8. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 0.87/1.02 9. (net_str T_1 T_0) (-. (net_str T_1 T_0)) ### Axiom
% 0.87/1.02 10. (subnetstr T_2 T_0 T_1) (-. (subnetstr T_2 T_0 T_1)) ### Axiom
% 0.87/1.02 11. (full_subnetstr T_2 T_0 T_1) (-. (full_subnetstr T_2 T_0 T_1)) ### Axiom
% 0.87/1.02 12. (-. (full_subrelstr T_2 T_1)) (full_subrelstr T_2 T_1) ### Axiom
% 0.87/1.02 13. ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1)) (-. (full_subrelstr T_2 T_1)) ### And 12
% 0.87/1.02 14. ((full_subnetstr T_2 T_0 T_1) <=> ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1))) (-. (full_subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### Equiv 11 13
% 0.87/1.02 15. ((subnetstr T_2 T_0 T_1) => ((full_subnetstr T_2 T_0 T_1) <=> ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1)))) (full_subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) ### Imply 10 14
% 0.87/1.02 16. (All C, ((subnetstr C T_0 T_1) => ((full_subnetstr C T_0 T_1) <=> ((full_subrelstr C T_1) /\ (subrelstr C T_1))))) (subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 15
% 0.87/1.02 17. ((net_str T_1 T_0) => (All C, ((subnetstr C T_0 T_1) => ((full_subnetstr C T_0 T_1) <=> ((full_subrelstr C T_1) /\ (subrelstr C T_1)))))) (full_subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) ### Imply 9 16
% 0.87/1.02 18. (All B, ((net_str B T_0) => (All C, ((subnetstr C T_0 B) => ((full_subnetstr C T_0 B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 17
% 0.87/1.02 19. ((one_sorted_str T_0) => (All B, ((net_str B T_0) => (All C, ((subnetstr C T_0 B) => ((full_subnetstr C T_0 B) <=> ((full_subrelstr C B) /\ (subrelstr C B)))))))) (full_subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (one_sorted_str T_0) ### Imply 8 18
% 0.87/1.02 20. (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (one_sorted_str T_0) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (full_subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 19
% 0.87/1.02 21. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 0.87/1.02 22. (net_str T_1 T_0) (-. (net_str T_1 T_0)) ### Axiom
% 0.87/1.02 23. (subnetstr T_2 T_0 T_1) (-. (subnetstr T_2 T_0 T_1)) ### Axiom
% 0.87/1.03 24. (full_subnetstr T_2 T_0 T_1) (-. (full_subnetstr T_2 T_0 T_1)) ### Axiom
% 0.87/1.03 25. (-. (subrelstr T_2 T_1)) (subrelstr T_2 T_1) ### Axiom
% 0.87/1.03 26. ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1)) (-. (subrelstr T_2 T_1)) ### And 25
% 0.87/1.03 27. ((full_subnetstr T_2 T_0 T_1) <=> ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1))) (-. (subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### Equiv 24 26
% 0.87/1.03 28. ((subnetstr T_2 T_0 T_1) => ((full_subnetstr T_2 T_0 T_1) <=> ((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1)))) (full_subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) ### Imply 23 27
% 0.87/1.03 29. (All C, ((subnetstr C T_0 T_1) => ((full_subnetstr C T_0 T_1) <=> ((full_subrelstr C T_1) /\ (subrelstr C T_1))))) (subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 28
% 0.87/1.03 30. ((net_str T_1 T_0) => (All C, ((subnetstr C T_0 T_1) => ((full_subnetstr C T_0 T_1) <=> ((full_subrelstr C T_1) /\ (subrelstr C T_1)))))) (full_subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) ### Imply 22 29
% 0.87/1.03 31. (All B, ((net_str B T_0) => (All C, ((subnetstr C T_0 B) => ((full_subnetstr C T_0 B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 30
% 0.87/1.03 32. ((one_sorted_str T_0) => (All B, ((net_str B T_0) => (All C, ((subnetstr C T_0 B) => ((full_subnetstr C T_0 B) <=> ((full_subrelstr C B) /\ (subrelstr C B)))))))) (full_subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (one_sorted_str T_0) ### Imply 21 31
% 0.87/1.03 33. (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (one_sorted_str T_0) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (subrelstr T_2 T_1)) (full_subnetstr T_2 T_0 T_1) ### All 32
% 0.87/1.03 34. (element T_3 (the_carrier T_1)) (-. (element T_3 (the_carrier T_1))) ### Axiom
% 0.87/1.03 35. (element T_4 (the_carrier T_1)) (-. (element T_4 (the_carrier T_1))) ### Axiom
% 0.87/1.03 36. (element T_5 (the_carrier T_2)) (-. (element T_5 (the_carrier T_2))) ### Axiom
% 0.87/1.03 37. (element T_6 (the_carrier T_2)) (-. (element T_6 (the_carrier T_2))) ### Axiom
% 0.87/1.03 38. (T_3 = T_5) (T_5 != T_3) ### Sym(=)
% 0.87/1.03 39. (T_4 = T_6) (T_6 != T_4) ### Sym(=)
% 0.87/1.03 40. (related T_1 T_3 T_4) (-. (related T_1 T_3 T_4)) ### Axiom
% 0.87/1.03 41. (-. (empty_carrier T_2)) (empty_carrier T_2) ### Axiom
% 0.87/1.03 42. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 0.87/1.03 43. (one_sorted_str T_0) (-. (one_sorted_str T_0)) ### Axiom
% 0.87/1.03 44. (net_str T_1 T_0) (-. (net_str T_1 T_0)) ### Axiom
% 0.87/1.03 45. (subnetstr T_2 T_0 T_1) (-. (subnetstr T_2 T_0 T_1)) ### Axiom
% 0.87/1.03 46. (-. (net_str T_2 T_0)) (net_str T_2 T_0) ### Axiom
% 0.87/1.03 47. ((subnetstr T_2 T_0 T_1) => (net_str T_2 T_0)) (-. (net_str T_2 T_0)) (subnetstr T_2 T_0 T_1) ### Imply 45 46
% 0.87/1.03 48. (All C, ((subnetstr C T_0 T_1) => (net_str C T_0))) (subnetstr T_2 T_0 T_1) (-. (net_str T_2 T_0)) ### All 47
% 0.87/1.03 49. (((one_sorted_str T_0) /\ (net_str T_1 T_0)) => (All C, ((subnetstr C T_0 T_1) => (net_str C T_0)))) (-. (net_str T_2 T_0)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (one_sorted_str T_0) ### DisjTree 43 44 48
% 0.87/1.03 50. (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (net_str T_2 T_0)) ### All 49
% 0.87/1.03 51. (-. (rel_str T_2)) (rel_str T_2) ### Axiom
% 0.87/1.03 52. ((net_str T_2 T_0) => (rel_str T_2)) (-. (rel_str T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) ### Imply 50 51
% 0.87/1.03 53. (All B, ((net_str B T_0) => (rel_str B))) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (rel_str T_2)) ### All 52
% 0.87/1.03 54. ((one_sorted_str T_0) => (All B, ((net_str B T_0) => (rel_str B)))) (-. (rel_str T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) ### Imply 42 53
% 0.87/1.03 55. (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (rel_str T_2)) ### All 54
% 0.87/1.03 56. (-. (one_sorted_str T_2)) (one_sorted_str T_2) ### Axiom
% 0.87/1.03 57. ((rel_str T_2) => (one_sorted_str T_2)) (-. (one_sorted_str T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) ### Imply 55 56
% 0.87/1.03 58. (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (-. (one_sorted_str T_2)) ### All 57
% 0.87/1.04 59. (element T_5 (the_carrier T_2)) (-. (element T_5 (the_carrier T_2))) ### Axiom
% 0.87/1.04 60. (-. (empty (the_carrier T_2))) (empty (the_carrier T_2)) ### Axiom
% 0.87/1.04 61. (-. (in T_5 (the_carrier T_2))) (in T_5 (the_carrier T_2)) ### Axiom
% 0.87/1.04 62. ((element T_5 (the_carrier T_2)) => ((empty (the_carrier T_2)) \/ (in T_5 (the_carrier T_2)))) (-. (in T_5 (the_carrier T_2))) (-. (empty (the_carrier T_2))) (element T_5 (the_carrier T_2)) ### DisjTree 59 60 61
% 0.87/1.04 63. (All B, ((element T_5 B) => ((empty B) \/ (in T_5 B)))) (element T_5 (the_carrier T_2)) (-. (empty (the_carrier T_2))) (-. (in T_5 (the_carrier T_2))) ### All 62
% 0.87/1.04 64. (((-. (empty_carrier T_2)) /\ (one_sorted_str T_2)) => (-. (empty (the_carrier T_2)))) (-. (in T_5 (the_carrier T_2))) (element T_5 (the_carrier T_2)) (All B, ((element T_5 B) => ((empty B) \/ (in T_5 B)))) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) ### DisjTree 41 58 63
% 0.87/1.04 65. (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (All B, ((element T_5 B) => ((empty B) \/ (in T_5 B)))) (element T_5 (the_carrier T_2)) (-. (in T_5 (the_carrier T_2))) ### All 64
% 0.87/1.04 66. (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (-. (in T_5 (the_carrier T_2))) (element T_5 (the_carrier T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) ### All 65
% 0.87/1.04 67. (-. (empty_carrier T_2)) (empty_carrier T_2) ### Axiom
% 0.87/1.04 68. (element T_6 (the_carrier T_2)) (-. (element T_6 (the_carrier T_2))) ### Axiom
% 0.87/1.04 69. (-. (empty (the_carrier T_2))) (empty (the_carrier T_2)) ### Axiom
% 0.87/1.04 70. (-. (in T_6 (the_carrier T_2))) (in T_6 (the_carrier T_2)) ### Axiom
% 0.87/1.04 71. ((element T_6 (the_carrier T_2)) => ((empty (the_carrier T_2)) \/ (in T_6 (the_carrier T_2)))) (-. (in T_6 (the_carrier T_2))) (-. (empty (the_carrier T_2))) (element T_6 (the_carrier T_2)) ### DisjTree 68 69 70
% 0.87/1.04 72. (All B, ((element T_6 B) => ((empty B) \/ (in T_6 B)))) (element T_6 (the_carrier T_2)) (-. (empty (the_carrier T_2))) (-. (in T_6 (the_carrier T_2))) ### All 71
% 0.87/1.04 73. (((-. (empty_carrier T_2)) /\ (one_sorted_str T_2)) => (-. (empty (the_carrier T_2)))) (-. (in T_6 (the_carrier T_2))) (element T_6 (the_carrier T_2)) (All B, ((element T_6 B) => ((empty B) \/ (in T_6 B)))) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) ### DisjTree 67 58 72
% 0.87/1.04 74. (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (All B, ((element T_6 B) => ((empty B) \/ (in T_6 B)))) (element T_6 (the_carrier T_2)) (-. (in T_6 (the_carrier T_2))) ### All 73
% 0.87/1.04 75. (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (-. (in T_6 (the_carrier T_2))) (element T_6 (the_carrier T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) ### All 74
% 0.87/1.04 76. (-. (related T_2 T_5 T_6)) (related T_2 T_5 T_6) ### Axiom
% 0.87/1.04 77. ((element T_6 (the_carrier T_2)) => (((T_5 = T_3) /\ ((T_6 = T_4) /\ ((related T_1 T_3 T_4) /\ ((in T_5 (the_carrier T_2)) /\ (in T_6 (the_carrier T_2)))))) => (related T_2 T_5 T_6))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (element T_5 (the_carrier T_2)) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) ### DisjTree 37 38 39 40 66 75 76
% 0.87/1.04 78. (All F, ((element F (the_carrier T_2)) => (((T_5 = T_3) /\ ((F = T_4) /\ ((related T_1 T_3 T_4) /\ ((in T_5 (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 T_5 F)))) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (element T_5 (the_carrier T_2)) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 77
% 0.87/1.04 79. ((element T_5 (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((T_5 = T_3) /\ ((F = T_4) /\ ((related T_1 T_3 T_4) /\ ((in T_5 (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 T_5 F))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) ### Imply 36 78
% 0.87/1.04 80. (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = T_3) /\ ((F = T_4) /\ ((related T_1 T_3 T_4) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F)))))) (element T_5 (the_carrier T_2)) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 79
% 0.87/1.04 81. ((element T_4 (the_carrier T_1)) => (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = T_3) /\ ((F = T_4) /\ ((related T_1 T_3 T_4) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F))))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) ### Imply 35 80
% 0.87/1.04 82. (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = T_3) /\ ((F = D) /\ ((related T_1 T_3 D) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F)))))))) (element T_4 (the_carrier T_1)) (element T_5 (the_carrier T_2)) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 81
% 0.87/1.04 83. ((element T_3 (the_carrier T_1)) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = T_3) /\ ((F = D) /\ ((related T_1 T_3 D) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F))))))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) ### Imply 34 82
% 0.87/1.04 84. (All C, ((element C (the_carrier T_1)) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = C) /\ ((F = D) /\ ((related T_1 C D) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F)))))))))) (element T_3 (the_carrier T_1)) (element T_4 (the_carrier T_1)) (element T_5 (the_carrier T_2)) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 83
% 0.87/1.04 85. (((full_subrelstr T_2 T_1) /\ (subrelstr T_2 T_1)) => (All C, ((element C (the_carrier T_1)) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_2)) => (All F, ((element F (the_carrier T_2)) => (((E = C) /\ ((F = D) /\ ((related T_1 C D) /\ ((in E (the_carrier T_2)) /\ (in F (the_carrier T_2)))))) => (related T_2 E F))))))))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) ### DisjTree 20 33 84
% 0.87/1.04 86. (All B, (((full_subrelstr B T_1) /\ (subrelstr B T_1)) => (All C, ((element C (the_carrier T_1)) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related T_1 C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (one_sorted_str T_0) (net_str T_1 T_0) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (element T_3 (the_carrier T_1)) (element T_4 (the_carrier T_1)) (element T_5 (the_carrier T_2)) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 85
% 0.87/1.04 87. ((rel_str T_1) => (All B, (((full_subrelstr B T_1) /\ (subrelstr B T_1)) => (All C, ((element C (the_carrier T_1)) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related T_1 C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F))))))))))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) ### Imply 7 86
% 0.87/1.04 88. (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (element T_3 (the_carrier T_1)) (element T_4 (the_carrier T_1)) (element T_5 (the_carrier T_2)) (element T_6 (the_carrier T_2)) (T_3 = T_5) (T_4 = T_6) (related T_1 T_3 T_4) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All B, (((one_sorted_str T_0) /\ (net_str B T_0)) => (All C, ((subnetstr C T_0 B) => (net_str C T_0))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (related T_2 T_5 T_6)) ### All 87
% 0.87/1.05 89. (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (-. (related T_2 T_5 T_6)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (related T_1 T_3 T_4) (T_4 = T_6) (T_3 = T_5) (element T_6 (the_carrier T_2)) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### All 88
% 0.87/1.05 90. (-. ((element T_6 (the_carrier T_2)) => (((T_3 = T_5) /\ ((T_4 = T_6) /\ (related T_1 T_3 T_4))) => (related T_2 T_5 T_6)))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (element T_3 (the_carrier T_1)) (element T_4 (the_carrier T_1)) (element T_5 (the_carrier T_2)) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### ConjTree 89
% 0.87/1.05 91. (-. (All G, ((element G (the_carrier T_2)) => (((T_3 = T_5) /\ ((T_4 = G) /\ (related T_1 T_3 T_4))) => (related T_2 T_5 G))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (element T_5 (the_carrier T_2)) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 90
% 0.87/1.05 92. (-. ((element T_5 (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((T_3 = T_5) /\ ((T_4 = G) /\ (related T_1 T_3 T_4))) => (related T_2 T_5 G)))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (element T_3 (the_carrier T_1)) (element T_4 (the_carrier T_1)) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### NotImply 91
% 0.87/1.05 93. (-. (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((T_3 = F) /\ ((T_4 = G) /\ (related T_1 T_3 T_4))) => (related T_2 F G))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (element T_4 (the_carrier T_1)) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 92
% 0.87/1.05 94. (-. ((element T_4 (the_carrier T_1)) => (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((T_3 = F) /\ ((T_4 = G) /\ (related T_1 T_3 T_4))) => (related T_2 F G)))))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (element T_3 (the_carrier T_1)) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### NotImply 93
% 0.87/1.05 95. (-. (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((T_3 = F) /\ ((E = G) /\ (related T_1 T_3 E))) => (related T_2 F G))))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (element T_3 (the_carrier T_1)) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 94
% 0.87/1.05 96. (-. ((element T_3 (the_carrier T_1)) => (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((T_3 = F) /\ ((E = G) /\ (related T_1 T_3 E))) => (related T_2 F G)))))))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (subnetstr T_2 T_0 T_1) (full_subnetstr T_2 T_0 T_1) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (-. (empty_carrier T_2)) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### NotImply 95
% 0.87/1.05 97. (-. (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((D = F) /\ ((E = G) /\ (related T_1 D E))) => (related T_2 F G))))))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (-. (empty_carrier T_2)) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (full_subnetstr T_2 T_0 T_1) (subnetstr T_2 T_0 T_1) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 96
% 0.87/1.05 98. (-. (((-. (empty_carrier T_2)) /\ ((full_subnetstr T_2 T_0 T_1) /\ (subnetstr T_2 T_0 T_1))) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier T_2)) => (All G, ((element G (the_carrier T_2)) => (((D = F) /\ ((E = G) /\ (related T_1 D E))) => (related T_2 F G)))))))))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (net_str T_1 T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### ConjTree 97
% 0.87/1.05 99. (-. (All C, (((-. (empty_carrier C)) /\ ((full_subnetstr C T_0 T_1) /\ (subnetstr C T_0 T_1))) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier C)) => (All G, ((element G (the_carrier C)) => (((D = F) /\ ((E = G) /\ (related T_1 D E))) => (related C F G))))))))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (net_str T_1 T_0) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 98
% 0.87/1.05 100. (-. (((-. (empty_carrier T_1)) /\ (net_str T_1 T_0)) => (All C, (((-. (empty_carrier C)) /\ ((full_subnetstr C T_0 T_1) /\ (subnetstr C T_0 T_1))) => (All D, ((element D (the_carrier T_1)) => (All E, ((element E (the_carrier T_1)) => (All F, ((element F (the_carrier C)) => (All G, ((element G (the_carrier C)) => (((D = F) /\ ((E = G) /\ (related T_1 D E))) => (related C F G)))))))))))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### ConjTree 99
% 0.87/1.05 101. (-. (All B, (((-. (empty_carrier B)) /\ (net_str B T_0)) => (All C, (((-. (empty_carrier C)) /\ ((full_subnetstr C T_0 B) /\ (subnetstr C T_0 B))) => (All D, ((element D (the_carrier B)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier C)) => (All G, ((element G (the_carrier C)) => (((D = F) /\ ((E = G) /\ (related B D E))) => (related C F G))))))))))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (one_sorted_str T_0) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 100
% 0.87/1.05 102. (-. ((one_sorted_str T_0) => (All B, (((-. (empty_carrier B)) /\ (net_str B T_0)) => (All C, (((-. (empty_carrier C)) /\ ((full_subnetstr C T_0 B) /\ (subnetstr C T_0 B))) => (All D, ((element D (the_carrier B)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier C)) => (All G, ((element G (the_carrier C)) => (((D = F) /\ ((E = G) /\ (related B D E))) => (related C F G)))))))))))))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) ### NotImply 101
% 0.87/1.05 103. (-. (All A, ((one_sorted_str A) => (All B, (((-. (empty_carrier B)) /\ (net_str B A)) => (All C, (((-. (empty_carrier C)) /\ ((full_subnetstr C A B) /\ (subnetstr C A B))) => (All D, ((element D (the_carrier B)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier C)) => (All G, ((element G (the_carrier C)) => (((D = F) /\ ((E = G) /\ (related B D E))) => (related C F G))))))))))))))))) (All A, (All B, (((one_sorted_str A) /\ (net_str B A)) => (All C, ((subnetstr C A B) => (net_str C A)))))) (All A, (((-. (empty_carrier A)) /\ (one_sorted_str A)) => (-. (empty (the_carrier A))))) (All A, ((rel_str A) => (one_sorted_str A))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (All C, ((subnetstr C A B) => ((full_subnetstr C A B) <=> ((full_subrelstr C B) /\ (subrelstr C B))))))))) (All A, ((one_sorted_str A) => (All B, ((net_str B A) => (rel_str B))))) (All A, ((rel_str A) => (All B, (((full_subrelstr B A) /\ (subrelstr B A)) => (All C, ((element C (the_carrier A)) => (All D, ((element D (the_carrier A)) => (All E, ((element E (the_carrier B)) => (All F, ((element F (the_carrier B)) => (((E = C) /\ ((F = D) /\ ((related A C D) /\ ((in E (the_carrier B)) /\ (in F (the_carrier B)))))) => (related B E F)))))))))))))) ### NotAllEx 102
% 0.87/1.05 % SZS output end Proof
% 0.87/1.05 (* END-PROOF *)
%------------------------------------------------------------------------------