TSTP Solution File: GRP644+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n015.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 : Sat Jul 16 11:55:24 EDT 2022
% Result : Theorem 2.94s 3.09s
% Output : Proof 2.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n015.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 : Mon Jun 13 07:03:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.94/3.09 % SZS status Theorem
% 2.94/3.09 (* PROOF-FOUND *)
% 2.94/3.09 (* BEGIN-PROOF *)
% 2.94/3.09 % SZS output start Proof
% 2.94/3.09 1. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.94/3.09 2. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 2.94/3.09 3. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 2.94/3.09 4. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.94/3.09 5. (v1_group_1 T_1) (-. (v1_group_1 T_1)) ### Axiom
% 2.94/3.09 6. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 2.94/3.09 7. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.94/3.09 8. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 2.94/3.09 9. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 2.94/3.09 10. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.94/3.09 11. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.94/3.09 12. (-. (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0))) (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0)) ### Axiom
% 2.94/3.09 13. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ ((l1_group_1 T_0) /\ (m1_subset_1 T_2 (u1_struct_0 T_0)))))) => (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0))) (-. (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 7 8 9 10 11 12
% 2.94/3.09 14. (All B, (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ ((l1_group_1 T_0) /\ (m1_subset_1 B (u1_struct_0 T_0)))))) => (m1_subset_1 (k3_group_1 T_0 B) (u1_struct_0 T_0)))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0))) ### All 13
% 2.94/3.09 15. (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (-. (m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### All 14
% 2.94/3.09 16. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.94/3.09 17. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 2.94/3.09 18. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 2.94/3.09 19. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.94/3.09 20. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.94/3.09 21. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 2.94/3.09 22. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.94/3.09 23. (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1))) ### Axiom
% 2.94/3.09 24. (-. (r1_rlvect_1 T_1 T_2)) (r1_rlvect_1 T_1 T_2) ### Axiom
% 2.94/3.09 25. ((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 T_2)) (-. (r1_rlvect_1 T_1 T_2)) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) ### Equiv 23 24
% 2.94/3.09 26. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => ((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 T_2))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 T_2)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### Imply 22 25
% 2.94/3.09 27. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (r1_rlvect_1 T_1 T_2)) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) ### All 26
% 2.94/3.09 28. (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2)) ### Axiom
% 2.94/3.09 29. ((m1_group_2 T_1 T_0) => ((r1_rlvect_1 T_1 T_2) => (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2)))) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_group_2 T_1 T_0) ### DisjTree 21 27 28
% 2.94/3.09 30. (All C, ((m1_group_2 C T_0) => ((r1_rlvect_1 C T_2) => (r1_rlvect_1 C (k3_group_1 T_0 T_2))))) (m1_group_2 T_1 T_0) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) ### All 29
% 2.94/3.09 31. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (All C, ((m1_group_2 C T_0) => ((r1_rlvect_1 C T_2) => (r1_rlvect_1 C (k3_group_1 T_0 T_2)))))) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_group_2 T_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### Imply 20 30
% 2.94/3.09 32. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_group_2 C T_0) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 T_0 B))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_group_2 T_1 T_0) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) ### All 31
% 2.94/3.09 33. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_group_2 C T_0) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 T_0 B)))))))) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_group_2 T_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 16 17 18 19 32
% 2.94/3.09 34. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_group_2 T_1 T_0) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) ### All 33
% 2.94/3.09 35. (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1)) ### Axiom
% 2.94/3.09 36. ((r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2))) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_group_2 T_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### Equiv 34 35
% 2.94/3.09 37. ((m1_subset_1 (k3_group_1 T_0 T_2) (u1_struct_0 T_0)) => ((r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 (k3_group_1 T_0 T_2)))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (m1_group_2 T_1 T_0) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) ### Imply 15 36
% 2.94/3.09 38. (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C)))) (m1_group_2 T_1 T_0) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### All 37
% 2.94/3.12 39. (((v1_group_1 T_1) /\ (m1_group_2 T_1 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 C))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### DisjTree 5 6 38
% 2.94/3.12 40. (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) <=> (r1_rlvect_1 B C)))))) (v1_group_1 T_1) (m1_group_2 T_1 T_0) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### All 39
% 2.94/3.12 41. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) <=> (r1_rlvect_1 B C))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 1 2 3 4 40
% 2.94/3.12 42. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (v1_group_1 T_1) (m1_group_2 T_1 T_0) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### All 41
% 2.94/3.12 43. (-. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => ((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) => (r2_hidden (k3_group_1 T_0 T_2) (k1_funct_1 (k1_latsubgr T_0) T_1))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) ### ConjTree 42
% 2.94/3.12 44. (-. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) => (r2_hidden (k3_group_1 T_0 C) (k1_funct_1 (k1_latsubgr T_0) T_1)))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (v1_group_1 T_1) (m1_group_2 T_1 T_0) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### NotAllEx 43
% 2.94/3.12 45. (-. (((v1_group_1 T_1) /\ (m1_group_2 T_1 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) => (r2_hidden (k3_group_1 T_0 C) (k1_funct_1 (k1_latsubgr T_0) T_1))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (l1_group_1 T_0) (v4_group_1 T_0) (v3_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) ### ConjTree 44
% 2.94/3.12 46. (-. (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) => (r2_hidden (k3_group_1 T_0 C) (k1_funct_1 (k1_latsubgr T_0) B)))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) (-. (v3_struct_0 T_0)) (v3_group_1 T_0) (v4_group_1 T_0) (l1_group_1 T_0) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### NotAllEx 45
% 2.94/3.13 47. (-. (((-. (v3_struct_0 T_0)) /\ ((v3_group_1 T_0) /\ ((v4_group_1 T_0) /\ (l1_group_1 T_0)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) => (r2_hidden (k3_group_1 T_0 C) (k1_funct_1 (k1_latsubgr T_0) B))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) ### ConjTree 46
% 2.94/3.13 48. (-. (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) => (r2_hidden (k3_group_1 A C) (k1_funct_1 (k1_latsubgr A) B)))))))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, (((v1_group_1 B) /\ (m1_group_2 B A)) => (All C, ((m1_subset_1 C (u1_struct_0 A)) => ((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) <=> (r1_rlvect_1 B C)))))))) (All A, (All B, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ ((l1_group_1 A) /\ (m1_subset_1 B (u1_struct_0 A)))))) => (m1_subset_1 (k3_group_1 A B) (u1_struct_0 A))))) (All A, (((-. (v3_struct_0 A)) /\ ((v3_group_1 A) /\ ((v4_group_1 A) /\ (l1_group_1 A)))) => (All B, ((m1_subset_1 B (u1_struct_0 A)) => (All C, ((m1_group_2 C A) => ((r1_rlvect_1 C B) => (r1_rlvect_1 C (k3_group_1 A B))))))))) ### NotAllEx 47
% 2.94/3.13 % SZS output end Proof
% 2.94/3.13 (* END-PROOF *)
%------------------------------------------------------------------------------