TSTP Solution File: GRP643+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : GRP643+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 : n022.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 2.83s 3.07s
% Output : Proof 2.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP643+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 : n022.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 17:41:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.83/3.07 % SZS status Theorem
% 2.83/3.07 (* PROOF-FOUND *)
% 2.83/3.07 (* BEGIN-PROOF *)
% 2.83/3.07 % SZS output start Proof
% 2.83/3.07 1. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.83/3.07 2. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 2.83/3.07 3. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 2.83/3.07 4. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.83/3.07 5. (v1_group_1 T_1) (-. (v1_group_1 T_1)) ### Axiom
% 2.83/3.07 6. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 2.83/3.07 7. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.83/3.07 8. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.83/3.07 9. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 10. (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (m1_subset_1 T_3 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 11. (-. (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0)) ### Axiom
% 2.83/3.07 12. (((-. (v3_struct_0 T_0)) /\ ((l1_group_1 T_0) /\ ((m1_subset_1 T_2 (u1_struct_0 T_0)) /\ (m1_subset_1 T_3 (u1_struct_0 T_0))))) => (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) (-. (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) (m1_subset_1 T_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (-. (v3_struct_0 T_0)) ### DisjTree 7 8 9 10 11
% 2.83/3.07 13. (All C, (((-. (v3_struct_0 T_0)) /\ ((l1_group_1 T_0) /\ ((m1_subset_1 T_2 (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0))))) => (m1_subset_1 (k1_group_1 T_0 T_2 C) (u1_struct_0 T_0)))) (-. (v3_struct_0 T_0)) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) ### All 12
% 2.83/3.07 14. (All B, (All C, (((-. (v3_struct_0 T_0)) /\ ((l1_group_1 T_0) /\ ((m1_subset_1 B (u1_struct_0 T_0)) /\ (m1_subset_1 C (u1_struct_0 T_0))))) => (m1_subset_1 (k1_group_1 T_0 B C) (u1_struct_0 T_0))))) (-. (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) (m1_subset_1 T_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (-. (v3_struct_0 T_0)) ### All 13
% 2.83/3.07 15. (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (-. (v3_struct_0 T_0)) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0))) ### All 14
% 2.83/3.07 16. (-. (v3_struct_0 T_0)) (v3_struct_0 T_0) ### Axiom
% 2.83/3.07 17. (v3_group_1 T_0) (-. (v3_group_1 T_0)) ### Axiom
% 2.83/3.07 18. (v4_group_1 T_0) (-. (v4_group_1 T_0)) ### Axiom
% 2.83/3.07 19. (l1_group_1 T_0) (-. (l1_group_1 T_0)) ### Axiom
% 2.83/3.07 20. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 21. (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (m1_subset_1 T_3 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 22. (m1_group_2 T_1 T_0) (-. (m1_group_2 T_1 T_0)) ### Axiom
% 2.83/3.07 23. (m1_subset_1 T_2 (u1_struct_0 T_0)) (-. (m1_subset_1 T_2 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 24. (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
% 2.83/3.07 25. (-. (r1_rlvect_1 T_1 T_2)) (r1_rlvect_1 T_1 T_2) ### Axiom
% 2.83/3.07 26. ((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 24 25
% 2.83/3.07 27. ((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 23 26
% 2.83/3.07 28. (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 27
% 2.83/3.07 29. (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (m1_subset_1 T_3 (u1_struct_0 T_0))) ### Axiom
% 2.83/3.07 30. (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1))) ### Axiom
% 2.83/3.07 31. (-. (r1_rlvect_1 T_1 T_3)) (r1_rlvect_1 T_1 T_3) ### Axiom
% 2.83/3.07 32. ((r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 T_3)) (-. (r1_rlvect_1 T_1 T_3)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) ### Equiv 30 31
% 2.83/3.07 33. ((m1_subset_1 T_3 (u1_struct_0 T_0)) => ((r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 T_3))) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 T_3)) (m1_subset_1 T_3 (u1_struct_0 T_0)) ### Imply 29 32
% 2.83/3.07 34. (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_3 (u1_struct_0 T_0)) (-. (r1_rlvect_1 T_1 T_3)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) ### All 33
% 2.83/3.07 35. (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3)) ### Axiom
% 2.83/3.07 36. ((m1_group_2 T_1 T_0) => (((r1_rlvect_1 T_1 T_2) /\ (r1_rlvect_1 T_1 T_3)) => (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3)))) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (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 22 28 34 35
% 2.83/3.07 37. (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D T_2) /\ (r1_rlvect_1 D T_3)) => (r1_rlvect_1 D (k1_group_1 T_0 T_2 T_3))))) (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)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) ### All 36
% 2.83/3.07 38. ((m1_subset_1 T_3 (u1_struct_0 T_0)) => (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D T_2) /\ (r1_rlvect_1 D T_3)) => (r1_rlvect_1 D (k1_group_1 T_0 T_2 T_3)))))) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (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) (m1_subset_1 T_3 (u1_struct_0 T_0)) ### Imply 21 37
% 2.83/3.07 39. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D T_2) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 T_0 T_2 C))))))) (m1_subset_1 T_3 (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)))) (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 T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) ### All 38
% 2.83/3.07 40. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D T_2) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 T_0 T_2 C)))))))) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (r2_hidden T_3 (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_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) ### Imply 20 39
% 2.83/3.07 41. (All B, ((m1_subset_1 B (u1_struct_0 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 T_0 B C))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (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)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) ### All 40
% 2.93/3.17 42. (((-. (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_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_group_2 D T_0) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 T_0 B C)))))))))) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (r2_hidden T_3 (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_3 (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 16 17 18 19 41
% 2.93/3.17 43. (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (-. (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 T_3 (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)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) ### All 42
% 2.93/3.17 44. (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1)) ### Axiom
% 2.93/3.17 45. ((r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3))) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_3 (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_3 (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 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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### Equiv 43 44
% 2.93/3.17 46. ((m1_subset_1 (k1_group_1 T_0 T_2 T_3) (u1_struct_0 T_0)) => ((r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1)) <=> (r1_rlvect_1 T_1 (k1_group_1 T_0 T_2 T_3)))) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (v3_group_1 T_0) (v4_group_1 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)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (m1_subset_1 T_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) ### Imply 15 45
% 2.93/3.17 47. (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (-. (v3_struct_0 T_0)) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_3 (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) (v4_group_1 T_0) (v3_group_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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### All 46
% 2.93/3.17 48. (((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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (v3_group_1 T_0) (v4_group_1 T_0) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (m1_subset_1 T_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (l1_group_1 T_0) (-. (v3_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (m1_group_2 T_1 T_0) (v1_group_1 T_1) ### DisjTree 5 6 47
% 2.93/3.17 49. (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (-. (v3_struct_0 T_0)) (l1_group_1 T_0) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (v4_group_1 T_0) (v3_group_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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### All 48
% 2.93/3.17 50. (((-. (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (m1_subset_1 T_3 (u1_struct_0 T_0)) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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 49
% 2.93/3.17 51. (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (m1_subset_1 T_3 (u1_struct_0 T_0)) (-. (r2_hidden (k1_group_1 T_0 T_2 T_3) (k1_funct_1 (k1_latsubgr T_0) T_1))) (r2_hidden T_3 (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### All 50
% 2.93/3.19 52. (-. ((m1_subset_1 T_3 (u1_struct_0 T_0)) => (((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) /\ (r2_hidden T_3 (k1_funct_1 (k1_latsubgr T_0) T_1))) => (r2_hidden (k1_group_1 T_0 T_2 T_3) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (m1_subset_1 T_2 (u1_struct_0 T_0)) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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 51
% 2.93/3.19 53. (-. (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) T_1))) => (r2_hidden (k1_group_1 T_0 T_2 D) (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (u1_struct_0 A)))))) (m1_subset_1 T_2 (u1_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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### NotAllEx 52
% 2.93/3.19 54. (-. ((m1_subset_1 T_2 (u1_struct_0 T_0)) => (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden T_2 (k1_funct_1 (k1_latsubgr T_0) T_1)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) T_1))) => (r2_hidden (k1_group_1 T_0 T_2 D) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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)))))))) ### NotImply 53
% 2.93/3.19 55. (-. (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) T_1))) => (r2_hidden (k1_group_1 T_0 C D) (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### NotAllEx 54
% 2.93/3.19 56. (-. (((v1_group_1 T_1) /\ (m1_group_2 T_1 T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) T_1)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) T_1))) => (r2_hidden (k1_group_1 T_0 C D) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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 55
% 2.93/3.19 57. (-. (All B, (((v1_group_1 B) /\ (m1_group_2 B T_0)) => (All C, ((m1_subset_1 C (u1_struct_0 T_0)) => (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) B))) => (r2_hidden (k1_group_1 T_0 C D) (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### NotAllEx 56
% 2.93/3.19 58. (-. (((-. (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)) => (All D, ((m1_subset_1 D (u1_struct_0 T_0)) => (((r2_hidden C (k1_funct_1 (k1_latsubgr T_0) B)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr T_0) B))) => (r2_hidden (k1_group_1 T_0 C D) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) (All A, (All B, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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 57
% 2.93/3.19 59. (-. (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)) => (All D, ((m1_subset_1 D (u1_struct_0 A)) => (((r2_hidden C (k1_funct_1 (k1_latsubgr A) B)) /\ (r2_hidden D (k1_funct_1 (k1_latsubgr A) B))) => (r2_hidden (k1_group_1 A C D) (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, (All C, (((-. (v3_struct_0 A)) /\ ((l1_group_1 A) /\ ((m1_subset_1 B (u1_struct_0 A)) /\ (m1_subset_1 C (u1_struct_0 A))))) => (m1_subset_1 (k1_group_1 A B C) (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_subset_1 C (u1_struct_0 A)) => (All D, ((m1_group_2 D A) => (((r1_rlvect_1 D B) /\ (r1_rlvect_1 D C)) => (r1_rlvect_1 D (k1_group_1 A B C))))))))))) ### NotAllEx 58
% 2.93/3.19 % SZS output end Proof
% 2.93/3.19 (* END-PROOF *)
%------------------------------------------------------------------------------