TSTP Solution File: GRP643+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n027.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 12:36:34 EDT 2022
% Result : Theorem 0.41s 0.57s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 17:52:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.41/0.57 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.41/0.57 (* PROOF-FOUND *)
% 0.41/0.57 % SZS status Theorem
% 0.41/0.57 (* BEGIN-PROOF *)
% 0.41/0.57 % SZS output start Proof
% 0.41/0.57 Theorem t21_latsubgr : (forall A : zenon_U, (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 A))->(forall D : zenon_U, ((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))))))))))).
% 0.41/0.57 Proof.
% 0.41/0.57 apply NNPP. intro zenon_G.
% 0.41/0.57 apply (zenon_notallex_s (fun A : zenon_U => (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 A))->(forall D : zenon_U, ((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))))))))))) zenon_G); [ zenon_intro zenon_H2f; idtac ].
% 0.41/0.57 elim zenon_H2f. zenon_intro zenon_TA_bw. zenon_intro zenon_H31.
% 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.41/0.57 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34.
% 0.41/0.57 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.41/0.57 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.41/0.57 apply (zenon_notallex_s (fun B : zenon_U => (((v1_group_1 B)/\(m1_group_2 B zenon_TA_bw))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 zenon_TA_bw))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden C (k1_funct_1 (k1_latsubgr zenon_TA_bw) B))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) B)))->(r2_hidden (k1_group_1 zenon_TA_bw C D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) B))))))))) zenon_H32); [ zenon_intro zenon_H3a; idtac ].
% 0.41/0.57 elim zenon_H3a. zenon_intro zenon_TB_ch. zenon_intro zenon_H3c.
% 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 0.41/0.57 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.41/0.57 apply (zenon_notallex_s (fun C : zenon_U => ((m1_subset_1 C (u1_struct_0 zenon_TA_bw))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden C (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch)))->(r2_hidden (k1_group_1 zenon_TA_bw C D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))))))) zenon_H3d); [ zenon_intro zenon_H41; idtac ].
% 0.41/0.57 elim zenon_H41. zenon_intro zenon_TC_co. zenon_intro zenon_H43.
% 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 0.41/0.57 apply (zenon_notallex_s (fun D : zenon_U => ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden zenon_TC_co (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch)))->(r2_hidden (k1_group_1 zenon_TA_bw zenon_TC_co D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))))) zenon_H44); [ zenon_intro zenon_H46; idtac ].
% 0.41/0.57 elim zenon_H46. zenon_intro zenon_TD_ct. zenon_intro zenon_H48.
% 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 0.41/0.57 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.41/0.57 generalize (t18_latsubgr zenon_TA_bw). zenon_intro zenon_H4f.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ].
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.41/0.57 exact (zenon_H53 zenon_H35).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.41/0.57 exact (zenon_H55 zenon_H37).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.41/0.57 exact (zenon_H57 zenon_H39).
% 0.41/0.57 exact (zenon_H56 zenon_H38).
% 0.41/0.57 generalize (zenon_H50 zenon_TB_ch). zenon_intro zenon_H58.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ].
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ].
% 0.41/0.57 exact (zenon_H5c zenon_H40).
% 0.41/0.57 exact (zenon_H5b zenon_H3f).
% 0.41/0.57 generalize (zenon_H59 (k1_group_1 zenon_TA_bw zenon_TC_co zenon_TD_ct)). zenon_intro zenon_H5d.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 0.41/0.57 generalize (dt_k1_group_1 zenon_TA_bw). zenon_intro zenon_H60.
% 0.41/0.57 generalize (zenon_H60 zenon_TC_co). zenon_intro zenon_H61.
% 0.41/0.57 generalize (zenon_H61 zenon_TD_ct). zenon_intro zenon_H62.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H53 | zenon_intro zenon_H65 ].
% 0.41/0.57 exact (zenon_H53 zenon_H35).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H56 | zenon_intro zenon_H66 ].
% 0.41/0.57 exact (zenon_H56 zenon_H38).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ].
% 0.41/0.57 exact (zenon_H68 zenon_H45).
% 0.41/0.57 exact (zenon_H67 zenon_H4a).
% 0.41/0.57 exact (zenon_H5f zenon_H63).
% 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H4b; zenon_intro zenon_H6b | zenon_intro zenon_H6a; zenon_intro zenon_H69 ].
% 0.41/0.57 generalize (t59_group_2 zenon_TA_bw). zenon_intro zenon_H6c.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H51 | zenon_intro zenon_H6d ].
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.41/0.57 exact (zenon_H53 zenon_H35).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.41/0.57 exact (zenon_H55 zenon_H37).
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.41/0.57 exact (zenon_H57 zenon_H39).
% 0.41/0.57 exact (zenon_H56 zenon_H38).
% 0.41/0.57 generalize (zenon_H6d zenon_TC_co). zenon_intro zenon_H6e.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H68 | zenon_intro zenon_H6f ].
% 0.41/0.57 exact (zenon_H68 zenon_H45).
% 0.41/0.57 generalize (zenon_H6f zenon_TD_ct). zenon_intro zenon_H70.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H67 | zenon_intro zenon_H71 ].
% 0.41/0.57 exact (zenon_H67 zenon_H4a).
% 0.41/0.57 generalize (zenon_H71 zenon_TB_ch). zenon_intro zenon_H72.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H5b | zenon_intro zenon_H73 ].
% 0.41/0.57 exact (zenon_H5b zenon_H3f).
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H74 | zenon_intro zenon_H69 ].
% 0.41/0.57 apply (zenon_notand_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ].
% 0.41/0.57 generalize (zenon_H59 zenon_TC_co). zenon_intro zenon_H77.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H68 | zenon_intro zenon_H78 ].
% 0.41/0.57 exact (zenon_H68 zenon_H45).
% 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H7a; zenon_intro zenon_H76 | zenon_intro zenon_H4e; zenon_intro zenon_H79 ].
% 0.41/0.57 exact (zenon_H7a zenon_H4e).
% 0.41/0.57 exact (zenon_H76 zenon_H79).
% 0.41/0.57 generalize (zenon_H59 zenon_TD_ct). zenon_intro zenon_H7b.
% 0.41/0.57 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H67 | zenon_intro zenon_H7c ].
% 0.41/0.57 exact (zenon_H67 zenon_H4a).
% 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7e; zenon_intro zenon_H75 | zenon_intro zenon_H4d; zenon_intro zenon_H7d ].
% 0.41/0.57 exact (zenon_H7e zenon_H4d).
% 0.41/0.57 exact (zenon_H75 zenon_H7d).
% 0.41/0.57 exact (zenon_H6b zenon_H69).
% 0.41/0.57 exact (zenon_H4b zenon_H6a).
% 0.41/0.57 Qed.
% 0.41/0.57 % SZS output end Proof
% 0.41/0.57 (* END-PROOF *)
% 0.41/0.57 nodes searched: 1553
% 0.41/0.57 max branch formulas: 813
% 0.41/0.57 proof nodes created: 167
% 0.41/0.57 formulas created: 7692
% 0.41/0.57
%------------------------------------------------------------------------------