TSTP Solution File: SET799+4 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SET799+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 06:38:39 EDT 2022
% Result : Theorem 0.39s 0.55s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET799+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n018.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 Jul 11 07:28:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.39/0.55 (* PROOF-FOUND *)
% 0.39/0.55 % SZS status Theorem
% 0.39/0.55 (* BEGIN-PROOF *)
% 0.39/0.55 % SZS output start Proof
% 0.39/0.55 Theorem thIV11 : (forall R : zenon_U, (forall E : zenon_U, ((order R E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((least_upper_bound M1 X1 R E)/\(least_upper_bound M2 X2 R E))->(apply R M1 M2)))))))))).
% 0.39/0.55 Proof.
% 0.39/0.55 apply NNPP. intro zenon_G.
% 0.39/0.55 apply (zenon_notallex_s (fun R : zenon_U => (forall E : zenon_U, ((order R E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((least_upper_bound M1 X1 R E)/\(least_upper_bound M2 X2 R E))->(apply R M1 M2)))))))))) zenon_G); [ zenon_intro zenon_H16; idtac ].
% 0.39/0.55 elim zenon_H16. zenon_intro zenon_TR_x. zenon_intro zenon_H18.
% 0.39/0.55 apply (zenon_notallex_s (fun E : zenon_U => ((order zenon_TR_x E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((least_upper_bound M1 X1 zenon_TR_x E)/\(least_upper_bound M2 X2 zenon_TR_x E))->(apply zenon_TR_x M1 M2))))))))) zenon_H18); [ zenon_intro zenon_H19; idtac ].
% 0.39/0.55 elim zenon_H19. zenon_intro zenon_TE_ba. zenon_intro zenon_H1b.
% 0.39/0.55 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.39/0.55 apply (zenon_notallex_s (fun X1 : zenon_U => (forall X2 : zenon_U, (((subset X1 zenon_TE_ba)/\((subset X2 zenon_TE_ba)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((least_upper_bound M1 X1 zenon_TR_x zenon_TE_ba)/\(least_upper_bound M2 X2 zenon_TR_x zenon_TE_ba))->(apply zenon_TR_x M1 M2))))))) zenon_H1c); [ zenon_intro zenon_H1e; idtac ].
% 0.39/0.55 elim zenon_H1e. zenon_intro zenon_TX1_bf. zenon_intro zenon_H20.
% 0.39/0.55 apply (zenon_notallex_s (fun X2 : zenon_U => (((subset zenon_TX1_bf zenon_TE_ba)/\((subset X2 zenon_TE_ba)/\(subset zenon_TX1_bf X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((least_upper_bound M1 zenon_TX1_bf zenon_TR_x zenon_TE_ba)/\(least_upper_bound M2 X2 zenon_TR_x zenon_TE_ba))->(apply zenon_TR_x M1 M2)))))) zenon_H20); [ zenon_intro zenon_H21; idtac ].
% 0.39/0.55 elim zenon_H21. zenon_intro zenon_TX2_bi. zenon_intro zenon_H23.
% 0.39/0.55 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.39/0.55 generalize (subset zenon_TX1_bf). zenon_intro zenon_H2a.
% 0.39/0.55 generalize (zenon_H2a zenon_TX2_bi). zenon_intro zenon_H2b.
% 0.39/0.55 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H28; zenon_intro zenon_H2c ].
% 0.39/0.55 exact (zenon_H2e zenon_H28).
% 0.39/0.55 apply (zenon_notallex_s (fun M1 : zenon_U => (forall M2 : zenon_U, (((least_upper_bound M1 zenon_TX1_bf zenon_TR_x zenon_TE_ba)/\(least_upper_bound M2 zenon_TX2_bi zenon_TR_x zenon_TE_ba))->(apply zenon_TR_x M1 M2)))) zenon_H24); [ zenon_intro zenon_H2f; idtac ].
% 0.39/0.55 elim zenon_H2f. zenon_intro zenon_TM1_bw. zenon_intro zenon_H31.
% 0.39/0.55 apply (zenon_notallex_s (fun M2 : zenon_U => (((least_upper_bound zenon_TM1_bw zenon_TX1_bf zenon_TR_x zenon_TE_ba)/\(least_upper_bound M2 zenon_TX2_bi zenon_TR_x zenon_TE_ba))->(apply zenon_TR_x zenon_TM1_bw M2))) zenon_H31); [ zenon_intro zenon_H32; idtac ].
% 0.39/0.55 elim zenon_H32. zenon_intro zenon_TM2_bz. zenon_intro zenon_H34.
% 0.39/0.55 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37.
% 0.39/0.55 generalize (least_upper_bound zenon_TM1_bw). zenon_intro zenon_H39.
% 0.39/0.55 generalize (zenon_H39 zenon_TX1_bf). zenon_intro zenon_H3a.
% 0.39/0.55 generalize (zenon_H3a zenon_TR_x). zenon_intro zenon_H3b.
% 0.39/0.55 generalize (zenon_H3b zenon_TE_ba). zenon_intro zenon_H3c.
% 0.39/0.55 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H38; zenon_intro zenon_H3d ].
% 0.39/0.55 exact (zenon_H3f zenon_H38).
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 0.39/0.55 generalize (least_upper_bound zenon_TM2_bz). zenon_intro zenon_H42.
% 0.39/0.55 generalize (zenon_H42 zenon_TX2_bi). zenon_intro zenon_H43.
% 0.39/0.55 generalize (zenon_H43 zenon_TR_x). zenon_intro zenon_H44.
% 0.39/0.55 generalize (zenon_H44 zenon_TE_ba). zenon_intro zenon_H45.
% 0.39/0.55 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H37; zenon_intro zenon_H46 ].
% 0.39/0.55 exact (zenon_H48 zenon_H37).
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.39/0.55 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 0.39/0.55 generalize (upper_bound zenon_TR_x). zenon_intro zenon_H4d.
% 0.39/0.55 generalize (zenon_H4d zenon_TX2_bi). zenon_intro zenon_H4e.
% 0.39/0.55 generalize (zenon_H4e zenon_TM2_bz). zenon_intro zenon_H4f.
% 0.39/0.55 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H4c; zenon_intro zenon_H50 ].
% 0.39/0.55 exact (zenon_H52 zenon_H4c).
% 0.39/0.55 generalize (zenon_H50 zenon_TM1_bw). zenon_intro zenon_H53.
% 0.39/0.55 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.39/0.55 generalize (zenon_H2c zenon_TM1_bw). zenon_intro zenon_H56.
% 0.39/0.55 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ].
% 0.39/0.55 exact (zenon_H58 zenon_H41).
% 0.39/0.55 exact (zenon_H55 zenon_H57).
% 0.39/0.55 exact (zenon_H35 zenon_H54).
% 0.39/0.55 Qed.
% 0.39/0.55 % SZS output end Proof
% 0.39/0.55 (* END-PROOF *)
% 0.39/0.55 nodes searched: 1504
% 0.39/0.55 max branch formulas: 962
% 0.39/0.55 proof nodes created: 86
% 0.39/0.55 formulas created: 11015
% 0.39/0.55
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