TSTP Solution File: SEU284+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n028.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 16:00:52 EDT 2022
% Result : Theorem 45.20s 45.37s
% Output : Proof 45.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU284+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n028.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 20 02:41:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 45.20/45.37 (* PROOF-FOUND *)
% 45.20/45.37 % SZS status Theorem
% 45.20/45.37 (* BEGIN-PROOF *)
% 45.20/45.37 % SZS output start Proof
% 45.20/45.37 Theorem s3_funct_1__e16_22__wellord2 : (forall A : zenon_U, (exists B : zenon_U, ((relation B)/\((function B)/\(((relation_dom B) = A)/\(forall C : zenon_U, ((in C A)->((apply B C) = (singleton C))))))))).
% 45.20/45.37 Proof.
% 45.20/45.37 assert (zenon_L1_ : forall (zenon_TA_y : zenon_U), (~(forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((in B zenon_TA_y)/\((C = (singleton B))/\(D = (singleton B))))->(C = D)))))) -> False).
% 45.20/45.37 do 1 intro. intros zenon_H17.
% 45.20/45.37 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((in B zenon_TA_y)/\((C = (singleton B))/\(D = (singleton B))))->(C = D))))) zenon_H17); [ zenon_intro zenon_H19; idtac ].
% 45.20/45.37 elim zenon_H19. zenon_intro zenon_TB_ba. zenon_intro zenon_H1b.
% 45.20/45.37 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((in zenon_TB_ba zenon_TA_y)/\((C = (singleton zenon_TB_ba))/\(D = (singleton zenon_TB_ba))))->(C = D)))) zenon_H1b); [ zenon_intro zenon_H1c; idtac ].
% 45.20/45.37 elim zenon_H1c. zenon_intro zenon_TC_bd. zenon_intro zenon_H1e.
% 45.20/45.37 apply (zenon_notallex_s (fun D : zenon_U => (((in zenon_TB_ba zenon_TA_y)/\((zenon_TC_bd = (singleton zenon_TB_ba))/\(D = (singleton zenon_TB_ba))))->(zenon_TC_bd = D))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ].
% 45.20/45.37 elim zenon_H1f. zenon_intro zenon_TD_bg. zenon_intro zenon_H21.
% 45.20/45.37 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 45.20/45.37 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 45.20/45.37 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 45.20/45.37 elim (classic (zenon_TD_bg = zenon_TD_bg)); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ].
% 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg) = (zenon_TC_bd = zenon_TD_bg)).
% 45.20/45.37 intro zenon_D_pnotp.
% 45.20/45.37 apply zenon_H22.
% 45.20/45.37 rewrite <- zenon_D_pnotp.
% 45.20/45.37 exact zenon_H28.
% 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg)); [idtac | apply NNPP; zenon_intro zenon_H29].
% 45.20/45.37 cut ((zenon_TD_bg = zenon_TC_bd)); [idtac | apply NNPP; zenon_intro zenon_H2a].
% 45.20/45.37 congruence.
% 45.20/45.37 cut ((zenon_TD_bg = (singleton zenon_TB_ba)) = (zenon_TD_bg = zenon_TC_bd)).
% 45.20/45.37 intro zenon_D_pnotp.
% 45.20/45.37 apply zenon_H2a.
% 45.20/45.37 rewrite <- zenon_D_pnotp.
% 45.20/45.37 exact zenon_H26.
% 45.20/45.37 cut (((singleton zenon_TB_ba) = zenon_TC_bd)); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.20/45.37 cut ((zenon_TD_bg = zenon_TD_bg)); [idtac | apply NNPP; zenon_intro zenon_H29].
% 45.20/45.37 congruence.
% 45.20/45.37 apply zenon_H29. apply refl_equal.
% 45.20/45.37 apply zenon_H2b. apply sym_equal. exact zenon_H27.
% 45.20/45.37 apply zenon_H29. apply refl_equal.
% 45.20/45.37 apply zenon_H29. apply refl_equal.
% 45.20/45.37 (* end of lemma zenon_L1_ *)
% 45.20/45.37 apply NNPP. intro zenon_G.
% 45.20/45.37 apply (zenon_notallex_s (fun A : zenon_U => (exists B : zenon_U, ((relation B)/\((function B)/\(((relation_dom B) = A)/\(forall C : zenon_U, ((in C A)->((apply B C) = (singleton C))))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 45.20/45.37 elim zenon_H2c. zenon_intro zenon_TA_y. zenon_intro zenon_H2d.
% 45.20/45.37 generalize (s2_funct_1__e16_22__wellord2__1 zenon_TA_y). zenon_intro zenon_H2e.
% 45.20/45.37 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 45.20/45.37 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H17 | zenon_intro zenon_H31 ].
% 45.20/45.37 apply (zenon_L1_ zenon_TA_y); trivial.
% 45.20/45.37 apply (zenon_notallex_s (fun B : zenon_U => (~((in B zenon_TA_y)/\(forall C : zenon_U, (~(C = (singleton B))))))) zenon_H31); [ zenon_intro zenon_H32; idtac ].
% 45.20/45.37 elim zenon_H32. zenon_intro zenon_TB_bz. zenon_intro zenon_H34.
% 45.20/45.37 apply zenon_H34. zenon_intro zenon_H35.
% 45.20/45.37 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 45.20/45.37 generalize (zenon_H36 (singleton zenon_TB_bz)). zenon_intro zenon_H38.
% 45.20/45.37 apply zenon_H38. apply refl_equal.
% 45.20/45.37 exact (zenon_H2d zenon_H2f).
% 45.20/45.37 Qed.
% 45.20/45.37 % SZS output end Proof
% 45.20/45.37 (* END-PROOF *)
% 45.20/45.37 nodes searched: 460070
% 45.20/45.37 max branch formulas: 13593
% 45.20/45.37 proof nodes created: 13561
% 45.20/45.37 formulas created: 440540
% 45.20/45.37
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