TSTP Solution File: SYN417+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 : Thu Jul 21 13:51:58 EDT 2022
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 12 02:55:42 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.55 (* PROOF-FOUND *)
% 0.21/0.55 % SZS status Theorem
% 0.21/0.55 (* BEGIN-PROOF *)
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Theorem cute : ((exists X : zenon_U, ((X = (f (g X)))/\(forall Y : zenon_U, ((Y = (f (g Y)))->(X = Y)))))<->(exists X : zenon_U, ((X = (g (f X)))/\(forall Y : zenon_U, ((Y = (g (f Y)))->(X = Y)))))).
% 0.21/0.55 Proof.
% 0.21/0.55 apply NNPP. intro zenon_G.
% 0.21/0.55 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H2; zenon_intro zenon_H1 ].
% 0.21/0.55 elim zenon_H3. zenon_intro zenon_TX_f. zenon_intro zenon_H6.
% 0.21/0.55 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_H8. zenon_intro zenon_H7.
% 0.21/0.55 apply zenon_H4. exists (f zenon_TX_f). apply NNPP. zenon_intro zenon_H9.
% 0.21/0.55 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ].
% 0.21/0.55 cut ((zenon_TX_f = (g (f zenon_TX_f)))); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 0.21/0.55 congruence.
% 0.21/0.55 exact (zenon_Hc zenon_H8).
% 0.21/0.55 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (f (g Y)))->((f zenon_TX_f) = Y))) zenon_Ha); [ zenon_intro zenon_Hd; idtac ].
% 0.21/0.55 elim zenon_Hd. zenon_intro zenon_TY_o. zenon_intro zenon_Hf.
% 0.21/0.55 apply (zenon_notimply_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 0.21/0.55 elim (classic (zenon_TY_o = zenon_TY_o)); [ zenon_intro zenon_H12 | zenon_intro zenon_H13 ].
% 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o) = ((f zenon_TX_f) = zenon_TY_o)).
% 0.21/0.55 intro zenon_D_pnotp.
% 0.21/0.55 apply zenon_H10.
% 0.21/0.55 rewrite <- zenon_D_pnotp.
% 0.21/0.55 exact zenon_H12.
% 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o)); [idtac | apply NNPP; zenon_intro zenon_H13].
% 0.21/0.55 cut ((zenon_TY_o = (f zenon_TX_f))); [idtac | apply NNPP; zenon_intro zenon_H14].
% 0.21/0.55 congruence.
% 0.21/0.55 cut ((zenon_TY_o = (f (g zenon_TY_o))) = (zenon_TY_o = (f zenon_TX_f))).
% 0.21/0.55 intro zenon_D_pnotp.
% 0.21/0.55 apply zenon_H14.
% 0.21/0.55 rewrite <- zenon_D_pnotp.
% 0.21/0.55 exact zenon_H11.
% 0.21/0.55 cut (((f (g zenon_TY_o)) = (f zenon_TX_f))); [idtac | apply NNPP; zenon_intro zenon_H15].
% 0.21/0.55 cut ((zenon_TY_o = zenon_TY_o)); [idtac | apply NNPP; zenon_intro zenon_H13].
% 0.21/0.55 congruence.
% 0.21/0.55 apply zenon_H13. apply refl_equal.
% 0.21/0.55 cut (((g zenon_TY_o) = zenon_TX_f)); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.21/0.55 congruence.
% 0.21/0.55 generalize (zenon_H7 (g zenon_TY_o)). zenon_intro zenon_H17.
% 0.21/0.55 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.21/0.55 cut ((zenon_TY_o = (f (g zenon_TY_o)))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 0.21/0.55 congruence.
% 0.21/0.55 exact (zenon_H1a zenon_H11).
% 0.21/0.55 apply zenon_H16. apply sym_equal. exact zenon_H18.
% 0.21/0.55 apply zenon_H13. apply refl_equal.
% 0.21/0.55 apply zenon_H13. apply refl_equal.
% 0.21/0.55 elim zenon_H2. zenon_intro zenon_TX_bb. zenon_intro zenon_H1c.
% 0.21/0.55 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 0.21/0.55 apply zenon_H1. exists (g zenon_TX_bb). apply NNPP. zenon_intro zenon_H1f.
% 0.21/0.55 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.21/0.55 cut ((zenon_TX_bb = (f (g zenon_TX_bb)))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 0.21/0.55 congruence.
% 0.21/0.55 exact (zenon_H22 zenon_H1e).
% 0.21/0.55 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (g (f Y)))->((g zenon_TX_bb) = Y))) zenon_H20); [ zenon_intro zenon_H23; idtac ].
% 0.21/0.55 elim zenon_H23. zenon_intro zenon_TY_bk. zenon_intro zenon_H25.
% 0.21/0.55 apply (zenon_notimply_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.21/0.55 elim (classic (zenon_TY_bk = zenon_TY_bk)); [ zenon_intro zenon_H28 | zenon_intro zenon_H29 ].
% 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk) = ((g zenon_TX_bb) = zenon_TY_bk)).
% 0.21/0.55 intro zenon_D_pnotp.
% 0.21/0.55 apply zenon_H26.
% 0.21/0.55 rewrite <- zenon_D_pnotp.
% 0.21/0.55 exact zenon_H28.
% 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk)); [idtac | apply NNPP; zenon_intro zenon_H29].
% 0.21/0.55 cut ((zenon_TY_bk = (g zenon_TX_bb))); [idtac | apply NNPP; zenon_intro zenon_H2a].
% 0.21/0.55 congruence.
% 0.21/0.55 cut ((zenon_TY_bk = (g (f zenon_TY_bk))) = (zenon_TY_bk = (g zenon_TX_bb))).
% 0.21/0.55 intro zenon_D_pnotp.
% 0.21/0.55 apply zenon_H2a.
% 0.21/0.55 rewrite <- zenon_D_pnotp.
% 0.21/0.55 exact zenon_H27.
% 0.21/0.55 cut (((g (f zenon_TY_bk)) = (g zenon_TX_bb))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 0.21/0.55 cut ((zenon_TY_bk = zenon_TY_bk)); [idtac | apply NNPP; zenon_intro zenon_H29].
% 0.21/0.55 congruence.
% 0.21/0.55 apply zenon_H29. apply refl_equal.
% 0.21/0.55 cut (((f zenon_TY_bk) = zenon_TX_bb)); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 0.21/0.55 congruence.
% 0.21/0.55 generalize (zenon_H1d (f zenon_TY_bk)). zenon_intro zenon_H2d.
% 0.21/0.55 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 0.21/0.55 cut ((zenon_TY_bk = (g (f zenon_TY_bk)))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 0.21/0.55 congruence.
% 0.21/0.55 exact (zenon_H30 zenon_H27).
% 0.21/0.55 apply zenon_H2c. apply sym_equal. exact zenon_H2e.
% 0.21/0.55 apply zenon_H29. apply refl_equal.
% 0.21/0.55 apply zenon_H29. apply refl_equal.
% 0.21/0.55 Qed.
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55 (* END-PROOF *)
% 0.21/0.55 nodes searched: 545
% 0.21/0.55 max branch formulas: 59
% 0.21/0.55 proof nodes created: 109
% 0.21/0.55 formulas created: 1420
% 0.21/0.55
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