TSTP Solution File: SYN551+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 13:54:17 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n024.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 : Tue Jul 12 07:27:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52 (* PROOF-FOUND *)
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 (* BEGIN-PROOF *)
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Theorem prove_this_cute_thing : ((exists X : zenon_U, ((X = (f (g X)))/\(forall Y : zenon_U, ((Y = (f (g Y)))->(Y = X)))))<->(exists X : zenon_U, ((X = (g (f X)))/\(forall Y : zenon_U, ((Y = (g (f Y)))->(Y = X)))))).
% 0.19/0.52 Proof.
% 0.19/0.52 apply NNPP. intro zenon_G.
% 0.19/0.52 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H2; zenon_intro zenon_H1 ].
% 0.19/0.52 elim zenon_H3. zenon_intro zenon_TX_f. zenon_intro zenon_H6.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_H8. zenon_intro zenon_H7.
% 0.19/0.52 apply zenon_H4. exists (f zenon_TX_f). apply NNPP. zenon_intro zenon_H9.
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ].
% 0.19/0.52 cut ((zenon_TX_f = (g (f zenon_TX_f)))); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 0.19/0.52 congruence.
% 0.19/0.52 exact (zenon_Hc zenon_H8).
% 0.19/0.52 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (f (g Y)))->(Y = (f zenon_TX_f)))) zenon_Ha); [ zenon_intro zenon_Hd; idtac ].
% 0.19/0.52 elim zenon_Hd. zenon_intro zenon_TY_o. zenon_intro zenon_Hf.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 0.19/0.52 cut ((zenon_TY_o = (f (g zenon_TY_o))) = (zenon_TY_o = (f zenon_TX_f))).
% 0.19/0.52 intro zenon_D_pnotp.
% 0.19/0.52 apply zenon_H10.
% 0.19/0.52 rewrite <- zenon_D_pnotp.
% 0.19/0.52 exact zenon_H11.
% 0.19/0.52 cut (((f (g zenon_TY_o)) = (f zenon_TX_f))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 0.19/0.52 cut ((zenon_TY_o = zenon_TY_o)); [idtac | apply NNPP; zenon_intro zenon_H13].
% 0.19/0.52 congruence.
% 0.19/0.52 apply zenon_H13. apply refl_equal.
% 0.19/0.52 cut (((g zenon_TY_o) = zenon_TX_f)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 0.19/0.52 congruence.
% 0.19/0.52 generalize (zenon_H7 (g zenon_TY_o)). zenon_intro zenon_H15.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 0.19/0.52 cut ((zenon_TY_o = (f (g zenon_TY_o)))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 0.19/0.52 congruence.
% 0.19/0.52 exact (zenon_H18 zenon_H11).
% 0.19/0.52 exact (zenon_H14 zenon_H16).
% 0.19/0.52 elim zenon_H2. zenon_intro zenon_TX_z. zenon_intro zenon_H1a.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 0.19/0.52 apply zenon_H1. exists (g zenon_TX_z). apply NNPP. zenon_intro zenon_H1d.
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.19/0.52 cut ((zenon_TX_z = (f (g zenon_TX_z)))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 0.19/0.52 congruence.
% 0.19/0.52 exact (zenon_H20 zenon_H1c).
% 0.19/0.52 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (g (f Y)))->(Y = (g zenon_TX_z)))) zenon_H1e); [ zenon_intro zenon_H21; idtac ].
% 0.19/0.52 elim zenon_H21. zenon_intro zenon_TY_bi. zenon_intro zenon_H23.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.19/0.52 cut ((zenon_TY_bi = (g (f zenon_TY_bi))) = (zenon_TY_bi = (g zenon_TX_z))).
% 0.19/0.52 intro zenon_D_pnotp.
% 0.19/0.52 apply zenon_H24.
% 0.19/0.52 rewrite <- zenon_D_pnotp.
% 0.19/0.52 exact zenon_H25.
% 0.19/0.52 cut (((g (f zenon_TY_bi)) = (g zenon_TX_z))); [idtac | apply NNPP; zenon_intro zenon_H26].
% 0.19/0.52 cut ((zenon_TY_bi = zenon_TY_bi)); [idtac | apply NNPP; zenon_intro zenon_H27].
% 0.19/0.52 congruence.
% 0.19/0.52 apply zenon_H27. apply refl_equal.
% 0.19/0.52 cut (((f zenon_TY_bi) = zenon_TX_z)); [idtac | apply NNPP; zenon_intro zenon_H28].
% 0.19/0.52 congruence.
% 0.19/0.52 generalize (zenon_H1b (f zenon_TY_bi)). zenon_intro zenon_H29.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.19/0.52 cut ((zenon_TY_bi = (g (f zenon_TY_bi)))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 0.19/0.52 congruence.
% 0.19/0.52 exact (zenon_H2c zenon_H25).
% 0.19/0.52 exact (zenon_H28 zenon_H2a).
% 0.19/0.52 Qed.
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 (* END-PROOF *)
% 0.19/0.52 nodes searched: 577
% 0.19/0.52 max branch formulas: 59
% 0.19/0.52 proof nodes created: 125
% 0.19/0.52 formulas created: 1448
% 0.19/0.52
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