TSTP Solution File: SYN551+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 2.23s 2.43s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN551+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.12/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n017.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 12:44:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.23/2.43 (* PROOF-FOUND *)
% 2.23/2.43 % SZS status Theorem
% 2.23/2.43 (* BEGIN-PROOF *)
% 2.23/2.43 % SZS output start Proof
% 2.23/2.43 Theorem prove_this_cute_thing : ((exists X : zenon_U, (forall Y : zenon_U, ((Y = (f (g Y)))<->(X = Y))))<->(exists X : zenon_U, (forall Y : zenon_U, ((Y = (g (f Y)))<->(X = Y))))).
% 2.23/2.43 Proof.
% 2.23/2.43 assert (zenon_L1_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f zenon_TX_d)))) = (g (f (g (f (g (f zenon_TX_d)))))))) -> ((g (f zenon_TX_d)) = (g (f (g (f zenon_TX_d))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H1 zenon_H2.
% 2.23/2.43 cut (((f (g (f zenon_TX_d))) = (f (g (f (g (f zenon_TX_d))))))); [idtac | apply NNPP; zenon_intro zenon_H4].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f zenon_TX_d)) = (g (f (g (f zenon_TX_d)))))); [idtac | apply NNPP; zenon_intro zenon_H5].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H5 zenon_H2).
% 2.23/2.43 (* end of lemma zenon_L1_ *)
% 2.23/2.43 assert (zenon_L2_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f (g (f zenon_TX_d)))))) = (g (f (g (f (g (f (g (f zenon_TX_d)))))))))) -> ((g (f (g (f zenon_TX_d)))) = (g (f (g (f (g (f zenon_TX_d))))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H6 zenon_H7.
% 2.23/2.43 cut (((f (g (f (g (f zenon_TX_d))))) = (f (g (f (g (f (g (f zenon_TX_d))))))))); [idtac | apply NNPP; zenon_intro zenon_H8].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f zenon_TX_d)))) = (g (f (g (f (g (f zenon_TX_d)))))))); [idtac | apply NNPP; zenon_intro zenon_H1].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H1 zenon_H7).
% 2.23/2.43 (* end of lemma zenon_L2_ *)
% 2.23/2.43 assert (zenon_L3_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f (g (f zenon_TX_d)))))) = (g (f zenon_TX_d)))) -> (zenon_TX_d = (g (f (g (f zenon_TX_d))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H9 zenon_Ha.
% 2.23/2.43 cut (((f (g (f (g (f zenon_TX_d))))) = (f zenon_TX_d))); [idtac | apply NNPP; zenon_intro zenon_Hb].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f zenon_TX_d)))) = zenon_TX_d)); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 2.23/2.43 congruence.
% 2.23/2.43 apply zenon_Hc. apply sym_equal. exact zenon_Ha.
% 2.23/2.43 (* end of lemma zenon_L3_ *)
% 2.23/2.43 assert (zenon_L4_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g (f (g (f zenon_TX_d)))))) -> (zenon_TX_d = (g (f (g (f zenon_TX_d))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_Hd zenon_Ha.
% 2.23/2.43 cut (((f (g (f (g (f (g (f zenon_TX_d))))))) = (f (g (f zenon_TX_d))))); [idtac | apply NNPP; zenon_intro zenon_He].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f zenon_TX_d)))))) = (g (f zenon_TX_d)))); [idtac | apply NNPP; zenon_intro zenon_H9].
% 2.23/2.43 congruence.
% 2.23/2.43 apply (zenon_L3_ zenon_TX_d); trivial.
% 2.23/2.43 (* end of lemma zenon_L4_ *)
% 2.23/2.43 assert (zenon_L5_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))) = (g (f (g (f (g (f zenon_TX_d)))))))) -> (zenon_TX_d = (g (f (g (f zenon_TX_d))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_Hf zenon_Ha.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g (f zenon_TX_d))))))))) = (f (g (f (g (f zenon_TX_d))))))); [idtac | apply NNPP; zenon_intro zenon_H10].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g (f (g (f zenon_TX_d)))))); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 2.23/2.43 congruence.
% 2.23/2.43 apply (zenon_L4_ zenon_TX_d); trivial.
% 2.23/2.43 (* end of lemma zenon_L5_ *)
% 2.23/2.43 assert (zenon_L6_ : forall (zenon_TY_t : zenon_U), (~((g zenon_TY_t) = (g (f (g zenon_TY_t))))) -> (zenon_TY_t = (f (g zenon_TY_t))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H11 zenon_H12.
% 2.23/2.43 cut ((zenon_TY_t = (f (g zenon_TY_t)))); [idtac | apply NNPP; zenon_intro zenon_H14].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H14 zenon_H12).
% 2.23/2.43 (* end of lemma zenon_L6_ *)
% 2.23/2.43 assert (zenon_L7_ : forall (zenon_TX_d : zenon_U), (~((g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))))) = (g (f (g (f (g (f zenon_TX_d)))))))) -> (zenon_TX_d = (g (f (g (f (g (f zenon_TX_d))))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H15 zenon_H16.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))) = (f (g (f (g (f zenon_TX_d))))))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))) = (g (f (g (f zenon_TX_d)))))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g (f zenon_TX_d))))))))) = (f (g (f zenon_TX_d))))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g (f zenon_TX_d)))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f zenon_TX_d))))))) = (f zenon_TX_d))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f zenon_TX_d)))))) = zenon_TX_d)); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 2.23/2.43 congruence.
% 2.23/2.43 apply zenon_H1c. apply sym_equal. exact zenon_H16.
% 2.23/2.43 (* end of lemma zenon_L7_ *)
% 2.23/2.43 assert (zenon_L8_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g zenon_TX_bf)))) = (f (g (f (g (f (g zenon_TX_bf)))))))) -> ((f (g zenon_TX_bf)) = (f (g (f (g zenon_TX_bf))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H1d zenon_H1e.
% 2.23/2.43 cut (((g (f (g zenon_TX_bf))) = (g (f (g (f (g zenon_TX_bf))))))); [idtac | apply NNPP; zenon_intro zenon_H20].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g zenon_TX_bf)) = (f (g (f (g zenon_TX_bf)))))); [idtac | apply NNPP; zenon_intro zenon_H21].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H21 zenon_H1e).
% 2.23/2.43 (* end of lemma zenon_L8_ *)
% 2.23/2.43 assert (zenon_L9_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g (f (g zenon_TX_bf)))))) = (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))) -> ((f (g (f (g zenon_TX_bf)))) = (f (g (f (g (f (g zenon_TX_bf))))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H22 zenon_H23.
% 2.23/2.43 cut (((g (f (g (f (g zenon_TX_bf))))) = (g (f (g (f (g (f (g zenon_TX_bf))))))))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g zenon_TX_bf)))) = (f (g (f (g (f (g zenon_TX_bf)))))))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H1d zenon_H23).
% 2.23/2.43 (* end of lemma zenon_L9_ *)
% 2.23/2.43 assert (zenon_L10_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g (f (g zenon_TX_bf)))))) = (f (g zenon_TX_bf)))) -> (zenon_TX_bf = (f (g (f (g zenon_TX_bf))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H25 zenon_H26.
% 2.23/2.43 cut (((g (f (g (f (g zenon_TX_bf))))) = (g zenon_TX_bf))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g zenon_TX_bf)))) = zenon_TX_bf)); [idtac | apply NNPP; zenon_intro zenon_H28].
% 2.23/2.43 congruence.
% 2.23/2.43 apply zenon_H28. apply sym_equal. exact zenon_H26.
% 2.23/2.43 (* end of lemma zenon_L10_ *)
% 2.23/2.43 assert (zenon_L11_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f (g (f (g zenon_TX_bf)))))) -> (zenon_TX_bf = (f (g (f (g zenon_TX_bf))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H29 zenon_H26.
% 2.23/2.43 cut (((g (f (g (f (g (f (g zenon_TX_bf))))))) = (g (f (g zenon_TX_bf))))); [idtac | apply NNPP; zenon_intro zenon_H2a].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g zenon_TX_bf)))))) = (f (g zenon_TX_bf)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 2.23/2.43 congruence.
% 2.23/2.43 apply (zenon_L10_ zenon_TX_bf); trivial.
% 2.23/2.43 (* end of lemma zenon_L11_ *)
% 2.23/2.43 assert (zenon_L12_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))) = (f (g (f (g (f (g zenon_TX_bf)))))))) -> (zenon_TX_bf = (f (g (f (g zenon_TX_bf))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H2b zenon_H26.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))) = (g (f (g (f (g zenon_TX_bf))))))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f (g (f (g zenon_TX_bf)))))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 2.23/2.43 congruence.
% 2.23/2.43 apply (zenon_L11_ zenon_TX_bf); trivial.
% 2.23/2.43 (* end of lemma zenon_L12_ *)
% 2.23/2.43 assert (zenon_L13_ : forall (zenon_TY_bv : zenon_U), (~((f zenon_TY_bv) = (f (g (f zenon_TY_bv))))) -> (zenon_TY_bv = (g (f zenon_TY_bv))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H2d zenon_H2e.
% 2.23/2.43 cut ((zenon_TY_bv = (g (f zenon_TY_bv)))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H30 zenon_H2e).
% 2.23/2.43 (* end of lemma zenon_L13_ *)
% 2.23/2.43 assert (zenon_L14_ : forall (zenon_TX_bf : zenon_U), (~((f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))))) = (f (g (f (g (f (g zenon_TX_bf)))))))) -> (zenon_TX_bf = (f (g (f (g (f (g zenon_TX_bf))))))) -> False).
% 2.23/2.43 do 1 intro. intros zenon_H31 zenon_H32.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))) = (g (f (g (f (g zenon_TX_bf))))))); [idtac | apply NNPP; zenon_intro zenon_H33].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))) = (f (g (f (g zenon_TX_bf)))))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))) = (g (f (g zenon_TX_bf))))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f (g zenon_TX_bf)))); [idtac | apply NNPP; zenon_intro zenon_H36].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g zenon_TX_bf))))))) = (g zenon_TX_bf))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g zenon_TX_bf)))))) = zenon_TX_bf)); [idtac | apply NNPP; zenon_intro zenon_H38].
% 2.23/2.43 congruence.
% 2.23/2.43 apply zenon_H38. apply sym_equal. exact zenon_H32.
% 2.23/2.43 (* end of lemma zenon_L14_ *)
% 2.23/2.43 apply NNPP. intro zenon_G.
% 2.23/2.43 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H3c; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H39 ].
% 2.23/2.43 elim zenon_H3b. zenon_intro zenon_TX_d. zenon_intro zenon_H3d.
% 2.23/2.43 generalize (zenon_H3d zenon_TX_d). zenon_intro zenon_H3e.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ].
% 2.23/2.43 apply zenon_H41. apply refl_equal.
% 2.23/2.43 generalize (zenon_H3d (g (f zenon_TX_d))). zenon_intro zenon_H43.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H5; zenon_intro zenon_H42 | zenon_intro zenon_H2; zenon_intro zenon_H40 ].
% 2.23/2.43 exact (zenon_H42 zenon_H40).
% 2.23/2.43 generalize (zenon_H3d (g (f (g (f zenon_TX_d))))). zenon_intro zenon_H44.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H1; zenon_intro zenon_H45 | zenon_intro zenon_H7; zenon_intro zenon_Ha ].
% 2.23/2.43 apply (zenon_L1_ zenon_TX_d); trivial.
% 2.23/2.43 generalize (zenon_H3d (g (f (g (f (g (f zenon_TX_d))))))). zenon_intro zenon_H46.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H6; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H16 ].
% 2.23/2.43 apply (zenon_L2_ zenon_TX_d); trivial.
% 2.23/2.43 generalize (zenon_H3d (g (f (g (f (g (f (g (f zenon_TX_d))))))))). zenon_intro zenon_H49.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H4b; zenon_intro zenon_H4a ].
% 2.23/2.43 cut (((f (g (f (g (f (g (f zenon_TX_d))))))) = (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))); [idtac | apply NNPP; zenon_intro zenon_H4e].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f zenon_TX_d)))))) = (g (f (g (f (g (f (g (f zenon_TX_d)))))))))); [idtac | apply NNPP; zenon_intro zenon_H6].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H6 zenon_H47).
% 2.23/2.43 generalize (zenon_H3d (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))). zenon_intro zenon_H4f.
% 2.23/2.43 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H53; zenon_intro zenon_H52 | zenon_intro zenon_H51; zenon_intro zenon_H50 ].
% 2.23/2.43 cut (((f (g (f (g (f (g (f (g (f zenon_TX_d))))))))) = (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 2.23/2.43 congruence.
% 2.23/2.43 exact (zenon_H4d zenon_H4b).
% 2.23/2.43 apply zenon_H3c. exists (f (g (f (g (f (g (f zenon_TX_d))))))). apply NNPP. zenon_intro zenon_H55.
% 2.23/2.43 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (f (g Y)))<->((f (g (f (g (f (g (f zenon_TX_d))))))) = Y))) zenon_H55); [ zenon_intro zenon_H56; idtac ].
% 2.23/2.43 elim zenon_H56. zenon_intro zenon_TY_t. zenon_intro zenon_H57.
% 2.23/2.43 apply (zenon_notequiv_s _ _ zenon_H57); [ zenon_intro zenon_H14; zenon_intro zenon_H59 | zenon_intro zenon_H12; zenon_intro zenon_H58 ].
% 2.23/2.43 elim (classic ((f (g zenon_TY_t)) = (f (g zenon_TY_t)))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 2.23/2.43 cut (((f (g zenon_TY_t)) = (f (g zenon_TY_t))) = (zenon_TY_t = (f (g zenon_TY_t)))).
% 2.23/2.43 intro zenon_D_pnotp.
% 2.23/2.43 apply zenon_H14.
% 2.23/2.43 rewrite <- zenon_D_pnotp.
% 2.23/2.43 exact zenon_H5a.
% 2.23/2.43 cut (((f (g zenon_TY_t)) = (f (g zenon_TY_t)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 2.23/2.43 cut (((f (g zenon_TY_t)) = zenon_TY_t)); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 2.23/2.43 congruence.
% 2.23/2.43 cut (((f (g (f (g (f (g (f zenon_TX_d))))))) = zenon_TY_t) = ((f (g zenon_TY_t)) = zenon_TY_t)).
% 2.23/2.43 intro zenon_D_pnotp.
% 2.23/2.43 apply zenon_H5c.
% 2.23/2.43 rewrite <- zenon_D_pnotp.
% 2.23/2.43 exact zenon_H59.
% 2.23/2.43 cut ((zenon_TY_t = zenon_TY_t)); [idtac | apply NNPP; zenon_intro zenon_H5d].
% 2.23/2.43 cut (((f (g (f (g (f (g (f zenon_TX_d))))))) = (f (g zenon_TY_t)))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 2.23/2.44 congruence.
% 2.23/2.44 elim (classic ((f (g zenon_TY_t)) = (f (g zenon_TY_t)))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 2.23/2.44 cut (((f (g zenon_TY_t)) = (f (g zenon_TY_t))) = ((f (g (f (g (f (g (f zenon_TX_d))))))) = (f (g zenon_TY_t)))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H5e.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H5a.
% 2.23/2.44 cut (((f (g zenon_TY_t)) = (f (g zenon_TY_t)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 2.23/2.44 cut (((f (g zenon_TY_t)) = (f (g (f (g (f (g (f zenon_TX_d))))))))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((g zenon_TY_t) = (g (f (g (f (g (f zenon_TX_d)))))))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))) = ((g zenon_TY_t) = (g (f (g (f (g (f zenon_TX_d)))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H60.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H4b.
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))) = (g (f (g (f (g (f zenon_TX_d)))))))); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g zenon_TY_t))); [idtac | apply NNPP; zenon_intro zenon_H61].
% 2.23/2.44 congruence.
% 2.23/2.44 elim (classic ((g zenon_TY_t) = (g zenon_TY_t))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ].
% 2.23/2.44 cut (((g zenon_TY_t) = (g zenon_TY_t)) = ((g (f (g (f (g (f (g (f zenon_TX_d)))))))) = (g zenon_TY_t))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H61.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H62.
% 2.23/2.44 cut (((g zenon_TY_t) = (g zenon_TY_t))); [idtac | apply NNPP; zenon_intro zenon_H63].
% 2.23/2.44 cut (((g zenon_TY_t) = (g (f (g (f (g (f (g (f zenon_TX_d)))))))))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 2.23/2.44 congruence.
% 2.23/2.44 cut ((zenon_TY_t = (f (g (f (g (f (g (f zenon_TX_d))))))))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 2.23/2.44 congruence.
% 2.23/2.44 apply zenon_H65. apply sym_equal. exact zenon_H59.
% 2.23/2.44 apply zenon_H63. apply refl_equal.
% 2.23/2.44 apply zenon_H63. apply refl_equal.
% 2.23/2.44 apply (zenon_L5_ zenon_TX_d); trivial.
% 2.23/2.44 apply zenon_H5b. apply refl_equal.
% 2.23/2.44 apply zenon_H5b. apply refl_equal.
% 2.23/2.44 apply zenon_H5d. apply refl_equal.
% 2.23/2.44 apply zenon_H5b. apply refl_equal.
% 2.23/2.44 apply zenon_H5b. apply refl_equal.
% 2.23/2.44 generalize (zenon_H3d (g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))))). zenon_intro zenon_H66.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H66); [ zenon_intro zenon_H6a; zenon_intro zenon_H69 | zenon_intro zenon_H68; zenon_intro zenon_H67 ].
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))) = (f (g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H6b].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))) = (g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_H53 zenon_H51).
% 2.23/2.44 elim (classic (zenon_TY_t = zenon_TY_t)); [ zenon_intro zenon_H6c | zenon_intro zenon_H5d ].
% 2.23/2.44 cut ((zenon_TY_t = zenon_TY_t) = ((f (g (f (g (f (g (f zenon_TX_d))))))) = zenon_TY_t)).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H58.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H6c.
% 2.23/2.44 cut ((zenon_TY_t = zenon_TY_t)); [idtac | apply NNPP; zenon_intro zenon_H5d].
% 2.23/2.44 cut ((zenon_TY_t = (f (g (f (g (f (g (f zenon_TX_d))))))))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 2.23/2.44 congruence.
% 2.23/2.44 cut ((zenon_TY_t = (f (g zenon_TY_t))) = (zenon_TY_t = (f (g (f (g (f (g (f zenon_TX_d))))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H65.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H12.
% 2.23/2.44 cut (((f (g zenon_TY_t)) = (f (g (f (g (f (g (f zenon_TX_d))))))))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 2.23/2.44 cut ((zenon_TY_t = zenon_TY_t)); [idtac | apply NNPP; zenon_intro zenon_H5d].
% 2.23/2.44 congruence.
% 2.23/2.44 apply zenon_H5d. apply refl_equal.
% 2.23/2.44 cut (((g zenon_TY_t) = (g (f (g (f (g (f zenon_TX_d)))))))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 2.23/2.44 congruence.
% 2.23/2.44 generalize (zenon_H3d (g zenon_TY_t)). zenon_intro zenon_H6d.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H6d); [ zenon_intro zenon_H11; zenon_intro zenon_H70 | zenon_intro zenon_H6f; zenon_intro zenon_H6e ].
% 2.23/2.44 apply (zenon_L6_ zenon_TY_t); trivial.
% 2.23/2.44 cut ((zenon_TX_d = (g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d))))))))))))) = ((g zenon_TY_t) = (g (f (g (f (g (f zenon_TX_d)))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H60.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H67.
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f (g (f (g (f zenon_TX_d)))))))))))) = (g (f (g (f (g (f zenon_TX_d)))))))); [idtac | apply NNPP; zenon_intro zenon_H15].
% 2.23/2.44 cut ((zenon_TX_d = (g zenon_TY_t))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_H70 zenon_H6e).
% 2.23/2.44 apply (zenon_L7_ zenon_TX_d); trivial.
% 2.23/2.44 apply zenon_H5d. apply refl_equal.
% 2.23/2.44 apply zenon_H5d. apply refl_equal.
% 2.23/2.44 elim zenon_H3a. zenon_intro zenon_TX_bf. zenon_intro zenon_H71.
% 2.23/2.44 generalize (zenon_H71 zenon_TX_bf). zenon_intro zenon_H72.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H76; zenon_intro zenon_H75 | zenon_intro zenon_H74; zenon_intro zenon_H73 ].
% 2.23/2.44 apply zenon_H75. apply refl_equal.
% 2.23/2.44 generalize (zenon_H71 (f (g zenon_TX_bf))). zenon_intro zenon_H77.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H77); [ zenon_intro zenon_H21; zenon_intro zenon_H76 | zenon_intro zenon_H1e; zenon_intro zenon_H74 ].
% 2.23/2.44 exact (zenon_H76 zenon_H74).
% 2.23/2.44 generalize (zenon_H71 (f (g (f (g zenon_TX_bf))))). zenon_intro zenon_H78.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H1d; zenon_intro zenon_H79 | zenon_intro zenon_H23; zenon_intro zenon_H26 ].
% 2.23/2.44 apply (zenon_L8_ zenon_TX_bf); trivial.
% 2.23/2.44 generalize (zenon_H71 (f (g (f (g (f (g zenon_TX_bf))))))). zenon_intro zenon_H7a.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H7a); [ zenon_intro zenon_H22; zenon_intro zenon_H7c | zenon_intro zenon_H7b; zenon_intro zenon_H32 ].
% 2.23/2.44 apply (zenon_L9_ zenon_TX_bf); trivial.
% 2.23/2.44 generalize (zenon_H71 (f (g (f (g (f (g (f (g zenon_TX_bf))))))))). zenon_intro zenon_H7d.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H81; zenon_intro zenon_H80 | zenon_intro zenon_H7f; zenon_intro zenon_H7e ].
% 2.23/2.44 cut (((g (f (g (f (g (f (g zenon_TX_bf))))))) = (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))); [idtac | apply NNPP; zenon_intro zenon_H82].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((f (g (f (g (f (g zenon_TX_bf)))))) = (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_H22 zenon_H7b).
% 2.23/2.44 generalize (zenon_H71 (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))). zenon_intro zenon_H83.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H87; zenon_intro zenon_H86 | zenon_intro zenon_H85; zenon_intro zenon_H84 ].
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))) = (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_H81 zenon_H7f).
% 2.23/2.44 apply zenon_H39. exists (g (f (g (f (g (f (g zenon_TX_bf))))))). apply NNPP. zenon_intro zenon_H89.
% 2.23/2.44 apply (zenon_notallex_s (fun Y : zenon_U => ((Y = (g (f Y)))<->((g (f (g (f (g (f (g zenon_TX_bf))))))) = Y))) zenon_H89); [ zenon_intro zenon_H8a; idtac ].
% 2.23/2.44 elim zenon_H8a. zenon_intro zenon_TY_bv. zenon_intro zenon_H8b.
% 2.23/2.44 apply (zenon_notequiv_s _ _ zenon_H8b); [ zenon_intro zenon_H30; zenon_intro zenon_H8d | zenon_intro zenon_H2e; zenon_intro zenon_H8c ].
% 2.23/2.44 elim (classic ((g (f zenon_TY_bv)) = (g (f zenon_TY_bv)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ].
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f zenon_TY_bv))) = (zenon_TY_bv = (g (f zenon_TY_bv)))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H30.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H8e.
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f zenon_TY_bv)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = zenon_TY_bv)); [idtac | apply NNPP; zenon_intro zenon_H90].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((g (f (g (f (g (f (g zenon_TX_bf))))))) = zenon_TY_bv) = ((g (f zenon_TY_bv)) = zenon_TY_bv)).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H90.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H8d.
% 2.23/2.44 cut ((zenon_TY_bv = zenon_TY_bv)); [idtac | apply NNPP; zenon_intro zenon_H91].
% 2.23/2.44 cut (((g (f (g (f (g (f (g zenon_TX_bf))))))) = (g (f zenon_TY_bv)))); [idtac | apply NNPP; zenon_intro zenon_H92].
% 2.23/2.44 congruence.
% 2.23/2.44 elim (classic ((g (f zenon_TY_bv)) = (g (f zenon_TY_bv)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ].
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f zenon_TY_bv))) = ((g (f (g (f (g (f (g zenon_TX_bf))))))) = (g (f zenon_TY_bv)))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H92.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H8e.
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f zenon_TY_bv)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f (g (f (g (f (g zenon_TX_bf))))))))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((f zenon_TY_bv) = (f (g (f (g (f (g zenon_TX_bf)))))))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))) = ((f zenon_TY_bv) = (f (g (f (g (f (g zenon_TX_bf)))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H94.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H7f.
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))) = (f (g (f (g (f (g zenon_TX_bf)))))))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f zenon_TY_bv))); [idtac | apply NNPP; zenon_intro zenon_H95].
% 2.23/2.44 congruence.
% 2.23/2.44 elim (classic ((f zenon_TY_bv) = (f zenon_TY_bv))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ].
% 2.23/2.44 cut (((f zenon_TY_bv) = (f zenon_TY_bv)) = ((f (g (f (g (f (g (f (g zenon_TX_bf)))))))) = (f zenon_TY_bv))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H95.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H96.
% 2.23/2.44 cut (((f zenon_TY_bv) = (f zenon_TY_bv))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 2.23/2.44 cut (((f zenon_TY_bv) = (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))); [idtac | apply NNPP; zenon_intro zenon_H98].
% 2.23/2.44 congruence.
% 2.23/2.44 cut ((zenon_TY_bv = (g (f (g (f (g (f (g zenon_TX_bf))))))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 2.23/2.44 congruence.
% 2.23/2.44 apply zenon_H99. apply sym_equal. exact zenon_H8d.
% 2.23/2.44 apply zenon_H97. apply refl_equal.
% 2.23/2.44 apply zenon_H97. apply refl_equal.
% 2.23/2.44 apply (zenon_L12_ zenon_TX_bf); trivial.
% 2.23/2.44 apply zenon_H8f. apply refl_equal.
% 2.23/2.44 apply zenon_H8f. apply refl_equal.
% 2.23/2.44 apply zenon_H91. apply refl_equal.
% 2.23/2.44 apply zenon_H8f. apply refl_equal.
% 2.23/2.44 apply zenon_H8f. apply refl_equal.
% 2.23/2.44 generalize (zenon_H71 (f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))))). zenon_intro zenon_H9a.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H9e; zenon_intro zenon_H9d | zenon_intro zenon_H9c; zenon_intro zenon_H9b ].
% 2.23/2.44 cut (((g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))) = (g (f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H9f].
% 2.23/2.44 congruence.
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))) = (f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))))))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_H87 zenon_H85).
% 2.23/2.44 elim (classic (zenon_TY_bv = zenon_TY_bv)); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H91 ].
% 2.23/2.44 cut ((zenon_TY_bv = zenon_TY_bv) = ((g (f (g (f (g (f (g zenon_TX_bf))))))) = zenon_TY_bv)).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H8c.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_Ha0.
% 2.23/2.44 cut ((zenon_TY_bv = zenon_TY_bv)); [idtac | apply NNPP; zenon_intro zenon_H91].
% 2.23/2.44 cut ((zenon_TY_bv = (g (f (g (f (g (f (g zenon_TX_bf))))))))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 2.23/2.44 congruence.
% 2.23/2.44 cut ((zenon_TY_bv = (g (f zenon_TY_bv))) = (zenon_TY_bv = (g (f (g (f (g (f (g zenon_TX_bf))))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H99.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H2e.
% 2.23/2.44 cut (((g (f zenon_TY_bv)) = (g (f (g (f (g (f (g zenon_TX_bf))))))))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 2.23/2.44 cut ((zenon_TY_bv = zenon_TY_bv)); [idtac | apply NNPP; zenon_intro zenon_H91].
% 2.23/2.44 congruence.
% 2.23/2.44 apply zenon_H91. apply refl_equal.
% 2.23/2.44 cut (((f zenon_TY_bv) = (f (g (f (g (f (g zenon_TX_bf)))))))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 2.23/2.44 congruence.
% 2.23/2.44 generalize (zenon_H71 (f zenon_TY_bv)). zenon_intro zenon_Ha1.
% 2.23/2.44 apply (zenon_equiv_s _ _ zenon_Ha1); [ zenon_intro zenon_H2d; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3; zenon_intro zenon_Ha2 ].
% 2.23/2.44 apply (zenon_L13_ zenon_TY_bv); trivial.
% 2.23/2.44 cut ((zenon_TX_bf = (f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf))))))))))))) = ((f zenon_TY_bv) = (f (g (f (g (f (g zenon_TX_bf)))))))).
% 2.23/2.44 intro zenon_D_pnotp.
% 2.23/2.44 apply zenon_H94.
% 2.23/2.44 rewrite <- zenon_D_pnotp.
% 2.23/2.44 exact zenon_H9b.
% 2.23/2.44 cut (((f (g (f (g (f (g (f (g (f (g (f (g zenon_TX_bf)))))))))))) = (f (g (f (g (f (g zenon_TX_bf)))))))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 2.23/2.44 cut ((zenon_TX_bf = (f zenon_TY_bv))); [idtac | apply NNPP; zenon_intro zenon_Ha4].
% 2.23/2.44 congruence.
% 2.23/2.44 exact (zenon_Ha4 zenon_Ha2).
% 2.23/2.44 apply (zenon_L14_ zenon_TX_bf); trivial.
% 2.23/2.44 apply zenon_H91. apply refl_equal.
% 2.23/2.44 apply zenon_H91. apply refl_equal.
% 2.23/2.44 Qed.
% 2.23/2.44 % SZS output end Proof
% 2.23/2.44 (* END-PROOF *)
% 2.23/2.44 nodes searched: 50903
% 2.23/2.44 max branch formulas: 631
% 2.23/2.44 proof nodes created: 1149
% 2.23/2.44 formulas created: 56014
% 2.23/2.44
%------------------------------------------------------------------------------