TSTP Solution File: ALG110+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : ALG110+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n032.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 14 18:29:27 EDT 2022
% Result : Theorem 29.61s 29.84s
% Output : Proof 29.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ALG110+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.11 % Command : run_zenon %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Wed Jun 8 12:22:51 EDT 2022
% 0.11/0.30 % CPUTime :
% 29.61/29.84 (* PROOF-FOUND *)
% 29.61/29.84 % SZS status Theorem
% 29.61/29.84 (* BEGIN-PROOF *)
% 29.61/29.84 % SZS output start Proof
% 29.61/29.84 Theorem co1 : ((((h1 (op1 (e10) (e10))) = (op2 (h1 (e10)) (h1 (e10))))/\(((h1 (op1 (e10) (e11))) = (op2 (h1 (e10)) (h1 (e11))))/\(((h1 (op1 (e10) (e12))) = (op2 (h1 (e10)) (h1 (e12))))/\(((h1 (op1 (e10) (e13))) = (op2 (h1 (e10)) (h1 (e13))))/\(((h1 (op1 (e11) (e10))) = (op2 (h1 (e11)) (h1 (e10))))/\(((h1 (op1 (e11) (e11))) = (op2 (h1 (e11)) (h1 (e11))))/\(((h1 (op1 (e11) (e12))) = (op2 (h1 (e11)) (h1 (e12))))/\(((h1 (op1 (e11) (e13))) = (op2 (h1 (e11)) (h1 (e13))))/\(((h1 (op1 (e12) (e10))) = (op2 (h1 (e12)) (h1 (e10))))/\(((h1 (op1 (e12) (e11))) = (op2 (h1 (e12)) (h1 (e11))))/\(((h1 (op1 (e12) (e12))) = (op2 (h1 (e12)) (h1 (e12))))/\(((h1 (op1 (e12) (e13))) = (op2 (h1 (e12)) (h1 (e13))))/\(((h1 (op1 (e13) (e10))) = (op2 (h1 (e13)) (h1 (e10))))/\(((h1 (op1 (e13) (e11))) = (op2 (h1 (e13)) (h1 (e11))))/\(((h1 (op1 (e13) (e12))) = (op2 (h1 (e13)) (h1 (e12))))/\(((h1 (op1 (e13) (e13))) = (op2 (h1 (e13)) (h1 (e13))))/\((((h1 (e10)) = (e20))\/(((h1 (e11)) = (e20))\/(((h1 (e12)) = (e20))\/((h1 (e13)) = (e20)))))/\((((h1 (e10)) = (e21))\/(((h1 (e11)) = (e21))\/(((h1 (e12)) = (e21))\/((h1 (e13)) = (e21)))))/\((((h1 (e10)) = (e22))\/(((h1 (e11)) = (e22))\/(((h1 (e12)) = (e22))\/((h1 (e13)) = (e22)))))/\(((h1 (e10)) = (e23))\/(((h1 (e11)) = (e23))\/(((h1 (e12)) = (e23))\/((h1 (e13)) = (e23))))))))))))))))))))))))\/((((h2 (op1 (e10) (e10))) = (op2 (h2 (e10)) (h2 (e10))))/\(((h2 (op1 (e10) (e11))) = (op2 (h2 (e10)) (h2 (e11))))/\(((h2 (op1 (e10) (e12))) = (op2 (h2 (e10)) (h2 (e12))))/\(((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))/\(((h2 (op1 (e11) (e10))) = (op2 (h2 (e11)) (h2 (e10))))/\(((h2 (op1 (e11) (e11))) = (op2 (h2 (e11)) (h2 (e11))))/\(((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))/\(((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))/\(((h2 (op1 (e12) (e10))) = (op2 (h2 (e12)) (h2 (e10))))/\(((h2 (op1 (e12) (e11))) = (op2 (h2 (e12)) (h2 (e11))))/\(((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))/\(((h2 (op1 (e12) (e13))) = (op2 (h2 (e12)) (h2 (e13))))/\(((h2 (op1 (e13) (e10))) = (op2 (h2 (e13)) (h2 (e10))))/\(((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))/\(((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))/\(((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))/\((((h2 (e10)) = (e20))\/(((h2 (e11)) = (e20))\/(((h2 (e12)) = (e20))\/((h2 (e13)) = (e20)))))/\((((h2 (e10)) = (e21))\/(((h2 (e11)) = (e21))\/(((h2 (e12)) = (e21))\/((h2 (e13)) = (e21)))))/\((((h2 (e10)) = (e22))\/(((h2 (e11)) = (e22))\/(((h2 (e12)) = (e22))\/((h2 (e13)) = (e22)))))/\(((h2 (e10)) = (e23))\/(((h2 (e11)) = (e23))\/(((h2 (e12)) = (e23))\/((h2 (e13)) = (e23))))))))))))))))))))))))\/((((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))/\(((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))/\(((h3 (op1 (e10) (e12))) = (op2 (h3 (e10)) (h3 (e12))))/\(((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))/\(((h3 (op1 (e11) (e10))) = (op2 (h3 (e11)) (h3 (e10))))/\(((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))/\(((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))/\(((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))/\(((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))/\(((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))/\(((h3 (op1 (e12) (e12))) = (op2 (h3 (e12)) (h3 (e12))))/\(((h3 (op1 (e12) (e13))) = (op2 (h3 (e12)) (h3 (e13))))/\(((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))/\(((h3 (op1 (e13) (e11))) = (op2 (h3 (e13)) (h3 (e11))))/\(((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))/\(((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))/\((((h3 (e10)) = (e20))\/(((h3 (e11)) = (e20))\/(((h3 (e12)) = (e20))\/((h3 (e13)) = (e20)))))/\((((h3 (e10)) = (e21))\/(((h3 (e11)) = (e21))\/(((h3 (e12)) = (e21))\/((h3 (e13)) = (e21)))))/\((((h3 (e10)) = (e22))\/(((h3 (e11)) = (e22))\/(((h3 (e12)) = (e22))\/((h3 (e13)) = (e22)))))/\(((h3 (e10)) = (e23))\/(((h3 (e11)) = (e23))\/(((h3 (e12)) = (e23))\/((h3 (e13)) = (e23))))))))))))))))))))))))\/(((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))/\(((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))/\(((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))/\(((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))/\(((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))/\(((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))/\(((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))/\(((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))/\(((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))/\(((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))/\(((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))/\(((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))/\(((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))/\(((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))/\(((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))/\(((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))/\((((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))/\((((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))/\((((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))/\(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23))))))))))))))))))))))))))).
% 29.61/29.84 Proof.
% 29.61/29.84 assert (zenon_L1_ : (((op2 (e20) (e20)) = (e20))/\(~((op2 (e20) (e20)) = (e20)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H12.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13.
% 29.61/29.84 exact (zenon_H13 zenon_H14).
% 29.61/29.84 (* end of lemma zenon_L1_ *)
% 29.61/29.84 assert (zenon_L2_ : (((op2 (e20) (e21)) = (e20))/\(~((op2 (e21) (e20)) = (e21)))) -> (~((op2 (e20) (e21)) = (e20))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H15 zenon_H16.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17.
% 29.61/29.84 exact (zenon_H16 zenon_H18).
% 29.61/29.84 (* end of lemma zenon_L2_ *)
% 29.61/29.84 assert (zenon_L3_ : (((op2 (e21) (e21)) = (e21))/\(~((op2 (e21) (e21)) = (e21)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H19.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 29.61/29.84 exact (zenon_H1a zenon_H1b).
% 29.61/29.84 (* end of lemma zenon_L3_ *)
% 29.61/29.84 assert (zenon_L4_ : (~((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H1c zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 29.61/29.84 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H1e. apply sym_equal. exact zenon_H1d.
% 29.61/29.84 apply zenon_H1e. apply sym_equal. exact zenon_H1d.
% 29.61/29.84 (* end of lemma zenon_L4_ *)
% 29.61/29.84 assert (zenon_L5_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e20) (e23)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H1f zenon_H20 zenon_H21 zenon_H1d.
% 29.61/29.84 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H1f.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H20.
% 29.61/29.84 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.61/29.84 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H23 | zenon_intro zenon_H24 ].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e20) = (op2 (e20) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H22.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H23.
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H25 zenon_H21).
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 apply (zenon_L4_); trivial.
% 29.61/29.84 (* end of lemma zenon_L5_ *)
% 29.61/29.84 assert (zenon_L6_ : (((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H26 zenon_H1d zenon_H20 zenon_H1f.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H21. zenon_intro zenon_H27.
% 29.61/29.84 apply (zenon_L5_); trivial.
% 29.61/29.84 (* end of lemma zenon_L6_ *)
% 29.61/29.84 assert (zenon_L7_ : (~((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H28 zenon_H1d zenon_H20.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 29.61/29.84 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H29. apply sym_equal. exact zenon_H20.
% 29.61/29.84 apply zenon_H1e. apply sym_equal. exact zenon_H1d.
% 29.61/29.84 (* end of lemma zenon_L7_ *)
% 29.61/29.84 assert (zenon_L8_ : ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e21) (e23)) = (e21)) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H2a zenon_H2b zenon_H1d zenon_H20 zenon_H2c.
% 29.61/29.84 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ].
% 29.61/29.84 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H2c.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H2d.
% 29.61/29.84 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 29.61/29.84 cut (((op2 (e21) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e21) (e23)) = (op2 (e20) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H2f.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H2a.
% 29.61/29.84 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 29.61/29.84 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ].
% 29.61/29.84 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e21) = (op2 (e21) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H30.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H2d.
% 29.61/29.84 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 29.61/29.84 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H31 zenon_H2b).
% 29.61/29.84 apply zenon_H2e. apply refl_equal.
% 29.61/29.84 apply zenon_H2e. apply refl_equal.
% 29.61/29.84 apply (zenon_L7_); trivial.
% 29.61/29.84 apply zenon_H2e. apply refl_equal.
% 29.61/29.84 apply zenon_H2e. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L8_ *)
% 29.61/29.84 assert (zenon_L9_ : (((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H32 zenon_H1d zenon_H20 zenon_H2a zenon_H2c.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H2b. zenon_intro zenon_H33.
% 29.61/29.84 apply (zenon_L8_); trivial.
% 29.61/29.84 (* end of lemma zenon_L9_ *)
% 29.61/29.84 assert (zenon_L10_ : (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e22) (e23)) = (e22)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H34 zenon_H35 zenon_H36.
% 29.61/29.84 cut (((op2 (e22) (e21)) = (e22)) = ((op2 (e22) (e21)) = (op2 (e22) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H34.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H35.
% 29.61/29.84 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 29.61/29.84 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H38].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H38. apply refl_equal.
% 29.61/29.84 apply zenon_H37. apply sym_equal. exact zenon_H36.
% 29.61/29.84 (* end of lemma zenon_L10_ *)
% 29.61/29.84 assert (zenon_L11_ : (((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H39 zenon_H35 zenon_H34.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.61/29.84 apply (zenon_L10_); trivial.
% 29.61/29.84 (* end of lemma zenon_L11_ *)
% 29.61/29.84 assert (zenon_L12_ : (((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H3b.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 29.61/29.84 exact (zenon_H3c zenon_H3d).
% 29.61/29.84 (* end of lemma zenon_L12_ *)
% 29.61/29.84 assert (zenon_L13_ : ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H3e zenon_H1f zenon_H2c zenon_H2a zenon_H20 zenon_H1d zenon_H34 zenon_H35.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.61/29.84 apply (zenon_L6_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.61/29.84 apply (zenon_L9_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.61/29.84 apply (zenon_L11_); trivial.
% 29.61/29.84 apply (zenon_L12_); trivial.
% 29.61/29.84 (* end of lemma zenon_L13_ *)
% 29.61/29.84 assert (zenon_L14_ : (((op2 (e22) (e21)) = (e22))/\(~((op2 (e21) (e22)) = (e21)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H41 zenon_H1d zenon_H20 zenon_H1f zenon_H2a zenon_H2c zenon_H34 zenon_H3e.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H35. zenon_intro zenon_H42.
% 29.61/29.84 apply (zenon_L13_); trivial.
% 29.61/29.84 (* end of lemma zenon_L14_ *)
% 29.61/29.84 assert (zenon_L15_ : (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H43 zenon_H44 zenon_H45.
% 29.61/29.84 cut (((op1 (e10) (e11)) = (e10)) = ((op1 (e10) (e11)) = (op1 (e10) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H43.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H44.
% 29.61/29.84 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 29.61/29.84 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H47. apply refl_equal.
% 29.61/29.84 apply zenon_H46. apply sym_equal. exact zenon_H45.
% 29.61/29.84 (* end of lemma zenon_L15_ *)
% 29.61/29.84 assert (zenon_L16_ : (~((e11) = (e11))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H48.
% 29.61/29.84 apply zenon_H48. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L16_ *)
% 29.61/29.84 assert (zenon_L17_ : (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e10)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H49 zenon_H4a zenon_H4b.
% 29.61/29.84 cut (((op1 (e11) (e12)) = (e11)) = ((e10) = (e11))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H49.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H4a.
% 29.61/29.84 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 29.61/29.84 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H4c zenon_H4b).
% 29.61/29.84 apply zenon_H48. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L17_ *)
% 29.61/29.84 assert (zenon_L18_ : (~((e13) = (e13))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H4d.
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L18_ *)
% 29.61/29.84 assert (zenon_L19_ : ((e13) = (op1 (e12) (e12))) -> ((op1 (e12) (e12)) = (e10)) -> (~((e10) = (e13))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H4e zenon_H4f zenon_H50.
% 29.61/29.84 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H51 | zenon_intro zenon_H4d ].
% 29.61/29.84 cut (((e13) = (e13)) = ((e10) = (e13))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H50.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H51.
% 29.61/29.84 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.61/29.84 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H52].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e13) = (op1 (e12) (e12))) = ((e13) = (e10))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H52.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H4e.
% 29.61/29.84 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 29.61/29.84 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 exact (zenon_H53 zenon_H4f).
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L19_ *)
% 29.61/29.84 assert (zenon_L20_ : (~((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H54 zenon_H4e.
% 29.61/29.84 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 29.61/29.84 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H55. apply sym_equal. exact zenon_H4e.
% 29.61/29.84 apply zenon_H55. apply sym_equal. exact zenon_H4e.
% 29.61/29.84 (* end of lemma zenon_L20_ *)
% 29.61/29.84 assert (zenon_L21_ : (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H56 zenon_H57 zenon_H58 zenon_H4e.
% 29.61/29.84 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e13) (e12)) = (op1 (e13) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H56.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H57.
% 29.61/29.84 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.61/29.84 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e10) = (op1 (e13) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H59.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H5a.
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H5c zenon_H58).
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 apply (zenon_L20_); trivial.
% 29.61/29.84 (* end of lemma zenon_L21_ *)
% 29.61/29.84 assert (zenon_L22_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((op1 (e11) (e12)) = (e11)) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H5d zenon_H44 zenon_H43 zenon_H4a zenon_H49 zenon_H50 zenon_H56 zenon_H57 zenon_H4e.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H45 | zenon_intro zenon_H5e ].
% 29.61/29.84 apply (zenon_L15_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H4b | zenon_intro zenon_H5f ].
% 29.61/29.84 apply (zenon_L17_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H4f | zenon_intro zenon_H58 ].
% 29.61/29.84 apply (zenon_L19_); trivial.
% 29.61/29.84 apply (zenon_L21_); trivial.
% 29.61/29.84 (* end of lemma zenon_L22_ *)
% 29.61/29.84 assert (zenon_L23_ : (((op1 (e12) (e12)) = (e12))/\(~((op1 (e12) (e12)) = (e12)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H60.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 29.61/29.84 exact (zenon_H61 zenon_H62).
% 29.61/29.84 (* end of lemma zenon_L23_ *)
% 29.61/29.84 assert (zenon_L24_ : (((op1 (e13) (e12)) = (e13))/\(~((op1 (e12) (e13)) = (e12)))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H63 zenon_H4e zenon_H64.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 29.61/29.84 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H64.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H5a.
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H67].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e13) = (op1 (e12) (e12))) = ((op1 (e13) (e12)) = (op1 (e12) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H67.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H4e.
% 29.61/29.84 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 29.61/29.84 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H5a | zenon_intro zenon_H5b ].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e13) = (op1 (e13) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H69.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H5a.
% 29.61/29.84 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 29.61/29.84 cut (((op1 (e13) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H6a zenon_H66).
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 apply zenon_H68. apply refl_equal.
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 apply zenon_H5b. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L24_ *)
% 29.61/29.84 assert (zenon_L25_ : (((op1 (e10) (e11)) = (e10))/\(~((op1 (e11) (e10)) = (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((((op1 (e10) (e12)) = (e10))/\(~((op1 (e12) (e10)) = (e12))))\/((((op1 (e11) (e12)) = (e11))/\(~((op1 (e12) (e11)) = (e12))))\/((((op1 (e12) (e12)) = (e12))/\(~((op1 (e12) (e12)) = (e12))))\/(((op1 (e13) (e12)) = (e13))/\(~((op1 (e12) (e13)) = (e12))))))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H6b zenon_H43 zenon_H49 zenon_H50 zenon_H4e zenon_H56 zenon_H57 zenon_H5d zenon_H64 zenon_H6c.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H44. zenon_intro zenon_H6d.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.61/29.84 apply (zenon_L15_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H4a. zenon_intro zenon_H73.
% 29.61/29.84 apply (zenon_L22_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.61/29.84 apply (zenon_L23_); trivial.
% 29.61/29.84 apply (zenon_L24_); trivial.
% 29.61/29.84 (* end of lemma zenon_L25_ *)
% 29.61/29.84 assert (zenon_L26_ : (((op1 (e11) (e11)) = (e11))/\(~((op1 (e11) (e11)) = (e11)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H74.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 29.61/29.84 exact (zenon_H75 zenon_H76).
% 29.61/29.84 (* end of lemma zenon_L26_ *)
% 29.61/29.84 assert (zenon_L27_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H77 zenon_H57 zenon_H78 zenon_H4e.
% 29.61/29.84 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H77.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H57.
% 29.61/29.84 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.61/29.84 cut (((e10) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H79].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ].
% 29.61/29.84 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e10) = (op1 (e10) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H79.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H7a.
% 29.61/29.84 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7b].
% 29.61/29.84 cut (((op1 (e10) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H7c zenon_H78).
% 29.61/29.84 apply zenon_H7b. apply refl_equal.
% 29.61/29.84 apply zenon_H7b. apply refl_equal.
% 29.61/29.84 apply (zenon_L20_); trivial.
% 29.61/29.84 (* end of lemma zenon_L27_ *)
% 29.61/29.84 assert (zenon_L28_ : (((op1 (e10) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H7d zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H78. zenon_intro zenon_H7e.
% 29.61/29.84 apply (zenon_L27_); trivial.
% 29.61/29.84 (* end of lemma zenon_L28_ *)
% 29.61/29.84 assert (zenon_L29_ : (~((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H7f zenon_H4e zenon_H57.
% 29.61/29.84 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 29.61/29.84 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H80. apply sym_equal. exact zenon_H57.
% 29.61/29.84 apply zenon_H55. apply sym_equal. exact zenon_H4e.
% 29.61/29.84 (* end of lemma zenon_L29_ *)
% 29.61/29.84 assert (zenon_L30_ : ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((op1 (e11) (e13)) = (e11)) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H81 zenon_H82 zenon_H4e zenon_H57 zenon_H83.
% 29.61/29.84 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 29.61/29.84 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H83.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H84.
% 29.61/29.84 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 29.61/29.84 cut (((op1 (e11) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H86].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e11) (e13)) = (op1 (e10) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H86.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H81.
% 29.61/29.84 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 29.61/29.84 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 29.61/29.84 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e11) = (op1 (e11) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H87.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H84.
% 29.61/29.84 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 29.61/29.84 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H88 zenon_H82).
% 29.61/29.84 apply zenon_H85. apply refl_equal.
% 29.61/29.84 apply zenon_H85. apply refl_equal.
% 29.61/29.84 apply (zenon_L29_); trivial.
% 29.61/29.84 apply zenon_H85. apply refl_equal.
% 29.61/29.84 apply zenon_H85. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L30_ *)
% 29.61/29.84 assert (zenon_L31_ : (((op1 (e11) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H89 zenon_H4e zenon_H57 zenon_H81 zenon_H83.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H82. zenon_intro zenon_H8a.
% 29.61/29.84 apply (zenon_L30_); trivial.
% 29.61/29.84 (* end of lemma zenon_L31_ *)
% 29.61/29.84 assert (zenon_L32_ : (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e12) (e13)) = (e12)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H8b zenon_H8c zenon_H8d.
% 29.61/29.84 cut (((op1 (e12) (e11)) = (e12)) = ((op1 (e12) (e11)) = (op1 (e12) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H8b.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H8c.
% 29.61/29.84 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H8e].
% 29.61/29.84 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H8f. apply refl_equal.
% 29.61/29.84 apply zenon_H8e. apply sym_equal. exact zenon_H8d.
% 29.61/29.84 (* end of lemma zenon_L32_ *)
% 29.61/29.84 assert (zenon_L33_ : (((op1 (e12) (e13)) = (e12))/\(~((op1 (e13) (e12)) = (e13)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H90 zenon_H8c zenon_H8b.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H8d. zenon_intro zenon_H6a.
% 29.61/29.84 apply (zenon_L32_); trivial.
% 29.61/29.84 (* end of lemma zenon_L33_ *)
% 29.61/29.84 assert (zenon_L34_ : (((op1 (e13) (e13)) = (e13))/\(~((op1 (e13) (e13)) = (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H91.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92.
% 29.61/29.84 exact (zenon_H92 zenon_H93).
% 29.61/29.84 (* end of lemma zenon_L34_ *)
% 29.61/29.84 assert (zenon_L35_ : ((((op1 (e10) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13))))\/((((op1 (e11) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13))))\/((((op1 (e12) (e13)) = (e12))/\(~((op1 (e13) (e12)) = (e13))))\/(((op1 (e13) (e13)) = (e13))/\(~((op1 (e13) (e13)) = (e13))))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e11)) = (e12)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H94 zenon_H77 zenon_H83 zenon_H81 zenon_H57 zenon_H4e zenon_H8b zenon_H8c.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H7d | zenon_intro zenon_H95 ].
% 29.61/29.84 apply (zenon_L28_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H89 | zenon_intro zenon_H96 ].
% 29.61/29.84 apply (zenon_L31_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H90 | zenon_intro zenon_H91 ].
% 29.61/29.84 apply (zenon_L33_); trivial.
% 29.61/29.84 apply (zenon_L34_); trivial.
% 29.61/29.84 (* end of lemma zenon_L35_ *)
% 29.61/29.84 assert (zenon_L36_ : (((op1 (e12) (e11)) = (e12))/\(~((op1 (e11) (e12)) = (e11)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((((op1 (e10) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13))))\/((((op1 (e11) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13))))\/((((op1 (e12) (e13)) = (e12))/\(~((op1 (e13) (e12)) = (e13))))\/(((op1 (e13) (e13)) = (e13))/\(~((op1 (e13) (e13)) = (e13))))))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H97 zenon_H4e zenon_H57 zenon_H77 zenon_H81 zenon_H83 zenon_H8b zenon_H94.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H8c. zenon_intro zenon_H98.
% 29.61/29.84 apply (zenon_L35_); trivial.
% 29.61/29.84 (* end of lemma zenon_L36_ *)
% 29.61/29.84 assert (zenon_L37_ : (~((h3 (e10)) = (e20))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H99 zenon_H9a zenon_H20.
% 29.61/29.84 cut (((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((h3 (e10)) = (e20))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H99.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H9a.
% 29.61/29.84 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 29.61/29.84 cut (((h3 (e10)) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H9b. apply refl_equal.
% 29.61/29.84 apply zenon_H29. apply sym_equal. exact zenon_H20.
% 29.61/29.84 (* end of lemma zenon_L37_ *)
% 29.61/29.84 assert (zenon_L38_ : ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H9c zenon_H9d zenon_H9e.
% 29.61/29.84 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ].
% 29.61/29.84 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H9e.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H9f.
% 29.61/29.84 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 29.61/29.84 cut (((op1 (e13) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op1 (e13) (e11)) = (e13)) = ((op1 (e13) (e11)) = (op1 (e10) (e11)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Ha1.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H9c.
% 29.61/29.84 cut (((e13) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 29.61/29.84 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_Ha0. apply refl_equal.
% 29.61/29.84 apply zenon_Ha2. apply sym_equal. exact zenon_H9d.
% 29.61/29.84 apply zenon_Ha0. apply refl_equal.
% 29.61/29.84 apply zenon_Ha0. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L38_ *)
% 29.61/29.84 assert (zenon_L39_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e10) (e12)) = (e13)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Ha3 zenon_H4e zenon_Ha4.
% 29.61/29.84 cut (((e13) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Ha3.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H4e.
% 29.61/29.84 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 29.61/29.84 cut (((e13) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha5].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha7 ].
% 29.61/29.84 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e13) = (op1 (e10) (e12)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Ha5.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Ha6.
% 29.61/29.84 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 29.61/29.84 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Ha8].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Ha8 zenon_Ha4).
% 29.61/29.84 apply zenon_Ha7. apply refl_equal.
% 29.61/29.84 apply zenon_Ha7. apply refl_equal.
% 29.61/29.84 apply zenon_H68. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L39_ *)
% 29.61/29.84 assert (zenon_L40_ : ((op1 (e10) (e13)) = (e11)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e11) = (e13))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Ha9 zenon_Haa zenon_Hab.
% 29.61/29.84 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H51 | zenon_intro zenon_H4d ].
% 29.61/29.84 cut (((e13) = (e13)) = ((e11) = (e13))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hab.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H51.
% 29.61/29.84 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.61/29.84 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op1 (e10) (e13)) = (e11)) = ((e13) = (e11))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hac.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Ha9.
% 29.61/29.84 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 29.61/29.84 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Had zenon_Haa).
% 29.61/29.84 apply zenon_H48. apply refl_equal.
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 apply zenon_H4d. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L40_ *)
% 29.61/29.84 assert (zenon_L41_ : ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((op1 (e12) (e13)) = (e11)) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H81 zenon_Hae zenon_H4e zenon_H57 zenon_Haf.
% 29.61/29.84 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 29.61/29.84 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Haf.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hb0.
% 29.61/29.84 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 29.61/29.84 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb2].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hb2.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H81.
% 29.61/29.84 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 29.61/29.84 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 29.61/29.84 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hb3.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hb0.
% 29.61/29.84 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 29.61/29.84 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hb4 zenon_Hae).
% 29.61/29.84 apply zenon_Hb1. apply refl_equal.
% 29.61/29.84 apply zenon_Hb1. apply refl_equal.
% 29.61/29.84 apply (zenon_L29_); trivial.
% 29.61/29.84 apply zenon_Hb1. apply refl_equal.
% 29.61/29.84 apply zenon_Hb1. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L41_ *)
% 29.61/29.84 assert (zenon_L42_ : ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((op1 (e13) (e13)) = (e11)) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H81 zenon_Hb5 zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.84 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ].
% 29.61/29.84 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H77.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hb6.
% 29.61/29.84 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 29.61/29.84 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb8].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hb8.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H81.
% 29.61/29.84 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 29.61/29.84 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb7 ].
% 29.61/29.84 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e11) = (op1 (e13) (e13)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hb9.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hb6.
% 29.61/29.84 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 29.61/29.84 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hba].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hba zenon_Hb5).
% 29.61/29.84 apply zenon_Hb7. apply refl_equal.
% 29.61/29.84 apply zenon_Hb7. apply refl_equal.
% 29.61/29.84 apply (zenon_L29_); trivial.
% 29.61/29.84 apply zenon_Hb7. apply refl_equal.
% 29.61/29.84 apply zenon_Hb7. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L42_ *)
% 29.61/29.84 assert (zenon_L43_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hbb zenon_Hab zenon_Haa zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.61/29.84 apply (zenon_L40_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.61/29.84 exact (zenon_H88 zenon_H82).
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.61/29.84 apply (zenon_L41_); trivial.
% 29.61/29.84 apply (zenon_L42_); trivial.
% 29.61/29.84 (* end of lemma zenon_L43_ *)
% 29.61/29.84 assert (zenon_L44_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e20) (e20)) = (e23)) -> ((h3 (e13)) = (op2 (e22) (e22))) -> (~((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hbe zenon_H20 zenon_H9a zenon_H1d zenon_Hbf zenon_Hc0 zenon_Hc1 zenon_H9e zenon_H9c zenon_Ha3 zenon_Hbb zenon_Hab zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 29.61/29.84 cut (((h3 (e13)) = (op2 (e22) (e22))) = ((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hc1.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hc0.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (h3 (e10)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 29.61/29.84 cut (((h3 (e13)) = (h3 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hc5].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((h3 (op1 (e10) (e10))) = (h3 (op1 (e10) (e10))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ].
% 29.61/29.84 cut (((h3 (op1 (e10) (e10))) = (h3 (op1 (e10) (e10)))) = ((h3 (e13)) = (h3 (op1 (e10) (e10))))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hc5.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hc6.
% 29.61/29.84 cut (((h3 (op1 (e10) (e10))) = (h3 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hc7].
% 29.61/29.84 cut (((h3 (op1 (e10) (e10))) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc8].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hc9].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hc9 zenon_Hc3).
% 29.61/29.84 apply zenon_Hc7. apply refl_equal.
% 29.61/29.84 apply zenon_Hc7. apply refl_equal.
% 29.61/29.84 elim (classic ((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10))))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ].
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10)))) = ((op2 (e22) (e22)) = (op2 (h3 (e10)) (h3 (e10))))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hc4.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hca.
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hcc].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op2 (e20) (e20)) = (e23)) = ((op2 (h3 (e10)) (h3 (e10))) = (op2 (e22) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hcc.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hbf.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hcd].
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (h3 (e10)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hce].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10))))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ].
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10)))) = ((op2 (e20) (e20)) = (op2 (h3 (e10)) (h3 (e10))))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hce.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hca.
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (h3 (e10)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 29.61/29.84 cut (((op2 (h3 (e10)) (h3 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hcf].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.61/29.84 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.61/29.84 congruence.
% 29.61/29.84 apply (zenon_L37_); trivial.
% 29.61/29.84 apply (zenon_L37_); trivial.
% 29.61/29.84 apply zenon_Hcb. apply refl_equal.
% 29.61/29.84 apply zenon_Hcb. apply refl_equal.
% 29.61/29.84 exact (zenon_Hcd zenon_H1d).
% 29.61/29.84 apply zenon_Hcb. apply refl_equal.
% 29.61/29.84 apply zenon_Hcb. apply refl_equal.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hd0 ].
% 29.61/29.84 apply (zenon_L38_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Haa ].
% 29.61/29.84 apply (zenon_L39_); trivial.
% 29.61/29.84 apply (zenon_L43_); trivial.
% 29.61/29.84 (* end of lemma zenon_L44_ *)
% 29.61/29.84 assert (zenon_L45_ : ((op2 (e23) (e21)) = (e23)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hd1 zenon_Hd2 zenon_Hd3.
% 29.61/29.84 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ].
% 29.61/29.84 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e20) (e21)) = (op2 (e23) (e21)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hd3.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hd4.
% 29.61/29.84 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 29.61/29.84 cut (((op2 (e23) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd6].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op2 (e23) (e21)) = (e23)) = ((op2 (e23) (e21)) = (op2 (e20) (e21)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hd6.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hd1.
% 29.61/29.84 cut (((e23) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd7].
% 29.61/29.84 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_Hd5. apply refl_equal.
% 29.61/29.84 apply zenon_Hd7. apply sym_equal. exact zenon_Hd2.
% 29.61/29.84 apply zenon_Hd5. apply refl_equal.
% 29.61/29.84 apply zenon_Hd5. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L45_ *)
% 29.61/29.84 assert (zenon_L46_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e20) (e22)) = (e23)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hd8 zenon_H1d zenon_Hd9.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hd8.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 29.61/29.84 cut (((e23) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdd ].
% 29.61/29.84 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e23) = (op2 (e20) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hdb.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hdc.
% 29.61/29.84 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 29.61/29.84 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hde zenon_Hd9).
% 29.61/29.84 apply zenon_Hdd. apply refl_equal.
% 29.61/29.84 apply zenon_Hdd. apply refl_equal.
% 29.61/29.84 apply zenon_Hda. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L46_ *)
% 29.61/29.84 assert (zenon_L47_ : ((e23) = (op2 (e22) (e22))) -> ((op2 (e20) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e20) (e20)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H1d zenon_Hbf zenon_Hdf.
% 29.61/29.84 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (e22) (e22)) = (op2 (e20) (e20)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hdf.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_He0.
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_He2].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e20) (e20)) = (op2 (e22) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_He2.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 29.61/29.84 cut (((e23) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He3].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ].
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((e23) = (op2 (e20) (e20)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_He3.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_He0.
% 29.61/29.84 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 29.61/29.84 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_He4].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_He4 zenon_Hbf).
% 29.61/29.84 apply zenon_He1. apply refl_equal.
% 29.61/29.84 apply zenon_He1. apply refl_equal.
% 29.61/29.84 apply zenon_Hda. apply refl_equal.
% 29.61/29.84 apply zenon_He1. apply refl_equal.
% 29.61/29.84 apply zenon_He1. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L47_ *)
% 29.61/29.84 assert (zenon_L48_ : ((op2 (e20) (e23)) = (e23)) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e20) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_He5 zenon_H1d zenon_Hbf zenon_He6.
% 29.61/29.84 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H23 | zenon_intro zenon_H24 ].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_He6.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H23.
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He7].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e20) (e23)) = (op2 (e20) (e20)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_He7.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 29.61/29.84 cut (((e23) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He8].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H23 | zenon_intro zenon_H24 ].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e23) = (op2 (e20) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_He8.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H23.
% 29.61/29.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 29.61/29.84 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_He9].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_He9 zenon_He5).
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 apply (zenon_L47_); trivial.
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 apply zenon_H24. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L48_ *)
% 29.61/29.84 assert (zenon_L49_ : (~((e21) = (e21))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hea.
% 29.61/29.84 apply zenon_Hea. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L49_ *)
% 29.61/29.84 assert (zenon_L50_ : ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e20)) = (e23)) -> (~((e21) = (e23))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Heb zenon_Hec zenon_Hed.
% 29.61/29.84 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hee | zenon_intro zenon_Hef ].
% 29.61/29.84 cut (((e23) = (e23)) = ((e21) = (e23))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hed.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hee.
% 29.61/29.84 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.61/29.84 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hf0].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((op2 (e21) (e20)) = (e21)) = ((e23) = (e21))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hf0.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Heb.
% 29.61/29.84 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hea].
% 29.61/29.84 cut (((op2 (e21) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hf1].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hf1 zenon_Hec).
% 29.61/29.84 apply zenon_Hea. apply refl_equal.
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L50_ *)
% 29.61/29.84 assert (zenon_L51_ : (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e20)) = (e23)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hf2 zenon_H1d zenon_Hf3.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e22) (e20)) = (op2 (e22) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hf2.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 29.61/29.84 cut (((e23) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf6 ].
% 29.61/29.84 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e23) = (op2 (e22) (e20)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hf4.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hf5.
% 29.61/29.84 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf6].
% 29.61/29.84 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hf7].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hf7 zenon_Hf3).
% 29.61/29.84 apply zenon_Hf6. apply refl_equal.
% 29.61/29.84 apply zenon_Hf6. apply refl_equal.
% 29.61/29.84 apply zenon_Hda. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L51_ *)
% 29.61/29.84 assert (zenon_L52_ : (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e21)) = (e20)) -> ((op2 (e20) (e22)) = (e20)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hf8 zenon_H18 zenon_Hf9.
% 29.61/29.84 cut (((op2 (e20) (e21)) = (e20)) = ((op2 (e20) (e21)) = (op2 (e20) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hf8.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H18.
% 29.61/29.84 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hfa].
% 29.61/29.84 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hfb].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_Hfb. apply refl_equal.
% 29.61/29.84 apply zenon_Hfa. apply sym_equal. exact zenon_Hf9.
% 29.61/29.84 (* end of lemma zenon_L52_ *)
% 29.61/29.84 assert (zenon_L53_ : (~((e20) = (e21))) -> ((op2 (e21) (e22)) = (e21)) -> ((op2 (e21) (e22)) = (e20)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hfc zenon_Hfd zenon_Hfe.
% 29.61/29.84 cut (((op2 (e21) (e22)) = (e21)) = ((e20) = (e21))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_Hfc.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hfd.
% 29.61/29.84 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hea].
% 29.61/29.84 cut (((op2 (e21) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hff].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_Hff zenon_Hfe).
% 29.61/29.84 apply zenon_Hea. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L53_ *)
% 29.61/29.84 assert (zenon_L54_ : (~((e23) = (e23))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_Hef.
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L54_ *)
% 29.61/29.84 assert (zenon_L55_ : ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e22)) = (e20)) -> (~((e20) = (e23))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H1d zenon_H100 zenon_H101.
% 29.61/29.84 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hee | zenon_intro zenon_Hef ].
% 29.61/29.84 cut (((e23) = (e23)) = ((e20) = (e23))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H101.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_Hee.
% 29.61/29.84 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.61/29.84 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H102].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((e23) = (e20))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H102.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H103].
% 29.61/29.84 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 exact (zenon_H103 zenon_H100).
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 apply zenon_Hef. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L55_ *)
% 29.61/29.84 assert (zenon_L56_ : (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e23) (e22)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H104 zenon_H20 zenon_H105 zenon_H1d.
% 29.61/29.84 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e23) (e22)) = (op2 (e23) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H104.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H20.
% 29.61/29.84 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.61/29.84 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e20) = (op2 (e23) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H106.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H107.
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H108].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H109].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H109 zenon_H105).
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 apply (zenon_L4_); trivial.
% 29.61/29.84 (* end of lemma zenon_L56_ *)
% 29.61/29.84 assert (zenon_L57_ : (((op2 (e22) (e22)) = (e22))/\(~((op2 (e22) (e22)) = (e22)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H10a.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H10a). zenon_intro zenon_H10c. zenon_intro zenon_H10b.
% 29.61/29.84 exact (zenon_H10b zenon_H10c).
% 29.61/29.84 (* end of lemma zenon_L57_ *)
% 29.61/29.84 assert (zenon_L58_ : (((op2 (e23) (e22)) = (e23))/\(~((op2 (e22) (e23)) = (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H10d zenon_H1d zenon_H10e.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f.
% 29.61/29.84 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H10e.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H107.
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H108].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H111].
% 29.61/29.84 congruence.
% 29.61/29.84 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e23) (e22)) = (op2 (e22) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H111.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H1d.
% 29.61/29.84 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 29.61/29.84 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H112].
% 29.61/29.84 congruence.
% 29.61/29.84 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e23) = (op2 (e23) (e22)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H112.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H107.
% 29.61/29.84 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H108].
% 29.61/29.84 cut (((op2 (e23) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3a].
% 29.61/29.84 congruence.
% 29.61/29.84 exact (zenon_H3a zenon_H110).
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 apply zenon_Hda. apply refl_equal.
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 apply zenon_H108. apply refl_equal.
% 29.61/29.84 (* end of lemma zenon_L58_ *)
% 29.61/29.84 assert (zenon_L59_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H113 zenon_H114 zenon_Hd1.
% 29.61/29.84 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H113.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H114.
% 29.61/29.84 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H115].
% 29.61/29.84 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H116].
% 29.61/29.84 congruence.
% 29.61/29.84 apply zenon_H116. apply refl_equal.
% 29.61/29.84 apply zenon_H115. apply sym_equal. exact zenon_Hd1.
% 29.61/29.84 (* end of lemma zenon_L59_ *)
% 29.61/29.84 assert (zenon_L60_ : (((op2 (e23) (e21)) = (e23))/\(~((op2 (e21) (e23)) = (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H117 zenon_H114 zenon_H113.
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.61/29.84 apply (zenon_L59_); trivial.
% 29.61/29.84 (* end of lemma zenon_L60_ *)
% 29.61/29.84 assert (zenon_L61_ : ((((op2 (e20) (e21)) = (e20))/\(~((op2 (e21) (e20)) = (e21))))\/((((op2 (e21) (e21)) = (e21))/\(~((op2 (e21) (e21)) = (e21))))\/((((op2 (e22) (e21)) = (e22))/\(~((op2 (e21) (e22)) = (e21))))\/(((op2 (e23) (e21)) = (e23))/\(~((op2 (e21) (e23)) = (e21))))))) -> ((((op2 (e20) (e22)) = (e20))/\(~((op2 (e22) (e20)) = (e22))))\/((((op2 (e21) (e22)) = (e21))/\(~((op2 (e22) (e21)) = (e22))))\/((((op2 (e22) (e22)) = (e22))/\(~((op2 (e22) (e22)) = (e22))))\/(((op2 (e23) (e22)) = (e23))/\(~((op2 (e22) (e23)) = (e22))))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H118 zenon_H119 zenon_H10e zenon_H11a zenon_H104 zenon_H101 zenon_Hfc zenon_Hf8 zenon_H3e zenon_H34 zenon_H2c zenon_H2a zenon_H1f zenon_H20 zenon_H1d zenon_H114 zenon_H113.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11d | zenon_intro zenon_H11c ].
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_Hf9. zenon_intro zenon_H11e.
% 29.61/29.84 apply (zenon_L52_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 29.61/29.84 apply (zenon_and_s _ _ zenon_H120). zenon_intro zenon_Hfd. zenon_intro zenon_H121.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H122 ].
% 29.61/29.84 apply (zenon_L52_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hfe | zenon_intro zenon_H123 ].
% 29.61/29.84 apply (zenon_L53_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H123); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ].
% 29.61/29.84 apply (zenon_L55_); trivial.
% 29.61/29.84 apply (zenon_L56_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H10a | zenon_intro zenon_H10d ].
% 29.61/29.84 apply (zenon_L57_); trivial.
% 29.61/29.84 apply (zenon_L58_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.61/29.84 apply (zenon_L3_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.61/29.84 apply (zenon_L14_); trivial.
% 29.61/29.84 apply (zenon_L60_); trivial.
% 29.61/29.84 (* end of lemma zenon_L61_ *)
% 29.61/29.84 assert (zenon_L62_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((e21) = (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((((op2 (e20) (e21)) = (e20))/\(~((op2 (e21) (e20)) = (e21))))\/((((op2 (e21) (e21)) = (e21))/\(~((op2 (e21) (e21)) = (e21))))\/((((op2 (e22) (e21)) = (e22))/\(~((op2 (e21) (e22)) = (e21))))\/(((op2 (e23) (e21)) = (e23))/\(~((op2 (e21) (e23)) = (e21))))))) -> ((((op2 (e20) (e22)) = (e20))/\(~((op2 (e22) (e20)) = (e22))))\/((((op2 (e21) (e22)) = (e21))/\(~((op2 (e22) (e21)) = (e22))))\/((((op2 (e22) (e22)) = (e22))/\(~((op2 (e22) (e22)) = (e22))))\/(((op2 (e23) (e22)) = (e23))/\(~((op2 (e22) (e23)) = (e22))))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H125 zenon_He6 zenon_He5 zenon_Hed zenon_Heb zenon_Hf2 zenon_H118 zenon_H119 zenon_H10e zenon_H11a zenon_H104 zenon_H101 zenon_Hfc zenon_Hf8 zenon_H3e zenon_H34 zenon_H2c zenon_H2a zenon_H1f zenon_H20 zenon_H1d zenon_H113.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_Hbf | zenon_intro zenon_H126 ].
% 29.61/29.84 apply (zenon_L48_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_Hec | zenon_intro zenon_H127 ].
% 29.61/29.84 apply (zenon_L50_); trivial.
% 29.61/29.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H114 ].
% 29.61/29.84 apply (zenon_L51_); trivial.
% 29.61/29.84 apply (zenon_L61_); trivial.
% 29.61/29.84 (* end of lemma zenon_L62_ *)
% 29.61/29.84 assert (zenon_L63_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e23)) = (e22)) -> False).
% 29.61/29.84 do 0 intro. intros zenon_H128 zenon_H129 zenon_H36.
% 29.61/29.84 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (e22) (e20)) = (op2 (e22) (e23)))).
% 29.61/29.84 intro zenon_D_pnotp.
% 29.61/29.84 apply zenon_H128.
% 29.61/29.84 rewrite <- zenon_D_pnotp.
% 29.61/29.84 exact zenon_H129.
% 29.61/29.84 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf6].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_Hf6. apply refl_equal.
% 29.61/29.85 apply zenon_H37. apply sym_equal. exact zenon_H36.
% 29.61/29.85 (* end of lemma zenon_L63_ *)
% 29.61/29.85 assert (zenon_L64_ : (((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H39 zenon_H129 zenon_H128.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.61/29.85 apply (zenon_L63_); trivial.
% 29.61/29.85 (* end of lemma zenon_L64_ *)
% 29.61/29.85 assert (zenon_L65_ : ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H3e zenon_H1f zenon_H2c zenon_H2a zenon_H20 zenon_H1d zenon_H128 zenon_H129.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.61/29.85 apply (zenon_L6_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.61/29.85 apply (zenon_L9_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.61/29.85 apply (zenon_L64_); trivial.
% 29.61/29.85 apply (zenon_L12_); trivial.
% 29.61/29.85 (* end of lemma zenon_L65_ *)
% 29.61/29.85 assert (zenon_L66_ : (((op2 (e22) (e20)) = (e22))/\(~((op2 (e20) (e22)) = (e20)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H12a zenon_H1d zenon_H20 zenon_H1f zenon_H2a zenon_H2c zenon_H128 zenon_H3e.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H12a). zenon_intro zenon_H129. zenon_intro zenon_H12b.
% 29.61/29.85 apply (zenon_L65_); trivial.
% 29.61/29.85 (* end of lemma zenon_L66_ *)
% 29.61/29.85 assert (zenon_L67_ : (((op2 (e23) (e20)) = (e23))/\(~((op2 (e20) (e23)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((e20) = (e21))) -> (~((e20) = (e23))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((((op2 (e20) (e22)) = (e20))/\(~((op2 (e22) (e20)) = (e22))))\/((((op2 (e21) (e22)) = (e21))/\(~((op2 (e22) (e21)) = (e22))))\/((((op2 (e22) (e22)) = (e22))/\(~((op2 (e22) (e22)) = (e22))))\/(((op2 (e23) (e22)) = (e23))/\(~((op2 (e22) (e23)) = (e22))))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((((op2 (e20) (e23)) = (e20))/\(~((op2 (e23) (e20)) = (e23))))\/((((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23))))\/((((op2 (e22) (e23)) = (e22))/\(~((op2 (e23) (e22)) = (e23))))\/(((op2 (e23) (e23)) = (e23))/\(~((op2 (e23) (e23)) = (e23))))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((((op2 (e20) (e21)) = (e20))/\(~((op2 (e21) (e20)) = (e21))))\/((((op2 (e21) (e21)) = (e21))/\(~((op2 (e21) (e21)) = (e21))))\/((((op2 (e22) (e21)) = (e22))/\(~((op2 (e21) (e22)) = (e21))))\/(((op2 (e23) (e21)) = (e23))/\(~((op2 (e21) (e23)) = (e21))))))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H12c zenon_Hf8 zenon_Hfc zenon_H101 zenon_H1d zenon_H104 zenon_H20 zenon_H11a zenon_H10e zenon_H119 zenon_H1f zenon_H2a zenon_H2c zenon_H34 zenon_H3e zenon_H113 zenon_H118.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H114. zenon_intro zenon_H25.
% 29.61/29.85 apply (zenon_L61_); trivial.
% 29.61/29.85 (* end of lemma zenon_L67_ *)
% 29.61/29.85 assert (zenon_L68_ : (((op1 (e10) (e10)) = (e10))/\(~((op1 (e10) (e10)) = (e10)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H12d.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H12d). zenon_intro zenon_H12f. zenon_intro zenon_H12e.
% 29.61/29.85 exact (zenon_H12e zenon_H12f).
% 29.61/29.85 (* end of lemma zenon_L68_ *)
% 29.61/29.85 assert (zenon_L69_ : (~((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e21) (e20)))) -> ((op2 (e20) (e23)) = (e21)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e21) (e20)) = (e21)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H130 zenon_H131 zenon_H20 zenon_H1d zenon_Heb.
% 29.61/29.85 cut (((op2 (e20) (e23)) = (e21)) = ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e21) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H130.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H131.
% 29.61/29.85 cut (((e21) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 29.61/29.85 cut (((op2 (e20) (e23)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H133].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e20) (e23)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H133.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H134.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H135].
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L7_); trivial.
% 29.61/29.85 apply zenon_H135. apply refl_equal.
% 29.61/29.85 apply zenon_H135. apply refl_equal.
% 29.61/29.85 apply zenon_H132. apply sym_equal. exact zenon_Heb.
% 29.61/29.85 (* end of lemma zenon_L69_ *)
% 29.61/29.85 assert (zenon_L70_ : ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e20) (e23)) = (e21)) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H2a zenon_H136 zenon_H131 zenon_Heb zenon_H20 zenon_H1d zenon_H137.
% 29.61/29.85 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf6 ].
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e21) (e20)) = (op2 (e22) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H137.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Hf5.
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf6].
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H138].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e22) (e20)) = (op2 (e21) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H138.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H2a.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H130].
% 29.61/29.85 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H139].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf6 ].
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e21) = (op2 (e22) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H139.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Hf5.
% 29.61/29.85 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf6].
% 29.61/29.85 cut (((op2 (e22) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H13a].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H13a zenon_H136).
% 29.61/29.85 apply zenon_Hf6. apply refl_equal.
% 29.61/29.85 apply zenon_Hf6. apply refl_equal.
% 29.61/29.85 apply (zenon_L69_); trivial.
% 29.61/29.85 apply zenon_Hf6. apply refl_equal.
% 29.61/29.85 apply zenon_Hf6. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L70_ *)
% 29.61/29.85 assert (zenon_L71_ : ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e22) (e23)) = (e21)) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H2a zenon_H13b zenon_H1d zenon_H20 zenon_H13c.
% 29.61/29.85 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H13d | zenon_intro zenon_H13e ].
% 29.61/29.85 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H13c.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H13d.
% 29.61/29.85 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.61/29.85 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13f].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H13f.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H2a.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 29.61/29.85 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H140].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H13d | zenon_intro zenon_H13e ].
% 29.61/29.85 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H140.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H13d.
% 29.61/29.85 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.61/29.85 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H141].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H141 zenon_H13b).
% 29.61/29.85 apply zenon_H13e. apply refl_equal.
% 29.61/29.85 apply zenon_H13e. apply refl_equal.
% 29.61/29.85 apply (zenon_L7_); trivial.
% 29.61/29.85 apply zenon_H13e. apply refl_equal.
% 29.61/29.85 apply zenon_H13e. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L71_ *)
% 29.61/29.85 assert (zenon_L72_ : ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e23) (e23)) = (e21)) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H2a zenon_H142 zenon_H1d zenon_H20 zenon_H1f.
% 29.61/29.85 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H143 | zenon_intro zenon_H144 ].
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1f.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H143.
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H144].
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H145].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H145.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H2a.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 29.61/29.85 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H146].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H143 | zenon_intro zenon_H144 ].
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((e21) = (op2 (e23) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H146.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H143.
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H144].
% 29.61/29.85 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H147].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H147 zenon_H142).
% 29.61/29.85 apply zenon_H144. apply refl_equal.
% 29.61/29.85 apply zenon_H144. apply refl_equal.
% 29.61/29.85 apply (zenon_L7_); trivial.
% 29.61/29.85 apply zenon_H144. apply refl_equal.
% 29.61/29.85 apply zenon_H144. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L72_ *)
% 29.61/29.85 assert (zenon_L73_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H148 zenon_H137 zenon_Heb zenon_H136 zenon_H31 zenon_H13c zenon_H2a zenon_H1d zenon_H20 zenon_H1f.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H131 | zenon_intro zenon_H149 ].
% 29.61/29.85 apply (zenon_L70_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H2b | zenon_intro zenon_H14a ].
% 29.61/29.85 exact (zenon_H31 zenon_H2b).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13b | zenon_intro zenon_H142 ].
% 29.61/29.85 apply (zenon_L71_); trivial.
% 29.61/29.85 apply (zenon_L72_); trivial.
% 29.61/29.85 (* end of lemma zenon_L73_ *)
% 29.61/29.85 assert (zenon_L74_ : (~((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e22) (e21)))) -> ((op2 (e20) (e23)) = (e21)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e21)) = (e21)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H14b zenon_H131 zenon_H20 zenon_H1d zenon_H14c.
% 29.61/29.85 cut (((op2 (e20) (e23)) = (e21)) = ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e22) (e21)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H14b.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H131.
% 29.61/29.85 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d].
% 29.61/29.85 cut (((op2 (e20) (e23)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H133].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [ zenon_intro zenon_H134 | zenon_intro zenon_H135 ].
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e20) (e23)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H133.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H134.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H135].
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L7_); trivial.
% 29.61/29.85 apply zenon_H135. apply refl_equal.
% 29.61/29.85 apply zenon_H135. apply refl_equal.
% 29.61/29.85 apply zenon_H14d. apply sym_equal. exact zenon_H14c.
% 29.61/29.85 (* end of lemma zenon_L74_ *)
% 29.61/29.85 assert (zenon_L75_ : (~((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e11) (e10)))) -> ((op1 (e10) (e13)) = (e11)) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e11) (e10)) = (e11)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H14e zenon_Ha9 zenon_H57 zenon_H4e zenon_H14f.
% 29.61/29.85 cut (((op1 (e10) (e13)) = (e11)) = ((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e11) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H14e.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Ha9.
% 29.61/29.85 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H150].
% 29.61/29.85 cut (((op1 (e10) (e13)) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H151].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [ zenon_intro zenon_H152 | zenon_intro zenon_H153 ].
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e10) (e13)) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H151.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H152.
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H153].
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L29_); trivial.
% 29.61/29.85 apply zenon_H153. apply refl_equal.
% 29.61/29.85 apply zenon_H153. apply refl_equal.
% 29.61/29.85 apply zenon_H150. apply sym_equal. exact zenon_H14f.
% 29.61/29.85 (* end of lemma zenon_L75_ *)
% 29.61/29.85 assert (zenon_L76_ : ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((op1 (e11) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H81 zenon_H154 zenon_Ha9 zenon_H14f zenon_H57 zenon_H4e zenon_H155.
% 29.61/29.85 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((op1 (e11) (e10)) = (op1 (e12) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H155.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H156.
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H157].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H158].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e12) (e10)) = (op1 (e11) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H158.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H81.
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 29.61/29.85 cut (((e11) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e11) = (op1 (e12) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H159.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H156.
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H157].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H15a].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H15a zenon_H154).
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 apply (zenon_L75_); trivial.
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L76_ *)
% 29.61/29.85 assert (zenon_L77_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_Hbb zenon_H155 zenon_H14f zenon_H154 zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.61/29.85 apply (zenon_L76_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.61/29.85 exact (zenon_H88 zenon_H82).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.61/29.85 apply (zenon_L41_); trivial.
% 29.61/29.85 apply (zenon_L42_); trivial.
% 29.61/29.85 (* end of lemma zenon_L77_ *)
% 29.61/29.85 assert (zenon_L78_ : (~((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e12) (e11)))) -> ((op1 (e10) (e13)) = (e11)) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e12) (e11)) = (e11)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H15b zenon_Ha9 zenon_H57 zenon_H4e zenon_H15c.
% 29.61/29.85 cut (((op1 (e10) (e13)) = (e11)) = ((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e12) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H15b.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Ha9.
% 29.61/29.85 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H15d].
% 29.61/29.85 cut (((op1 (e10) (e13)) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H151].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [ zenon_intro zenon_H152 | zenon_intro zenon_H153 ].
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e10) (e13)) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H151.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H152.
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H153].
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L29_); trivial.
% 29.61/29.85 apply zenon_H153. apply refl_equal.
% 29.61/29.85 apply zenon_H153. apply refl_equal.
% 29.61/29.85 apply zenon_H15d. apply sym_equal. exact zenon_H15c.
% 29.61/29.85 (* end of lemma zenon_L78_ *)
% 29.61/29.85 assert (zenon_L79_ : (~((h3 (e11)) = (e21))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H15e zenon_H15f zenon_H2a.
% 29.61/29.85 cut (((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((h3 (e11)) = (e21))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H15e.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H15f.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H160].
% 29.61/29.85 cut (((h3 (e11)) = (h3 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H161].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H161. apply refl_equal.
% 29.61/29.85 apply zenon_H160. apply sym_equal. exact zenon_H2a.
% 29.61/29.85 (* end of lemma zenon_L79_ *)
% 29.61/29.85 assert (zenon_L80_ : (~((e22) = (e22))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H162.
% 29.61/29.85 apply zenon_H162. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L80_ *)
% 29.61/29.85 assert (zenon_L81_ : (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((h3 (e12)) = (e22)) -> ((op1 (e10) (e11)) = (e12)) -> ((op2 (e20) (e21)) = (e22)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H163 zenon_H164 zenon_H165 zenon_H166 zenon_H9a zenon_H20 zenon_H15f zenon_H2a.
% 29.61/29.85 cut (((h3 (e12)) = (e22)) = ((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H163.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H164.
% 29.61/29.85 cut (((e22) = (op2 (h3 (e10)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 29.61/29.85 cut (((h3 (e12)) = (h3 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H168].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((h3 (op1 (e10) (e11))) = (h3 (op1 (e10) (e11))))); [ zenon_intro zenon_H169 | zenon_intro zenon_H16a ].
% 29.61/29.85 cut (((h3 (op1 (e10) (e11))) = (h3 (op1 (e10) (e11)))) = ((h3 (e12)) = (h3 (op1 (e10) (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H168.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H169.
% 29.61/29.85 cut (((h3 (op1 (e10) (e11))) = (h3 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H16a].
% 29.61/29.85 cut (((h3 (op1 (e10) (e11))) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H16c zenon_H165).
% 29.61/29.85 apply zenon_H16a. apply refl_equal.
% 29.61/29.85 apply zenon_H16a. apply refl_equal.
% 29.61/29.85 elim (classic ((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11))))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11)))) = ((e22) = (op2 (h3 (e10)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H167.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H16d.
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H16e].
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H16f].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((op2 (e20) (e21)) = (e22)) = ((op2 (h3 (e10)) (h3 (e11))) = (e22))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H16f.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H166.
% 29.61/29.85 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H162].
% 29.61/29.85 cut (((op2 (e20) (e21)) = (op2 (h3 (e10)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H170].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11))))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16e ].
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11)))) = ((op2 (e20) (e21)) = (op2 (h3 (e10)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H170.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H16d.
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (op2 (h3 (e10)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H16e].
% 29.61/29.85 cut (((op2 (h3 (e10)) (h3 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H171].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.61/29.85 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L37_); trivial.
% 29.61/29.85 apply (zenon_L79_); trivial.
% 29.61/29.85 apply zenon_H16e. apply refl_equal.
% 29.61/29.85 apply zenon_H16e. apply refl_equal.
% 29.61/29.85 apply zenon_H162. apply refl_equal.
% 29.61/29.85 apply zenon_H16e. apply refl_equal.
% 29.61/29.85 apply zenon_H16e. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L81_ *)
% 29.61/29.85 assert (zenon_L82_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (e10))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e20) (e21)) = (e22)) -> ((h3 (e12)) = (e22)) -> (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H172 zenon_H173 zenon_H4e zenon_H57 zenon_H15c zenon_Ha9 zenon_H81 zenon_H174 zenon_H2a zenon_H15f zenon_H20 zenon_H9a zenon_H166 zenon_H164 zenon_H163 zenon_H9c zenon_H9e.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H44 | zenon_intro zenon_H175 ].
% 29.61/29.85 exact (zenon_H173 zenon_H44).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H177 | zenon_intro zenon_H176 ].
% 29.61/29.85 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H174.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H81.
% 29.61/29.85 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H15b].
% 29.61/29.85 cut (((e11) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H178].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H179 | zenon_intro zenon_H47 ].
% 29.61/29.85 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e11) = (op1 (e10) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H178.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H179.
% 29.61/29.85 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 29.61/29.85 cut (((op1 (e10) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17a].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H17a zenon_H177).
% 29.61/29.85 apply zenon_H47. apply refl_equal.
% 29.61/29.85 apply zenon_H47. apply refl_equal.
% 29.61/29.85 apply (zenon_L78_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H165 | zenon_intro zenon_H9d ].
% 29.61/29.85 apply (zenon_L81_); trivial.
% 29.61/29.85 apply (zenon_L38_); trivial.
% 29.61/29.85 (* end of lemma zenon_L82_ *)
% 29.61/29.85 assert (zenon_L83_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((h3 (e12)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_Hbb zenon_H9e zenon_H9c zenon_H163 zenon_H164 zenon_H166 zenon_H9a zenon_H20 zenon_H15f zenon_H2a zenon_H174 zenon_H15c zenon_H173 zenon_H172 zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.61/29.85 apply (zenon_L82_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.61/29.85 exact (zenon_H88 zenon_H82).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.61/29.85 apply (zenon_L41_); trivial.
% 29.61/29.85 apply (zenon_L42_); trivial.
% 29.61/29.85 (* end of lemma zenon_L83_ *)
% 29.61/29.85 assert (zenon_L84_ : ((e13) = (op1 (e12) (e12))) -> ((op1 (e12) (e12)) = (e11)) -> (~((e11) = (e13))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H4e zenon_H17b zenon_Hab.
% 29.61/29.85 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H51 | zenon_intro zenon_H4d ].
% 29.61/29.85 cut (((e13) = (e13)) = ((e11) = (e13))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_Hab.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H51.
% 29.61/29.85 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.61/29.85 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e13) = (op1 (e12) (e12))) = ((e13) = (e11))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_Hac.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H4e.
% 29.61/29.85 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17c].
% 29.61/29.85 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H4d. apply refl_equal.
% 29.61/29.85 exact (zenon_H17c zenon_H17b).
% 29.61/29.85 apply zenon_H4d. apply refl_equal.
% 29.61/29.85 apply zenon_H4d. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L84_ *)
% 29.61/29.85 assert (zenon_L85_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e20) (e21)) = (e22)) -> ((h3 (e12)) = (e22)) -> (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H17d zenon_H14f zenon_H155 zenon_H77 zenon_H88 zenon_H172 zenon_H173 zenon_H174 zenon_H2a zenon_H15f zenon_H20 zenon_H9a zenon_H166 zenon_H164 zenon_H163 zenon_H9c zenon_H9e zenon_Hbb zenon_Hab zenon_H81 zenon_H4e zenon_H57 zenon_Haf.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H154 | zenon_intro zenon_H17e ].
% 29.61/29.85 apply (zenon_L77_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H15c | zenon_intro zenon_H17f ].
% 29.61/29.85 apply (zenon_L83_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H17b | zenon_intro zenon_Hae ].
% 29.61/29.85 apply (zenon_L84_); trivial.
% 29.61/29.85 apply (zenon_L41_); trivial.
% 29.61/29.85 (* end of lemma zenon_L85_ *)
% 29.61/29.85 assert (zenon_L86_ : (((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e21)) = (e22))\/((op2 (e20) (e21)) = (e23))))) -> (~((op2 (e20) (e21)) = (e20))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e20) (e23)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((h3 (e12)) = (e22)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H180 zenon_H16 zenon_H1d zenon_H14c zenon_H131 zenon_H181 zenon_Haf zenon_H57 zenon_H4e zenon_H81 zenon_Hab zenon_Hbb zenon_H9e zenon_H9c zenon_H163 zenon_H164 zenon_H9a zenon_H20 zenon_H15f zenon_H2a zenon_H174 zenon_H173 zenon_H172 zenon_H88 zenon_H77 zenon_H155 zenon_H14f zenon_H17d zenon_Hd1 zenon_Hd3.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H18 | zenon_intro zenon_H182 ].
% 29.61/29.85 exact (zenon_H16 zenon_H18).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H184 | zenon_intro zenon_H183 ].
% 29.61/29.85 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H181.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H2a.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14b].
% 29.61/29.85 cut (((e21) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H185].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H186 | zenon_intro zenon_Hfb ].
% 29.61/29.85 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e21) = (op2 (e20) (e21)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H185.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H186.
% 29.61/29.85 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hfb].
% 29.61/29.85 cut (((op2 (e20) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H187 zenon_H184).
% 29.61/29.85 apply zenon_Hfb. apply refl_equal.
% 29.61/29.85 apply zenon_Hfb. apply refl_equal.
% 29.61/29.85 apply (zenon_L74_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_H166 | zenon_intro zenon_Hd2 ].
% 29.61/29.85 apply (zenon_L85_); trivial.
% 29.61/29.85 apply (zenon_L45_); trivial.
% 29.61/29.85 (* end of lemma zenon_L86_ *)
% 29.61/29.85 assert (zenon_L87_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> (~((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e21)) = (e22))\/((op2 (e20) (e21)) = (e23))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H148 zenon_Hd3 zenon_Hd1 zenon_H17d zenon_H14f zenon_H155 zenon_H77 zenon_H88 zenon_H172 zenon_H173 zenon_H174 zenon_H15f zenon_H9a zenon_H164 zenon_H163 zenon_H9c zenon_H9e zenon_Hbb zenon_Hab zenon_H81 zenon_H4e zenon_H57 zenon_Haf zenon_H181 zenon_H14c zenon_H16 zenon_H180 zenon_H31 zenon_H13c zenon_H2a zenon_H1d zenon_H20 zenon_H1f.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H131 | zenon_intro zenon_H149 ].
% 29.61/29.85 apply (zenon_L86_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H2b | zenon_intro zenon_H14a ].
% 29.61/29.85 exact (zenon_H31 zenon_H2b).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13b | zenon_intro zenon_H142 ].
% 29.61/29.85 apply (zenon_L71_); trivial.
% 29.61/29.85 apply (zenon_L72_); trivial.
% 29.61/29.85 (* end of lemma zenon_L87_ *)
% 29.61/29.85 assert (zenon_L88_ : ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e22)) = (e21)) -> (~((e21) = (e23))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1d zenon_H188 zenon_Hed.
% 29.61/29.85 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hee | zenon_intro zenon_Hef ].
% 29.61/29.85 cut (((e23) = (e23)) = ((e21) = (e23))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_Hed.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Hee.
% 29.61/29.85 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.61/29.85 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hf0].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e23) = (op2 (e22) (e22))) = ((e23) = (e21))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_Hf0.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1d.
% 29.61/29.85 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H189].
% 29.61/29.85 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_Hef. apply refl_equal.
% 29.61/29.85 exact (zenon_H189 zenon_H188).
% 29.61/29.85 apply zenon_Hef. apply refl_equal.
% 29.61/29.85 apply zenon_Hef. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L88_ *)
% 29.61/29.85 assert (zenon_L89_ : (((op1 (e12) (e10)) = (e12))/\(~((op1 (e10) (e12)) = (e10)))) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((((op1 (e10) (e12)) = (e10))/\(~((op1 (e12) (e10)) = (e12))))\/((((op1 (e11) (e12)) = (e11))/\(~((op1 (e12) (e11)) = (e12))))\/((((op1 (e12) (e12)) = (e12))/\(~((op1 (e12) (e12)) = (e12))))\/(((op1 (e13) (e12)) = (e13))/\(~((op1 (e12) (e13)) = (e12))))))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H18a zenon_H49 zenon_H50 zenon_H4e zenon_H56 zenon_H57 zenon_H5d zenon_H64 zenon_H6c.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H18a). zenon_intro zenon_H18c. zenon_intro zenon_H18b.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.61/29.85 exact (zenon_H18b zenon_H45).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H4a. zenon_intro zenon_H73.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H45 | zenon_intro zenon_H5e ].
% 29.61/29.85 exact (zenon_H18b zenon_H45).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H4b | zenon_intro zenon_H5f ].
% 29.61/29.85 apply (zenon_L17_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H4f | zenon_intro zenon_H58 ].
% 29.61/29.85 apply (zenon_L19_); trivial.
% 29.61/29.85 apply (zenon_L21_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.61/29.85 apply (zenon_L23_); trivial.
% 29.61/29.85 apply (zenon_L24_); trivial.
% 29.61/29.85 (* end of lemma zenon_L89_ *)
% 29.61/29.85 assert (zenon_L90_ : (((op1 (e10) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13)))) -> (~((op1 (e10) (e13)) = (e10))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H7d zenon_H7c.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H78. zenon_intro zenon_H7e.
% 29.61/29.85 exact (zenon_H7c zenon_H78).
% 29.61/29.85 (* end of lemma zenon_L90_ *)
% 29.61/29.85 assert (zenon_L91_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H18d zenon_H18e zenon_H9c.
% 29.61/29.85 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H18d.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H18e.
% 29.61/29.85 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18f].
% 29.61/29.85 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H190. apply refl_equal.
% 29.61/29.85 apply zenon_H18f. apply sym_equal. exact zenon_H9c.
% 29.61/29.85 (* end of lemma zenon_L91_ *)
% 29.61/29.85 assert (zenon_L92_ : (((op1 (e13) (e10)) = (e13))/\(~((op1 (e10) (e13)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((((op1 (e10) (e12)) = (e10))/\(~((op1 (e12) (e10)) = (e12))))\/((((op1 (e11) (e12)) = (e11))/\(~((op1 (e12) (e11)) = (e12))))\/((((op1 (e12) (e12)) = (e12))/\(~((op1 (e12) (e12)) = (e12))))\/(((op1 (e13) (e12)) = (e13))/\(~((op1 (e12) (e13)) = (e12))))))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((((op1 (e10) (e13)) = (e10))/\(~((op1 (e13) (e10)) = (e13))))\/((((op1 (e11) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13))))\/((((op1 (e12) (e13)) = (e12))/\(~((op1 (e13) (e12)) = (e13))))\/(((op1 (e13) (e13)) = (e13))/\(~((op1 (e13) (e13)) = (e13))))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((((op1 (e10) (e11)) = (e10))/\(~((op1 (e11) (e10)) = (e11))))\/((((op1 (e11) (e11)) = (e11))/\(~((op1 (e11) (e11)) = (e11))))\/((((op1 (e12) (e11)) = (e12))/\(~((op1 (e11) (e12)) = (e11))))\/(((op1 (e13) (e11)) = (e13))/\(~((op1 (e11) (e13)) = (e11))))))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H191 zenon_H43 zenon_H49 zenon_H50 zenon_H4e zenon_H56 zenon_H57 zenon_H5d zenon_H64 zenon_H6c zenon_H81 zenon_H83 zenon_H8b zenon_H94 zenon_H18d zenon_H192.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H191). zenon_intro zenon_H18e. zenon_intro zenon_H7c.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.61/29.85 apply (zenon_L25_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.61/29.85 apply (zenon_L26_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H8c. zenon_intro zenon_H98.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H7d | zenon_intro zenon_H95 ].
% 29.61/29.85 apply (zenon_L90_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H89 | zenon_intro zenon_H96 ].
% 29.61/29.85 apply (zenon_L31_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H90 | zenon_intro zenon_H91 ].
% 29.61/29.85 apply (zenon_L33_); trivial.
% 29.61/29.85 apply (zenon_L34_); trivial.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.61/29.85 apply (zenon_L91_); trivial.
% 29.61/29.85 (* end of lemma zenon_L92_ *)
% 29.61/29.85 assert (zenon_L93_ : (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H196 zenon_H14f zenon_H4a.
% 29.61/29.85 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H196.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H14f.
% 29.61/29.85 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H197].
% 29.61/29.85 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H198].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H198. apply refl_equal.
% 29.61/29.85 apply zenon_H197. apply sym_equal. exact zenon_H4a.
% 29.61/29.85 (* end of lemma zenon_L93_ *)
% 29.61/29.85 assert (zenon_L94_ : (((op1 (e11) (e12)) = (e11))/\(~((op1 (e12) (e11)) = (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H72 zenon_H14f zenon_H196.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H4a. zenon_intro zenon_H73.
% 29.61/29.85 apply (zenon_L93_); trivial.
% 29.61/29.85 (* end of lemma zenon_L94_ *)
% 29.61/29.85 assert (zenon_L95_ : (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H199 zenon_Heb zenon_Hfd.
% 29.61/29.85 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H199.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Heb.
% 29.61/29.85 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H19a].
% 29.61/29.85 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H19b].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H19b. apply refl_equal.
% 29.61/29.85 apply zenon_H19a. apply sym_equal. exact zenon_Hfd.
% 29.61/29.85 (* end of lemma zenon_L95_ *)
% 29.61/29.85 assert (zenon_L96_ : (((op2 (e21) (e22)) = (e21))/\(~((op2 (e22) (e21)) = (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H120 zenon_Heb zenon_H199.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H120). zenon_intro zenon_Hfd. zenon_intro zenon_H121.
% 29.61/29.85 apply (zenon_L95_); trivial.
% 29.61/29.85 (* end of lemma zenon_L96_ *)
% 29.61/29.85 assert (zenon_L97_ : (~((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op1 (e10) (e13)) = (e11)) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H19c zenon_H15f zenon_Ha9 zenon_Hc0 zenon_H9a.
% 29.61/29.85 cut (((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H19c.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H15f.
% 29.61/29.85 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e10)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H19d].
% 29.61/29.85 cut (((h3 (e11)) = (h3 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H19e].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((h3 (op1 (e10) (e13))) = (h3 (op1 (e10) (e13))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ].
% 29.61/29.85 cut (((h3 (op1 (e10) (e13))) = (h3 (op1 (e10) (e13)))) = ((h3 (e11)) = (h3 (op1 (e10) (e13))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H19e.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H19f.
% 29.61/29.85 cut (((h3 (op1 (e10) (e13))) = (h3 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1a0].
% 29.61/29.85 cut (((h3 (op1 (e10) (e13))) = (h3 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1a2 zenon_Ha9).
% 29.61/29.85 apply zenon_H1a0. apply refl_equal.
% 29.61/29.85 apply zenon_H1a0. apply refl_equal.
% 29.61/29.85 cut (((op2 (e22) (e22)) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a3].
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a4].
% 29.61/29.85 congruence.
% 29.61/29.85 apply zenon_H1a4. apply sym_equal. exact zenon_H9a.
% 29.61/29.85 apply zenon_H1a3. apply sym_equal. exact zenon_Hc0.
% 29.61/29.85 (* end of lemma zenon_L97_ *)
% 29.61/29.85 assert (zenon_L98_ : (((op2 (e21) (e23)) = (e21))/\(~((op2 (e23) (e21)) = (e23)))) -> (~((op2 (e21) (e23)) = (e21))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H32 zenon_H31.
% 29.61/29.85 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H2b. zenon_intro zenon_H33.
% 29.61/29.85 exact (zenon_H31 zenon_H2b).
% 29.61/29.85 (* end of lemma zenon_L98_ *)
% 29.61/29.85 assert (zenon_L99_ : (~((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op1 (e11) (e11)) = (e10)) -> ((op2 (e21) (e21)) = (e20)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1a5 zenon_H9a zenon_H1a6 zenon_H1a7 zenon_H20 zenon_H15f zenon_H2a.
% 29.61/29.85 cut (((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1a5.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H9a.
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e11)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 29.61/29.85 cut (((h3 (e10)) = (h3 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1a9].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((h3 (op1 (e11) (e11))) = (h3 (op1 (e11) (e11))))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ].
% 29.61/29.85 cut (((h3 (op1 (e11) (e11))) = (h3 (op1 (e11) (e11)))) = ((h3 (e10)) = (h3 (op1 (e11) (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1a9.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1aa.
% 29.61/29.85 cut (((h3 (op1 (e11) (e11))) = (h3 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1ab].
% 29.61/29.85 cut (((h3 (op1 (e11) (e11))) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1ac].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1ad].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1ad zenon_H1a6).
% 29.61/29.85 apply zenon_H1ab. apply refl_equal.
% 29.61/29.85 apply zenon_H1ab. apply refl_equal.
% 29.61/29.85 elim (classic ((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ].
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11)))) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e11)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1a8.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1ae.
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1af].
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1b0].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((op2 (e21) (e21)) = (e20)) = ((op2 (h3 (e11)) (h3 (e11))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1b0.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1a7.
% 29.61/29.85 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1b1].
% 29.61/29.85 cut (((op2 (e21) (e21)) = (op2 (h3 (e11)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1b2].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11))))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ].
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11)))) = ((op2 (e21) (e21)) = (op2 (h3 (e11)) (h3 (e11))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1b2.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1ae.
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (h3 (e11)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1af].
% 29.61/29.85 cut (((op2 (h3 (e11)) (h3 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b3].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.61/29.85 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L79_); trivial.
% 29.61/29.85 apply (zenon_L79_); trivial.
% 29.61/29.85 apply zenon_H1af. apply refl_equal.
% 29.61/29.85 apply zenon_H1af. apply refl_equal.
% 29.61/29.85 exact (zenon_H1b1 zenon_H20).
% 29.61/29.85 apply zenon_H1af. apply refl_equal.
% 29.61/29.85 apply zenon_H1af. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L99_ *)
% 29.61/29.85 assert (zenon_L100_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e13) (e10)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1b4 zenon_H57 zenon_H1b5 zenon_H4e.
% 29.61/29.85 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1b4.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H57.
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.61/29.85 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1b6].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H190 ].
% 29.61/29.85 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1b6.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1b7.
% 29.61/29.85 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.61/29.85 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1b8].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1b8 zenon_H1b5).
% 29.61/29.85 apply zenon_H190. apply refl_equal.
% 29.61/29.85 apply zenon_H190. apply refl_equal.
% 29.61/29.85 apply (zenon_L20_); trivial.
% 29.61/29.85 (* end of lemma zenon_L100_ *)
% 29.61/29.85 assert (zenon_L101_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1b9 zenon_H57 zenon_H1ba zenon_H4e.
% 29.61/29.85 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e13) (e11)) = (op1 (e13) (e13)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1b9.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H57.
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.61/29.85 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ].
% 29.61/29.85 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e10) = (op1 (e13) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1bb.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H9f.
% 29.61/29.85 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 29.61/29.85 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1bc].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1bc zenon_H1ba).
% 29.61/29.85 apply zenon_Ha0. apply refl_equal.
% 29.61/29.85 apply zenon_Ha0. apply refl_equal.
% 29.61/29.85 apply (zenon_L20_); trivial.
% 29.61/29.85 (* end of lemma zenon_L101_ *)
% 29.61/29.85 assert (zenon_L102_ : (~((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e12) (e10)))) -> ((op1 (e13) (e13)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e12) (e10)) = (e10)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1bd zenon_H1be zenon_H4e zenon_H1bf.
% 29.61/29.85 cut (((op1 (e13) (e13)) = (e10)) = ((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e12) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1bd.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1be.
% 29.61/29.85 cut (((e10) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1c0].
% 29.61/29.85 cut (((op1 (e13) (e13)) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c1].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H1c3 ].
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e13) (e13)) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1c1.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1c2.
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c3].
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L20_); trivial.
% 29.61/29.85 apply zenon_H1c3. apply refl_equal.
% 29.61/29.85 apply zenon_H1c3. apply refl_equal.
% 29.61/29.85 apply zenon_H1c0. apply sym_equal. exact zenon_H1bf.
% 29.61/29.85 (* end of lemma zenon_L102_ *)
% 29.61/29.85 assert (zenon_L103_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e12) (e10)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1c4 zenon_H1b4 zenon_H1b9 zenon_H56 zenon_H57 zenon_H1c5 zenon_H1bf zenon_H4e zenon_H1c6.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1c7 ].
% 29.61/29.85 apply (zenon_L100_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1c8 ].
% 29.61/29.85 apply (zenon_L101_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H58 | zenon_intro zenon_H1be ].
% 29.61/29.85 apply (zenon_L21_); trivial.
% 29.61/29.85 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H8f ].
% 29.61/29.85 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e12) (e10)) = (op1 (e12) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1c6.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1c9.
% 29.61/29.85 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 29.61/29.85 cut (((op1 (e12) (e11)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1ca].
% 29.61/29.85 congruence.
% 29.61/29.85 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e12) (e11)) = (op1 (e12) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1ca.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H57.
% 29.61/29.85 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1bd].
% 29.61/29.85 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1cb].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H8f ].
% 29.61/29.85 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1cb.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1c9.
% 29.61/29.85 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 29.61/29.85 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1cc].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1cc zenon_H1c5).
% 29.61/29.85 apply zenon_H8f. apply refl_equal.
% 29.61/29.85 apply zenon_H8f. apply refl_equal.
% 29.61/29.85 apply (zenon_L102_); trivial.
% 29.61/29.85 apply zenon_H8f. apply refl_equal.
% 29.61/29.85 apply zenon_H8f. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L103_ *)
% 29.61/29.85 assert (zenon_L104_ : (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e12) (e10)) = (e13)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1cd zenon_H4e zenon_H1ce.
% 29.61/29.85 cut (((e13) = (op1 (e12) (e12))) = ((op1 (e12) (e10)) = (op1 (e12) (e12)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1cd.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H4e.
% 29.61/29.85 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 29.61/29.85 cut (((e13) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1cf].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e13) = (op1 (e12) (e10)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1cf.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H156.
% 29.61/29.85 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H157].
% 29.61/29.85 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1d0].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1d0 zenon_H1ce).
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 apply zenon_H157. apply refl_equal.
% 29.61/29.85 apply zenon_H68. apply refl_equal.
% 29.61/29.85 (* end of lemma zenon_L104_ *)
% 29.61/29.85 assert (zenon_L105_ : (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1d1 zenon_H1c6 zenon_H1c5 zenon_H56 zenon_H1b9 zenon_H1b4 zenon_H1c4 zenon_H155 zenon_H57 zenon_H14f zenon_Ha9 zenon_H81 zenon_H70 zenon_H1cd zenon_H4e.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1d2 ].
% 29.61/29.85 apply (zenon_L103_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H154 | zenon_intro zenon_H1d3 ].
% 29.61/29.85 apply (zenon_L76_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H18c | zenon_intro zenon_H1ce ].
% 29.61/29.85 exact (zenon_H70 zenon_H18c).
% 29.61/29.85 apply (zenon_L104_); trivial.
% 29.61/29.85 (* end of lemma zenon_L105_ *)
% 29.61/29.85 assert (zenon_L106_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e21) (e21)) = (e20)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1d4 zenon_H173 zenon_H2a zenon_H15f zenon_H20 zenon_H1a7 zenon_H9a zenon_H1a5 zenon_H77 zenon_H81 zenon_Haf zenon_H88 zenon_H1d1 zenon_H1c6 zenon_H56 zenon_H1b4 zenon_H1c4 zenon_H155 zenon_H14f zenon_H70 zenon_H1cd zenon_Hbb zenon_H1b9 zenon_H57 zenon_H4e.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d4); [ zenon_intro zenon_H44 | zenon_intro zenon_H1d5 ].
% 29.61/29.85 exact (zenon_H173 zenon_H44).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d5); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1d6 ].
% 29.61/29.85 apply (zenon_L99_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_H1d6); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1ba ].
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.61/29.85 apply (zenon_L105_); trivial.
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.61/29.85 exact (zenon_H88 zenon_H82).
% 29.61/29.85 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.61/29.85 apply (zenon_L41_); trivial.
% 29.61/29.85 apply (zenon_L42_); trivial.
% 29.61/29.85 apply (zenon_L101_); trivial.
% 29.61/29.85 (* end of lemma zenon_L106_ *)
% 29.61/29.85 assert (zenon_L107_ : (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e23) (e20)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1d7 zenon_H20 zenon_H1d8 zenon_H1d.
% 29.61/29.85 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1d7.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H20.
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.61/29.85 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d9].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H1da | zenon_intro zenon_H116 ].
% 29.61/29.85 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1d9.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1da.
% 29.61/29.85 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H116].
% 29.61/29.85 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1db].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1db zenon_H1d8).
% 29.61/29.85 apply zenon_H116. apply refl_equal.
% 29.61/29.85 apply zenon_H116. apply refl_equal.
% 29.61/29.85 apply (zenon_L4_); trivial.
% 29.61/29.85 (* end of lemma zenon_L107_ *)
% 29.61/29.85 assert (zenon_L108_ : (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1dc zenon_H20 zenon_H1dd zenon_H1d.
% 29.61/29.85 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e23) (e21)) = (op2 (e23) (e23)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1dc.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H20.
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.61/29.85 cut (((e20) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1de].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ].
% 29.61/29.85 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e20) = (op2 (e23) (e21)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1de.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_Hd4.
% 29.61/29.85 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 29.61/29.85 cut (((op2 (e23) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1df].
% 29.61/29.85 congruence.
% 29.61/29.85 exact (zenon_H1df zenon_H1dd).
% 29.61/29.85 apply zenon_Hd5. apply refl_equal.
% 29.61/29.85 apply zenon_Hd5. apply refl_equal.
% 29.61/29.85 apply (zenon_L4_); trivial.
% 29.61/29.85 (* end of lemma zenon_L108_ *)
% 29.61/29.85 assert (zenon_L109_ : (~((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e22) (e20)))) -> ((op2 (e23) (e23)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e22) (e20)) = (e20)) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H1e0 zenon_H1e1 zenon_H1d zenon_H1e2.
% 29.61/29.85 cut (((op2 (e23) (e23)) = (e20)) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e22) (e20)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1e0.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1e1.
% 29.61/29.85 cut (((e20) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e3].
% 29.61/29.85 cut (((op2 (e23) (e23)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1e4].
% 29.61/29.85 congruence.
% 29.61/29.85 elim (classic ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ].
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e23) (e23)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1e4.
% 29.61/29.85 rewrite <- zenon_D_pnotp.
% 29.61/29.85 exact zenon_H1e5.
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1e6].
% 29.61/29.85 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.61/29.85 congruence.
% 29.61/29.85 apply (zenon_L4_); trivial.
% 29.61/29.85 apply zenon_H1e6. apply refl_equal.
% 29.61/29.85 apply zenon_H1e6. apply refl_equal.
% 29.61/29.85 apply zenon_H1e3. apply sym_equal. exact zenon_H1e2.
% 29.61/29.85 (* end of lemma zenon_L109_ *)
% 29.61/29.85 assert (zenon_L110_ : ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e23) (e23)) = (e20)) -> ((op2 (e22) (e20)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> False).
% 29.61/29.85 do 0 intro. intros zenon_H20 zenon_H1e7 zenon_H1e1 zenon_H1e2 zenon_H1d zenon_H1e8.
% 29.61/29.85 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H1e9 | zenon_intro zenon_H38 ].
% 29.61/29.85 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e22) (e20)) = (op2 (e22) (e21)))).
% 29.61/29.85 intro zenon_D_pnotp.
% 29.61/29.85 apply zenon_H1e8.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H1e9.
% 29.61/29.86 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H38].
% 29.61/29.86 cut (((op2 (e22) (e21)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ea].
% 29.61/29.86 congruence.
% 29.61/29.86 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e22) (e21)) = (op2 (e22) (e20)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1ea.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H20.
% 29.61/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e0].
% 29.61/29.86 cut (((e20) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1eb].
% 29.61/29.86 congruence.
% 29.61/29.86 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H1e9 | zenon_intro zenon_H38 ].
% 29.61/29.86 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e20) = (op2 (e22) (e21)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1eb.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H1e9.
% 29.61/29.86 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H38].
% 29.61/29.86 cut (((op2 (e22) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1ec].
% 29.61/29.86 congruence.
% 29.61/29.86 exact (zenon_H1ec zenon_H1e7).
% 29.61/29.86 apply zenon_H38. apply refl_equal.
% 29.61/29.86 apply zenon_H38. apply refl_equal.
% 29.61/29.86 apply (zenon_L109_); trivial.
% 29.61/29.86 apply zenon_H38. apply refl_equal.
% 29.61/29.86 apply zenon_H38. apply refl_equal.
% 29.61/29.86 (* end of lemma zenon_L110_ *)
% 29.61/29.86 assert (zenon_L111_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e20) (e23)) = (e21)) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H1ed zenon_H1d7 zenon_H1dc zenon_H104 zenon_H1ee zenon_H1e8 zenon_H1e7 zenon_H137 zenon_H20 zenon_Heb zenon_H131 zenon_H2a zenon_H11e zenon_Hf2 zenon_H1d.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H1ef ].
% 29.61/29.86 apply (zenon_L107_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1f0 ].
% 29.61/29.86 apply (zenon_L108_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H105 | zenon_intro zenon_H1e1 ].
% 29.61/29.86 apply (zenon_L56_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1f1 ].
% 29.61/29.86 apply (zenon_L110_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H136 | zenon_intro zenon_H1f2 ].
% 29.61/29.86 apply (zenon_L70_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H129 | zenon_intro zenon_Hf3 ].
% 29.61/29.86 exact (zenon_H11e zenon_H129).
% 29.61/29.86 apply (zenon_L51_); trivial.
% 29.61/29.86 (* end of lemma zenon_L111_ *)
% 29.61/29.86 assert (zenon_L112_ : ((op2 (e22) (e23)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H36 zenon_H1f3 zenon_H13c.
% 29.61/29.86 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H13d | zenon_intro zenon_H13e ].
% 29.61/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H13c.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H13d.
% 29.61/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.61/29.86 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13f].
% 29.61/29.86 congruence.
% 29.61/29.86 cut (((op2 (e22) (e23)) = (e22)) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H13f.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H36.
% 29.61/29.86 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f4].
% 29.61/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.61/29.86 congruence.
% 29.61/29.86 apply zenon_H13e. apply refl_equal.
% 29.61/29.86 apply zenon_H1f4. apply sym_equal. exact zenon_H1f3.
% 29.61/29.86 apply zenon_H13e. apply refl_equal.
% 29.61/29.86 apply zenon_H13e. apply refl_equal.
% 29.61/29.86 (* end of lemma zenon_L112_ *)
% 29.61/29.86 assert (zenon_L113_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (e22))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e21)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e22)) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e20) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H1f5 zenon_H1f zenon_Hf2 zenon_H11e zenon_H2a zenon_Heb zenon_H20 zenon_H137 zenon_H1e7 zenon_H1e8 zenon_H1ee zenon_H104 zenon_H1dc zenon_H1d7 zenon_H1ed zenon_H13c zenon_H36 zenon_H1d zenon_Hbf zenon_He6.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H21 | zenon_intro zenon_H1f6 ].
% 29.61/29.86 apply (zenon_L5_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H131 | zenon_intro zenon_H1f7 ].
% 29.61/29.86 apply (zenon_L111_); trivial.
% 29.61/29.86 apply (zenon_or_s _ _ zenon_H1f7); [ zenon_intro zenon_H1f3 | zenon_intro zenon_He5 ].
% 29.61/29.86 apply (zenon_L112_); trivial.
% 29.61/29.86 apply (zenon_L48_); trivial.
% 29.61/29.86 (* end of lemma zenon_L113_ *)
% 29.61/29.86 assert (zenon_L114_ : (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e21) (e22)) = (e20)) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H1f8 zenon_Hf9 zenon_Hfe.
% 29.61/29.86 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (e22)) = (op2 (e21) (e22)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1f8.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_Hf9.
% 29.61/29.86 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f9].
% 29.61/29.86 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 29.61/29.86 congruence.
% 29.61/29.86 apply zenon_Hdd. apply refl_equal.
% 29.61/29.86 apply zenon_H1f9. apply sym_equal. exact zenon_Hfe.
% 29.61/29.86 (* end of lemma zenon_L114_ *)
% 29.61/29.86 assert (zenon_L115_ : (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H1fa zenon_H45 zenon_H4b.
% 29.61/29.86 cut (((op1 (e10) (e12)) = (e10)) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1fa.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H45.
% 29.61/29.86 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1fb].
% 29.61/29.86 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 29.61/29.86 congruence.
% 29.61/29.86 apply zenon_Ha7. apply refl_equal.
% 29.61/29.86 apply zenon_H1fb. apply sym_equal. exact zenon_H4b.
% 29.61/29.86 (* end of lemma zenon_L115_ *)
% 29.61/29.86 assert (zenon_L116_ : (~((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))) -> ((op1 (e11) (e12)) = (e12)) -> ((op2 (e21) (e22)) = (e22)) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H1fc zenon_H1fd zenon_H1fe zenon_H15f zenon_H2a zenon_H164.
% 29.61/29.86 cut (((h3 (e12)) = (e22)) = ((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1fc.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H164.
% 29.61/29.86 cut (((e22) = (op2 (h3 (e11)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1ff].
% 29.61/29.86 cut (((h3 (e12)) = (h3 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H200].
% 29.61/29.86 congruence.
% 29.61/29.86 elim (classic ((h3 (op1 (e11) (e12))) = (h3 (op1 (e11) (e12))))); [ zenon_intro zenon_H201 | zenon_intro zenon_H202 ].
% 29.61/29.86 cut (((h3 (op1 (e11) (e12))) = (h3 (op1 (e11) (e12)))) = ((h3 (e12)) = (h3 (op1 (e11) (e12))))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H200.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H201.
% 29.61/29.86 cut (((h3 (op1 (e11) (e12))) = (h3 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H202].
% 29.61/29.86 cut (((h3 (op1 (e11) (e12))) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H203].
% 29.61/29.86 congruence.
% 29.61/29.86 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H204].
% 29.61/29.86 congruence.
% 29.61/29.86 exact (zenon_H204 zenon_H1fd).
% 29.61/29.86 apply zenon_H202. apply refl_equal.
% 29.61/29.86 apply zenon_H202. apply refl_equal.
% 29.61/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12))))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ].
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12)))) = ((e22) = (op2 (h3 (e11)) (h3 (e12))))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H1ff.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H205.
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H206].
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H207].
% 29.61/29.86 congruence.
% 29.61/29.86 cut (((op2 (e21) (e22)) = (e22)) = ((op2 (h3 (e11)) (h3 (e12))) = (e22))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H207.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H1fe.
% 29.61/29.86 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H162].
% 29.61/29.86 cut (((op2 (e21) (e22)) = (op2 (h3 (e11)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H208].
% 29.61/29.86 congruence.
% 29.61/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12))))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ].
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12)))) = ((op2 (e21) (e22)) = (op2 (h3 (e11)) (h3 (e12))))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H208.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H205.
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (op2 (h3 (e11)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H206].
% 29.61/29.86 cut (((op2 (h3 (e11)) (h3 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H209].
% 29.61/29.86 congruence.
% 29.61/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.61/29.86 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.61/29.86 congruence.
% 29.61/29.86 apply (zenon_L79_); trivial.
% 29.61/29.86 exact (zenon_H20a zenon_H164).
% 29.61/29.86 apply zenon_H206. apply refl_equal.
% 29.61/29.86 apply zenon_H206. apply refl_equal.
% 29.61/29.86 apply zenon_H162. apply refl_equal.
% 29.61/29.86 apply zenon_H206. apply refl_equal.
% 29.61/29.86 apply zenon_H206. apply refl_equal.
% 29.61/29.86 (* end of lemma zenon_L116_ *)
% 29.61/29.86 assert (zenon_L117_ : (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((op1 (e11) (e12)) = (e13)) -> False).
% 29.61/29.86 do 0 intro. intros zenon_H20b zenon_H4e zenon_H20c.
% 29.61/29.86 cut (((e13) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H20b.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H4e.
% 29.61/29.86 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 29.61/29.86 cut (((e13) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H20d].
% 29.61/29.86 congruence.
% 29.61/29.86 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H20e | zenon_intro zenon_H20f ].
% 29.61/29.86 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e13) = (op1 (e11) (e12)))).
% 29.61/29.86 intro zenon_D_pnotp.
% 29.61/29.86 apply zenon_H20d.
% 29.61/29.86 rewrite <- zenon_D_pnotp.
% 29.61/29.86 exact zenon_H20e.
% 29.61/29.86 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H20f].
% 29.61/29.86 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H210].
% 29.61/29.86 congruence.
% 29.61/29.86 exact (zenon_H210 zenon_H20c).
% 29.61/29.86 apply zenon_H20f. apply refl_equal.
% 29.61/29.86 apply zenon_H20f. apply refl_equal.
% 29.61/29.86 apply zenon_H68. apply refl_equal.
% 29.61/29.86 (* end of lemma zenon_L117_ *)
% 29.61/29.86 assert (zenon_L118_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((h3 (e12)) = (e22)) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H211 zenon_H45 zenon_H1fa zenon_H14f zenon_H196 zenon_H164 zenon_H2a zenon_H15f zenon_H1fe zenon_H1fc zenon_H20b zenon_H4e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H4b | zenon_intro zenon_H212 ].
% 29.69/29.86 apply (zenon_L115_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H4a | zenon_intro zenon_H213 ].
% 29.69/29.86 apply (zenon_L93_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H1fd | zenon_intro zenon_H20c ].
% 29.69/29.86 apply (zenon_L116_); trivial.
% 29.69/29.86 apply (zenon_L117_); trivial.
% 29.69/29.86 (* end of lemma zenon_L118_ *)
% 29.69/29.86 assert (zenon_L119_ : (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((op2 (e21) (e22)) = (e23)) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H214 zenon_H1d zenon_H215.
% 29.69/29.86 cut (((e23) = (op2 (e22) (e22))) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H214.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1d.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 29.69/29.86 cut (((e23) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H216].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H217 | zenon_intro zenon_H218 ].
% 29.69/29.86 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e23) = (op2 (e21) (e22)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H216.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H217.
% 29.69/29.86 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H218].
% 29.69/29.86 cut (((op2 (e21) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H219].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H219 zenon_H215).
% 29.69/29.86 apply zenon_H218. apply refl_equal.
% 29.69/29.86 apply zenon_H218. apply refl_equal.
% 29.69/29.86 apply zenon_Hda. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L119_ *)
% 29.69/29.86 assert (zenon_L120_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e21) (e23)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H21a zenon_H20 zenon_H21b zenon_H1d.
% 29.69/29.86 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H21a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H20.
% 29.69/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.69/29.86 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H21c].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ].
% 29.69/29.86 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H21c.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H2d.
% 29.69/29.86 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 29.69/29.86 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H21d].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H21d zenon_H21b).
% 29.69/29.86 apply zenon_H2e. apply refl_equal.
% 29.69/29.86 apply zenon_H2e. apply refl_equal.
% 29.69/29.86 apply (zenon_L4_); trivial.
% 29.69/29.86 (* end of lemma zenon_L120_ *)
% 29.69/29.86 assert (zenon_L121_ : ((op2 (e22) (e23)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H36 zenon_H21e zenon_H21f.
% 29.69/29.86 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H13d | zenon_intro zenon_H13e ].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H21f.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H13d.
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H220].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e22) (e23)) = (e22)) = ((op2 (e22) (e23)) = (op2 (e21) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H220.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H36.
% 29.69/29.86 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H221].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H13e. apply refl_equal.
% 29.69/29.86 apply zenon_H221. apply sym_equal. exact zenon_H21e.
% 29.69/29.86 apply zenon_H13e. apply refl_equal.
% 29.69/29.86 apply zenon_H13e. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L121_ *)
% 29.69/29.86 assert (zenon_L122_ : ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e11) = (e13))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H14f zenon_H222 zenon_Hab.
% 29.69/29.86 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H51 | zenon_intro zenon_H4d ].
% 29.69/29.86 cut (((e13) = (e13)) = ((e11) = (e13))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_Hab.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H51.
% 29.69/29.86 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.69/29.86 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e11) (e10)) = (e11)) = ((e13) = (e11))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_Hac.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H14f.
% 29.69/29.86 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 29.69/29.86 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H223].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H223 zenon_H222).
% 29.69/29.86 apply zenon_H48. apply refl_equal.
% 29.69/29.86 apply zenon_H4d. apply refl_equal.
% 29.69/29.86 apply zenon_H4d. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L122_ *)
% 29.69/29.86 assert (zenon_L123_ : ((op1 (e13) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H9c zenon_H224 zenon_H225.
% 29.69/29.86 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha0 ].
% 29.69/29.86 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H225.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9f.
% 29.69/29.86 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 29.69/29.86 cut (((op1 (e13) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H226].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e11)) = (e13)) = ((op1 (e13) (e11)) = (op1 (e11) (e11)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H226.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9c.
% 29.69/29.86 cut (((e13) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H227].
% 29.69/29.86 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_Ha0. apply refl_equal.
% 29.69/29.86 apply zenon_H227. apply sym_equal. exact zenon_H224.
% 29.69/29.86 apply zenon_Ha0. apply refl_equal.
% 29.69/29.86 apply zenon_Ha0. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L123_ *)
% 29.69/29.86 assert (zenon_L124_ : (~((h3 (e13)) = (e23))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H228 zenon_Hc0 zenon_H1d.
% 29.69/29.86 cut (((h3 (e13)) = (op2 (e22) (e22))) = ((h3 (e13)) = (e23))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H228.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hc0.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 29.69/29.86 cut (((h3 (e13)) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H229].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H229. apply refl_equal.
% 29.69/29.86 apply zenon_H1e. apply sym_equal. exact zenon_H1d.
% 29.69/29.86 (* end of lemma zenon_L124_ *)
% 29.69/29.86 assert (zenon_L125_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H22a zenon_Hab zenon_H14f zenon_H225 zenon_H9c zenon_H4e zenon_H20b zenon_H22b zenon_H22c zenon_H15f zenon_H2a zenon_Hc0 zenon_H1d.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H222 | zenon_intro zenon_H22d ].
% 29.69/29.86 apply (zenon_L122_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H224 | zenon_intro zenon_H22e ].
% 29.69/29.86 apply (zenon_L123_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H20c | zenon_intro zenon_H22f ].
% 29.69/29.86 apply (zenon_L117_); trivial.
% 29.69/29.86 cut (((h3 (e13)) = (op2 (e22) (e22))) = ((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H22b.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hc0.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (op2 (h3 (e11)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H230].
% 29.69/29.86 cut (((h3 (e13)) = (h3 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H231].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e11) (e13))) = (h3 (op1 (e11) (e13))))); [ zenon_intro zenon_H232 | zenon_intro zenon_H233 ].
% 29.69/29.86 cut (((h3 (op1 (e11) (e13))) = (h3 (op1 (e11) (e13)))) = ((h3 (e13)) = (h3 (op1 (e11) (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H231.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H232.
% 29.69/29.86 cut (((h3 (op1 (e11) (e13))) = (h3 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H233].
% 29.69/29.86 cut (((h3 (op1 (e11) (e13))) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H234].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H235].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H235 zenon_H22f).
% 29.69/29.86 apply zenon_H233. apply refl_equal.
% 29.69/29.86 apply zenon_H233. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13))))); [ zenon_intro zenon_H236 | zenon_intro zenon_H237 ].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13)))) = ((op2 (e22) (e22)) = (op2 (h3 (e11)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H230.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H236.
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H237].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H238].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e21) (e23)) = (e23)) = ((op2 (h3 (e11)) (h3 (e13))) = (op2 (e22) (e22)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H238.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H22c.
% 29.69/29.86 cut (((e23) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hcd].
% 29.69/29.86 cut (((op2 (e21) (e23)) = (op2 (h3 (e11)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H239].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13))))); [ zenon_intro zenon_H236 | zenon_intro zenon_H237 ].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13)))) = ((op2 (e21) (e23)) = (op2 (h3 (e11)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H239.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H236.
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (h3 (e11)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H237].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23a].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H228].
% 29.69/29.86 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L79_); trivial.
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 apply zenon_H237. apply refl_equal.
% 29.69/29.86 apply zenon_H237. apply refl_equal.
% 29.69/29.86 exact (zenon_Hcd zenon_H1d).
% 29.69/29.86 apply zenon_H237. apply refl_equal.
% 29.69/29.86 apply zenon_H237. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L125_ *)
% 29.69/29.86 assert (zenon_L126_ : (~((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))) -> ((op1 (e12) (e10)) = (e10)) -> ((op2 (e22) (e20)) = (e20)) -> ((h3 (e12)) = (e22)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H23b zenon_H1bf zenon_H1e2 zenon_H164 zenon_H9a zenon_H20.
% 29.69/29.86 cut (((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H23b.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9a.
% 29.69/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e12)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H23c].
% 29.69/29.86 cut (((h3 (e10)) = (h3 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H23d].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e12) (e10))) = (h3 (op1 (e12) (e10))))); [ zenon_intro zenon_H23e | zenon_intro zenon_H23f ].
% 29.69/29.86 cut (((h3 (op1 (e12) (e10))) = (h3 (op1 (e12) (e10)))) = ((h3 (e10)) = (h3 (op1 (e12) (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H23d.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H23e.
% 29.69/29.86 cut (((h3 (op1 (e12) (e10))) = (h3 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H23f].
% 29.69/29.86 cut (((h3 (op1 (e12) (e10))) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H240].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e12) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H241].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H241 zenon_H1bf).
% 29.69/29.86 apply zenon_H23f. apply refl_equal.
% 29.69/29.86 apply zenon_H23f. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10))))); [ zenon_intro zenon_H242 | zenon_intro zenon_H243 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10)))) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e12)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H23c.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H242.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H243].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H244].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e22) (e20)) = (e20)) = ((op2 (h3 (e12)) (h3 (e10))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H244.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1e2.
% 29.69/29.86 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1b1].
% 29.69/29.86 cut (((op2 (e22) (e20)) = (op2 (h3 (e12)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H245].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10))))); [ zenon_intro zenon_H242 | zenon_intro zenon_H243 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10)))) = ((op2 (e22) (e20)) = (op2 (h3 (e12)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H245.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H242.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (h3 (e12)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H243].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H246].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.69/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply (zenon_L37_); trivial.
% 29.69/29.86 apply zenon_H243. apply refl_equal.
% 29.69/29.86 apply zenon_H243. apply refl_equal.
% 29.69/29.86 exact (zenon_H1b1 zenon_H20).
% 29.69/29.86 apply zenon_H243. apply refl_equal.
% 29.69/29.86 apply zenon_H243. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L126_ *)
% 29.69/29.86 assert (zenon_L127_ : (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> ((op2 (e22) (e20)) = (e20)) -> (~((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H1d1 zenon_H20 zenon_H9a zenon_H164 zenon_H1e2 zenon_H23b zenon_H155 zenon_H57 zenon_H14f zenon_Ha9 zenon_H81 zenon_H70 zenon_H1cd zenon_H4e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1d2 ].
% 29.69/29.86 apply (zenon_L126_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H154 | zenon_intro zenon_H1d3 ].
% 29.69/29.86 apply (zenon_L76_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_H18c | zenon_intro zenon_H1ce ].
% 29.69/29.86 exact (zenon_H70 zenon_H18c).
% 29.69/29.86 apply (zenon_L104_); trivial.
% 29.69/29.86 (* end of lemma zenon_L127_ *)
% 29.69/29.86 assert (zenon_L128_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (e12))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))) -> ((op2 (e22) (e20)) = (e20)) -> ((h3 (e12)) = (e22)) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_Hbb zenon_H1cd zenon_H70 zenon_H14f zenon_H155 zenon_H23b zenon_H1e2 zenon_H164 zenon_H9a zenon_H20 zenon_H1d1 zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.69/29.86 apply (zenon_L127_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.69/29.86 exact (zenon_H88 zenon_H82).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.69/29.86 apply (zenon_L41_); trivial.
% 29.69/29.86 apply (zenon_L42_); trivial.
% 29.69/29.86 (* end of lemma zenon_L128_ *)
% 29.69/29.86 assert (zenon_L129_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H247 zenon_H20 zenon_H248 zenon_H1d.
% 29.69/29.86 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H247.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H20.
% 29.69/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 29.69/29.86 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H249].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H13d | zenon_intro zenon_H13e ].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e20) = (op2 (e22) (e23)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H249.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H13d.
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H13e].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H24a].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H24a zenon_H248).
% 29.69/29.86 apply zenon_H13e. apply refl_equal.
% 29.69/29.86 apply zenon_H13e. apply refl_equal.
% 29.69/29.86 apply (zenon_L4_); trivial.
% 29.69/29.86 (* end of lemma zenon_L129_ *)
% 29.69/29.86 assert (zenon_L130_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> (~((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op2 (e22) (e20)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H24b zenon_H77 zenon_H57 zenon_H4e zenon_H81 zenon_Haf zenon_H88 zenon_H1d1 zenon_H9a zenon_H164 zenon_H23b zenon_H155 zenon_H14f zenon_H70 zenon_H1cd zenon_Hbb zenon_He6 zenon_Hbf zenon_H36 zenon_H13c zenon_H1ed zenon_H1d7 zenon_H1dc zenon_H104 zenon_H1ee zenon_H1e8 zenon_H137 zenon_Heb zenon_H2a zenon_H11e zenon_Hf2 zenon_H1f zenon_H1f5 zenon_H101 zenon_H247 zenon_H20 zenon_H1d.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H24c ].
% 29.69/29.86 apply (zenon_L128_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H24d ].
% 29.69/29.86 apply (zenon_L113_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H100 | zenon_intro zenon_H248 ].
% 29.69/29.86 apply (zenon_L55_); trivial.
% 29.69/29.86 apply (zenon_L129_); trivial.
% 29.69/29.86 (* end of lemma zenon_L130_ *)
% 29.69/29.86 assert (zenon_L131_ : (~((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))) -> ((op1 (e12) (e11)) = (e11)) -> ((op2 (e22) (e21)) = (e21)) -> ((h3 (e12)) = (e22)) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H24e zenon_H15c zenon_H14c zenon_H164 zenon_H15f zenon_H2a.
% 29.69/29.86 cut (((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H24e.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H15f.
% 29.69/29.86 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e12)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H24f].
% 29.69/29.86 cut (((h3 (e11)) = (h3 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H250].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e12) (e11))) = (h3 (op1 (e12) (e11))))); [ zenon_intro zenon_H251 | zenon_intro zenon_H252 ].
% 29.69/29.86 cut (((h3 (op1 (e12) (e11))) = (h3 (op1 (e12) (e11)))) = ((h3 (e11)) = (h3 (op1 (e12) (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H250.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H251.
% 29.69/29.86 cut (((h3 (op1 (e12) (e11))) = (h3 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H252].
% 29.69/29.86 cut (((h3 (op1 (e12) (e11))) = (h3 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H253].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H254].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H254 zenon_H15c).
% 29.69/29.86 apply zenon_H252. apply refl_equal.
% 29.69/29.86 apply zenon_H252. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11))))); [ zenon_intro zenon_H255 | zenon_intro zenon_H256 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11)))) = ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e12)) (h3 (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H24f.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H255.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H256].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H257].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (h3 (e12)) (h3 (e11))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H257.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H14c.
% 29.69/29.86 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H258].
% 29.69/29.86 cut (((op2 (e22) (e21)) = (op2 (h3 (e12)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H259].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11))))); [ zenon_intro zenon_H255 | zenon_intro zenon_H256 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11)))) = ((op2 (e22) (e21)) = (op2 (h3 (e12)) (h3 (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H259.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H255.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (h3 (e12)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H256].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H25a].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.69/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply (zenon_L79_); trivial.
% 29.69/29.86 apply zenon_H256. apply refl_equal.
% 29.69/29.86 apply zenon_H256. apply refl_equal.
% 29.69/29.86 exact (zenon_H258 zenon_H2a).
% 29.69/29.86 apply zenon_H256. apply refl_equal.
% 29.69/29.86 apply zenon_H256. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L131_ *)
% 29.69/29.86 assert (zenon_L132_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> ((op2 (e22) (e21)) = (e21)) -> (~((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H17d zenon_H77 zenon_H88 zenon_H14f zenon_H155 zenon_Hbb zenon_H2a zenon_H15f zenon_H164 zenon_H14c zenon_H24e zenon_Hab zenon_H81 zenon_H4e zenon_H57 zenon_Haf.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H154 | zenon_intro zenon_H17e ].
% 29.69/29.86 apply (zenon_L77_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H15c | zenon_intro zenon_H17f ].
% 29.69/29.86 apply (zenon_L131_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H17b | zenon_intro zenon_Hae ].
% 29.69/29.86 apply (zenon_L84_); trivial.
% 29.69/29.86 apply (zenon_L41_); trivial.
% 29.69/29.86 (* end of lemma zenon_L132_ *)
% 29.69/29.86 assert (zenon_L133_ : (((op1 (e11) (e13)) = (e11))/\(~((op1 (e13) (e11)) = (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H89 zenon_H88.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H82. zenon_intro zenon_H8a.
% 29.69/29.86 exact (zenon_H88 zenon_H82).
% 29.69/29.86 (* end of lemma zenon_L133_ *)
% 29.69/29.86 assert (zenon_L134_ : ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e20) (e23)) = (e21)) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H2a zenon_H25b zenon_H131 zenon_Heb zenon_H20 zenon_H1d zenon_H25c.
% 29.69/29.86 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H1da | zenon_intro zenon_H116 ].
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e21) (e20)) = (op2 (e23) (e20)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H25c.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1da.
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H116].
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25d].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((op2 (e23) (e20)) = (op2 (e21) (e20)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H25d.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H2a.
% 29.69/29.86 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H130].
% 29.69/29.86 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25e].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H1da | zenon_intro zenon_H116 ].
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e21) = (op2 (e23) (e20)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H25e.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1da.
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H116].
% 29.69/29.86 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H25f].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H25f zenon_H25b).
% 29.69/29.86 apply zenon_H116. apply refl_equal.
% 29.69/29.86 apply zenon_H116. apply refl_equal.
% 29.69/29.86 apply (zenon_L69_); trivial.
% 29.69/29.86 apply zenon_H116. apply refl_equal.
% 29.69/29.86 apply zenon_H116. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L134_ *)
% 29.69/29.86 assert (zenon_L135_ : ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((op1 (e11) (e10)) = (e11)) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H81 zenon_H260 zenon_Ha9 zenon_H14f zenon_H57 zenon_H4e zenon_H261.
% 29.69/29.86 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H190 ].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e11) (e10)) = (op1 (e13) (e10)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H261.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1b7.
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H262].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) = ((op1 (e13) (e10)) = (op1 (e11) (e10)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H262.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H81.
% 29.69/29.86 cut (((op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12))) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 29.69/29.86 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H263].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H190 ].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H263.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1b7.
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H264].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H264 zenon_H260).
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 apply (zenon_L75_); trivial.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L135_ *)
% 29.69/29.86 assert (zenon_L136_ : ((h3 (e12)) = (e22)) -> ((op1 (e13) (e10)) = (e12)) -> (~((e22) = (h3 (op1 (e13) (e10))))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H164 zenon_H265 zenon_H266.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10))))); [ zenon_intro zenon_H267 | zenon_intro zenon_H268 ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10)))) = ((e22) = (h3 (op1 (e13) (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H266.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H267.
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H268].
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H269].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e12)) = (e22)) = ((h3 (op1 (e13) (e10))) = (e22))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H269.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H164.
% 29.69/29.86 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H162].
% 29.69/29.86 cut (((h3 (e12)) = (h3 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H26a].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10))))); [ zenon_intro zenon_H267 | zenon_intro zenon_H268 ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10)))) = ((h3 (e12)) = (h3 (op1 (e13) (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H26a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H267.
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (h3 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H268].
% 29.69/29.86 cut (((h3 (op1 (e13) (e10))) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26b].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H26c].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H26c zenon_H265).
% 29.69/29.86 apply zenon_H268. apply refl_equal.
% 29.69/29.86 apply zenon_H268. apply refl_equal.
% 29.69/29.86 apply zenon_H162. apply refl_equal.
% 29.69/29.86 apply zenon_H268. apply refl_equal.
% 29.69/29.86 apply zenon_H268. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L136_ *)
% 29.69/29.86 assert (zenon_L137_ : ((op2 (e23) (e20)) = (e22)) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> ((op1 (e13) (e10)) = (e12)) -> (~((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H26d zenon_Hc0 zenon_H1d zenon_H9a zenon_H20 zenon_H164 zenon_H265 zenon_H26e.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10))))); [ zenon_intro zenon_H26f | zenon_intro zenon_H270 ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10)))) = ((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H26e.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H26f.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H270].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (h3 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H271].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (h3 (e13)) (h3 (e10))) = (h3 (op1 (e13) (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H271.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H26d.
% 29.69/29.86 cut (((e22) = (h3 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H266].
% 29.69/29.86 cut (((op2 (e23) (e20)) = (op2 (h3 (e13)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H272].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10))))); [ zenon_intro zenon_H26f | zenon_intro zenon_H270 ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10)))) = ((op2 (e23) (e20)) = (op2 (h3 (e13)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H272.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H26f.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (op2 (h3 (e13)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H270].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H273].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.69/29.86 cut (((h3 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H228].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 apply (zenon_L37_); trivial.
% 29.69/29.86 apply zenon_H270. apply refl_equal.
% 29.69/29.86 apply zenon_H270. apply refl_equal.
% 29.69/29.86 apply (zenon_L136_); trivial.
% 29.69/29.86 apply zenon_H270. apply refl_equal.
% 29.69/29.86 apply zenon_H270. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L137_ *)
% 29.69/29.86 assert (zenon_L138_ : ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H18e zenon_Hc3 zenon_H274.
% 29.69/29.86 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H190 ].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H274.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H1b7.
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H275].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e10) (e10)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H275.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H18e.
% 29.69/29.86 cut (((e13) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H276].
% 29.69/29.86 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H190].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 apply zenon_H276. apply sym_equal. exact zenon_Hc3.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 apply zenon_H190. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L138_ *)
% 29.69/29.86 assert (zenon_L139_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e11)) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))) -> ((h3 (e12)) = (e22)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((op2 (e23) (e20)) = (e22)) -> ((op1 (e10) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H277 zenon_H1b4 zenon_H261 zenon_H4e zenon_H57 zenon_H14f zenon_Ha9 zenon_H81 zenon_H26e zenon_H164 zenon_H20 zenon_H9a zenon_H1d zenon_Hc0 zenon_H26d zenon_Hc3 zenon_H274.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H277); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H278 ].
% 29.69/29.86 apply (zenon_L100_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H278); [ zenon_intro zenon_H260 | zenon_intro zenon_H279 ].
% 29.69/29.86 apply (zenon_L135_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H265 | zenon_intro zenon_H18e ].
% 29.69/29.86 apply (zenon_L137_); trivial.
% 29.69/29.86 apply (zenon_L138_); trivial.
% 29.69/29.86 (* end of lemma zenon_L139_ *)
% 29.69/29.86 assert (zenon_L140_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))) -> ((h3 (e12)) = (e22)) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_Hbe zenon_H277 zenon_H1b4 zenon_H261 zenon_H14f zenon_H26e zenon_H164 zenon_H20 zenon_H9a zenon_H1d zenon_Hc0 zenon_H26d zenon_H274 zenon_H9e zenon_H9c zenon_Ha3 zenon_Hbb zenon_Hab zenon_H88 zenon_Haf zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.69/29.86 apply (zenon_L139_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.69/29.86 exact (zenon_H88 zenon_H82).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.69/29.86 apply (zenon_L41_); trivial.
% 29.69/29.86 apply (zenon_L42_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hd0 ].
% 29.69/29.86 apply (zenon_L38_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Haa ].
% 29.69/29.86 apply (zenon_L39_); trivial.
% 29.69/29.86 apply (zenon_L43_); trivial.
% 29.69/29.86 (* end of lemma zenon_L140_ *)
% 29.69/29.86 assert (zenon_L141_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e20) (e23)) = (e21)) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e12)) = (e22)) -> (~((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H27a zenon_H1d7 zenon_H25c zenon_Heb zenon_H131 zenon_H2a zenon_H77 zenon_H57 zenon_H4e zenon_H81 zenon_Haf zenon_H88 zenon_Hab zenon_Hbb zenon_Ha3 zenon_H9c zenon_H9e zenon_H274 zenon_Hc0 zenon_H1d zenon_H9a zenon_H20 zenon_H164 zenon_H26e zenon_H14f zenon_H261 zenon_H1b4 zenon_H277 zenon_Hbe zenon_H113 zenon_Hd1.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H27b ].
% 29.69/29.86 apply (zenon_L107_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H25b | zenon_intro zenon_H27c ].
% 29.69/29.86 apply (zenon_L134_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H26d | zenon_intro zenon_H114 ].
% 29.69/29.86 apply (zenon_L140_); trivial.
% 29.69/29.86 apply (zenon_L59_); trivial.
% 29.69/29.86 (* end of lemma zenon_L141_ *)
% 29.69/29.86 assert (zenon_L142_ : ((h3 (e13)) = (op2 (e22) (e22))) -> ((op1 (e13) (e11)) = (e13)) -> ((e23) = (op2 (e22) (e22))) -> (~((e23) = (h3 (op1 (e13) (e11))))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_Hc0 zenon_H9c zenon_H1d zenon_H27d.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11))))); [ zenon_intro zenon_H27e | zenon_intro zenon_H27f ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11)))) = ((e23) = (h3 (op1 (e13) (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H27d.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H27e.
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H27f].
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H280].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e13)) = (op2 (e22) (e22))) = ((h3 (op1 (e13) (e11))) = (e23))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H280.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hc0.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 29.69/29.86 cut (((h3 (e13)) = (h3 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H281].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11))))); [ zenon_intro zenon_H27e | zenon_intro zenon_H27f ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11)))) = ((h3 (e13)) = (h3 (op1 (e13) (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H281.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H27e.
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (h3 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H27f].
% 29.69/29.86 cut (((h3 (op1 (e13) (e11))) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H282].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H8a zenon_H9c).
% 29.69/29.86 apply zenon_H27f. apply refl_equal.
% 29.69/29.86 apply zenon_H27f. apply refl_equal.
% 29.69/29.86 apply zenon_H1e. apply sym_equal. exact zenon_H1d.
% 29.69/29.86 apply zenon_H27f. apply refl_equal.
% 29.69/29.86 apply zenon_H27f. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L142_ *)
% 29.69/29.86 assert (zenon_L143_ : (~((e21) = (e23))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e21)) -> False).
% 29.69/29.86 do 0 intro. intros zenon_Hed zenon_Hd1 zenon_H283.
% 29.69/29.86 cut (((op2 (e23) (e21)) = (e23)) = ((e21) = (e23))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_Hed.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hd1.
% 29.69/29.86 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hef].
% 29.69/29.86 cut (((op2 (e23) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H284].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H284 zenon_H283).
% 29.69/29.86 apply zenon_Hef. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L143_ *)
% 29.69/29.86 assert (zenon_L144_ : (~((e11) = (e13))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e11)) -> False).
% 29.69/29.86 do 0 intro. intros zenon_Hab zenon_H9c zenon_H285.
% 29.69/29.86 cut (((op1 (e13) (e11)) = (e13)) = ((e11) = (e13))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_Hab.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9c.
% 29.69/29.86 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 29.69/29.86 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H286].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H286 zenon_H285).
% 29.69/29.86 apply zenon_H4d. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L144_ *)
% 29.69/29.86 assert (zenon_L145_ : (~((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op1 (e13) (e12)) = (e11)) -> ((op2 (e23) (e22)) = (e21)) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e12)) = (e22)) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H287 zenon_H15f zenon_H288 zenon_H289 zenon_H2a zenon_Hc0 zenon_H1d zenon_H164.
% 29.69/29.86 cut (((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H287.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H15f.
% 29.69/29.86 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e13)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28a].
% 29.69/29.86 cut (((h3 (e11)) = (h3 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28b].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e12))) = (h3 (op1 (e13) (e12))))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e12))) = (h3 (op1 (e13) (e12)))) = ((h3 (e11)) = (h3 (op1 (e13) (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H28b.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H28c.
% 29.69/29.86 cut (((h3 (op1 (e13) (e12))) = (h3 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28d].
% 29.69/29.86 cut (((h3 (op1 (e13) (e12))) = (h3 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H28e].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H28f].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H28f zenon_H288).
% 29.69/29.86 apply zenon_H28d. apply refl_equal.
% 29.69/29.86 apply zenon_H28d. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12)))) = ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e13)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H28a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H290.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H291].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H292].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e23) (e22)) = (e21)) = ((op2 (h3 (e13)) (h3 (e12))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H292.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H289.
% 29.69/29.86 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H258].
% 29.69/29.86 cut (((op2 (e23) (e22)) = (op2 (h3 (e13)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H293].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12))))); [ zenon_intro zenon_H290 | zenon_intro zenon_H291 ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12)))) = ((op2 (e23) (e22)) = (op2 (h3 (e13)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H293.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H290.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (h3 (e13)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H291].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H294].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.69/29.86 cut (((h3 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H228].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply zenon_H291. apply refl_equal.
% 29.69/29.86 apply zenon_H291. apply refl_equal.
% 29.69/29.86 exact (zenon_H258 zenon_H2a).
% 29.69/29.86 apply zenon_H291. apply refl_equal.
% 29.69/29.86 apply zenon_H291. apply refl_equal.
% 29.69/29.86 (* end of lemma zenon_L145_ *)
% 29.69/29.86 assert (zenon_L146_ : (((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e12)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((e11) = (e13))) -> ((h3 (e12)) = (e22)) -> ((e23) = (op2 (e22) (e22))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> ((op2 (e23) (e22)) = (e21)) -> ((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) -> (~((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))) -> ((e11) = (op1 (op1 (op1 (e12) (e12)) (op1 (e12) (e12))) (op1 (e12) (e12)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H295 zenon_Haf zenon_H88 zenon_H14f zenon_H261 zenon_Hbb zenon_H9c zenon_Hab zenon_H164 zenon_H1d zenon_Hc0 zenon_H2a zenon_H289 zenon_H15f zenon_H287 zenon_H81 zenon_H4e zenon_H57 zenon_H77.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H260 | zenon_intro zenon_H296 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.69/29.86 apply (zenon_L135_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.69/29.86 exact (zenon_H88 zenon_H82).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.69/29.86 apply (zenon_L41_); trivial.
% 29.69/29.86 apply (zenon_L42_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H285 | zenon_intro zenon_H297 ].
% 29.69/29.86 apply (zenon_L144_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_H288 | zenon_intro zenon_Hb5 ].
% 29.69/29.86 apply (zenon_L145_); trivial.
% 29.69/29.86 apply (zenon_L42_); trivial.
% 29.69/29.86 (* end of lemma zenon_L146_ *)
% 29.69/29.86 assert (zenon_L147_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e11) (e13)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H298 zenon_H57 zenon_H299 zenon_H4e.
% 29.69/29.86 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H298.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H57.
% 29.69/29.86 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.69/29.86 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29a].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ].
% 29.69/29.86 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H29a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H84.
% 29.69/29.86 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 29.69/29.86 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H29b].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H29b zenon_H299).
% 29.69/29.86 apply zenon_H85. apply refl_equal.
% 29.69/29.86 apply zenon_H85. apply refl_equal.
% 29.69/29.86 apply (zenon_L20_); trivial.
% 29.69/29.86 (* end of lemma zenon_L147_ *)
% 29.69/29.86 assert (zenon_L148_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> ((op1 (e12) (e13)) = (e10)) -> ((e13) = (op1 (e12) (e12))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H29c zenon_H57 zenon_H29d zenon_H4e.
% 29.69/29.86 cut (((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H29c.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H57.
% 29.69/29.86 cut (((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 29.69/29.86 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29e].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 29.69/29.86 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e10) = (op1 (e12) (e13)))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H29e.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hb0.
% 29.69/29.86 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 29.69/29.86 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H29f].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H29f zenon_H29d).
% 29.69/29.86 apply zenon_Hb1. apply refl_equal.
% 29.69/29.86 apply zenon_Hb1. apply refl_equal.
% 29.69/29.86 apply (zenon_L20_); trivial.
% 29.69/29.86 (* end of lemma zenon_L148_ *)
% 29.69/29.86 assert (zenon_L149_ : (~((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((op1 (e13) (e13)) = (e10)) -> ((h3 (e13)) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H2a0 zenon_H9a zenon_H1be zenon_Hc0.
% 29.69/29.86 cut (((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H2a0.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9a.
% 29.69/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e13)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2a1].
% 29.69/29.86 cut (((h3 (e10)) = (h3 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2a2].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e13) (e13))) = (h3 (op1 (e13) (e13))))); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2a4 ].
% 29.69/29.86 cut (((h3 (op1 (e13) (e13))) = (h3 (op1 (e13) (e13)))) = ((h3 (e10)) = (h3 (op1 (e13) (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H2a2.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H2a3.
% 29.69/29.86 cut (((h3 (op1 (e13) (e13))) = (h3 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2a4].
% 29.69/29.86 cut (((h3 (op1 (e13) (e13))) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2a5].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a6].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H2a6 zenon_H1be).
% 29.69/29.86 apply zenon_H2a4. apply refl_equal.
% 29.69/29.86 apply zenon_H2a4. apply refl_equal.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a3].
% 29.69/29.86 cut (((op2 (e22) (e22)) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a3].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H1a3. apply sym_equal. exact zenon_Hc0.
% 29.69/29.86 apply zenon_H1a3. apply sym_equal. exact zenon_Hc0.
% 29.69/29.86 (* end of lemma zenon_L149_ *)
% 29.69/29.86 assert (zenon_L150_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e13) = (op1 (e12) (e12))) -> ((e10) = (op1 (op1 (e12) (e12)) (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))) -> ((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H2a7 zenon_H77 zenon_H298 zenon_H4e zenon_H57 zenon_H29c zenon_H2a0 zenon_H9a zenon_Hc0.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H78 | zenon_intro zenon_H2a8 ].
% 29.69/29.86 apply (zenon_L27_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H299 | zenon_intro zenon_H2a9 ].
% 29.69/29.86 apply (zenon_L147_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H29d | zenon_intro zenon_H1be ].
% 29.69/29.86 apply (zenon_L148_); trivial.
% 29.69/29.86 apply (zenon_L149_); trivial.
% 29.69/29.86 (* end of lemma zenon_L150_ *)
% 29.69/29.86 assert (zenon_L151_ : (~(((h3 (e10)) = (e23))\/(((h3 (e11)) = (e23))\/(((h3 (e12)) = (e23))\/((h3 (e13)) = (e23)))))) -> ((h3 (e13)) = (op2 (e22) (e22))) -> ((e23) = (op2 (e22) (e22))) -> False).
% 29.69/29.86 do 0 intro. intros zenon_H2aa zenon_Hc0 zenon_H1d.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H2aa). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H2ab). zenon_intro zenon_H2ae. zenon_intro zenon_H2ad.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H2ad). zenon_intro zenon_H2af. zenon_intro zenon_H228.
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 (* end of lemma zenon_L151_ *)
% 29.69/29.86 apply NNPP. intro zenon_G.
% 29.69/29.86 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H172. zenon_intro zenon_H2b2.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H2b4. zenon_intro zenon_H2b3.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H2b6. zenon_intro zenon_H2b5.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H2b8. zenon_intro zenon_H2b7.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2ba. zenon_intro zenon_H2b9.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H211. zenon_intro zenon_H2bb.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H2bd. zenon_intro zenon_H2bc.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H1d1. zenon_intro zenon_H2be.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H2c0. zenon_intro zenon_H2bf.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2bf). zenon_intro zenon_H2c2. zenon_intro zenon_H2c1.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H2c4. zenon_intro zenon_H2c3.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H277. zenon_intro zenon_H2c5.
% 29.69/29.86 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6.
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% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_H3b8. zenon_intro zenon_H3b7.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H3ba. zenon_intro zenon_H3b9.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3b9). zenon_intro zenon_H1e8. zenon_intro zenon_H3bb.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_Hf2. zenon_intro zenon_H3bc.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H128. zenon_intro zenon_H3bd.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H3bf. zenon_intro zenon_H3be.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H34. zenon_intro zenon_H3c0.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c0). zenon_intro zenon_H3c2. zenon_intro zenon_H3c1.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H113. zenon_intro zenon_H3c3.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H3c5. zenon_intro zenon_H3c4.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H1d7. zenon_intro zenon_H3c6.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c6). zenon_intro zenon_H3c8. zenon_intro zenon_H3c7.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H1dc. zenon_intro zenon_H104.
% 29.69/29.86 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H49. zenon_intro zenon_H3c9.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3c9). zenon_intro zenon_H3cb. zenon_intro zenon_H3ca.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H50. zenon_intro zenon_H3cc.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3cc). zenon_intro zenon_H3ce. zenon_intro zenon_H3cd.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_Hab. zenon_intro zenon_H3cf.
% 29.69/29.86 apply (zenon_and_s _ _ ax8). zenon_intro zenon_Hfc. zenon_intro zenon_H3d0.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_H3d2. zenon_intro zenon_H3d1.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_H101. zenon_intro zenon_H3d3.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_H3d5. zenon_intro zenon_H3d4.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_Hed. zenon_intro zenon_H3d6.
% 29.69/29.86 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H3d8. zenon_intro zenon_H3d7.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H192. zenon_intro zenon_H3d9.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H6c. zenon_intro zenon_H94.
% 29.69/29.86 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H3db. zenon_intro zenon_H3da.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H118. zenon_intro zenon_H3dc.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H119. zenon_intro zenon_H3e.
% 29.69/29.86 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H57. zenon_intro zenon_H3dd.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H81. zenon_intro zenon_H4e.
% 29.69/29.86 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H20. zenon_intro zenon_H3de.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3de). zenon_intro zenon_H2a. zenon_intro zenon_H1d.
% 29.69/29.86 apply (zenon_and_s _ _ ax16). zenon_intro zenon_H164. zenon_intro zenon_H3df.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_H9a. zenon_intro zenon_H3e0.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H15f. zenon_intro zenon_Hc0.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H3e2. zenon_intro zenon_H3e1.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H3e1). zenon_intro zenon_H3e4. zenon_intro zenon_H3e3.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H3e3). zenon_intro zenon_H3e6. zenon_intro zenon_H3e5.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H3e6); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H3e7 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_Hbf | zenon_intro zenon_H3eb ].
% 29.69/29.86 apply (zenon_L44_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3eb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H3ec ].
% 29.69/29.86 apply (zenon_L45_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ec); [ zenon_intro zenon_Hd9 | zenon_intro zenon_He5 ].
% 29.69/29.86 apply (zenon_L46_); trivial.
% 29.69/29.86 apply (zenon_L62_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H3e7); [ zenon_intro zenon_H163 | zenon_intro zenon_H3ed ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H32d); [ zenon_intro zenon_H136 | zenon_intro zenon_H3f1 ].
% 29.69/29.86 apply (zenon_L73_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f1); [ zenon_intro zenon_H14c | zenon_intro zenon_H3f2 ].
% 29.69/29.86 apply (zenon_L87_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f2); [ zenon_intro zenon_H188 | zenon_intro zenon_H13b ].
% 29.69/29.86 apply (zenon_L88_); trivial.
% 29.69/29.86 apply (zenon_L71_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H3ed); [ zenon_intro zenon_H3f4 | zenon_intro zenon_H3f3 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11d | zenon_intro zenon_H11c ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_Hf9. zenon_intro zenon_H11e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.69/29.86 cut (((h3 (e10)) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22)))) = ((h3 (op1 (e10) (e12))) = (op2 (h3 (e10)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H3f4.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H9a.
% 29.69/29.86 cut (((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e10)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3f5].
% 29.69/29.86 cut (((h3 (e10)) = (h3 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3f6].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e10) (e12))) = (h3 (op1 (e10) (e12))))); [ zenon_intro zenon_H3f7 | zenon_intro zenon_H3f8 ].
% 29.69/29.86 cut (((h3 (op1 (e10) (e12))) = (h3 (op1 (e10) (e12)))) = ((h3 (e10)) = (h3 (op1 (e10) (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H3f6.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H3f7.
% 29.69/29.86 cut (((h3 (op1 (e10) (e12))) = (h3 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3f8].
% 29.69/29.86 cut (((h3 (op1 (e10) (e12))) = (h3 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3f9].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e10) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18b].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H18b zenon_H45).
% 29.69/29.86 apply zenon_H3f8. apply refl_equal.
% 29.69/29.86 apply zenon_H3f8. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12))))); [ zenon_intro zenon_H3fa | zenon_intro zenon_H3fb ].
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12)))) = ((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (op2 (h3 (e10)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H3f5.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H3fa.
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3fb].
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H3fc].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (h3 (e10)) (h3 (e12))) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H3fc.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hf9.
% 29.69/29.86 cut (((e20) = (op2 (op2 (e22) (e22)) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1b1].
% 29.69/29.86 cut (((op2 (e20) (e22)) = (op2 (h3 (e10)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3fd].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12))))); [ zenon_intro zenon_H3fa | zenon_intro zenon_H3fb ].
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12)))) = ((op2 (e20) (e22)) = (op2 (h3 (e10)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H3fd.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H3fa.
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (h3 (e10)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3fb].
% 29.69/29.86 cut (((op2 (h3 (e10)) (h3 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3fe].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.69/29.86 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L37_); trivial.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply zenon_H3fb. apply refl_equal.
% 29.69/29.86 apply zenon_H3fb. apply refl_equal.
% 29.69/29.86 exact (zenon_H1b1 zenon_H20).
% 29.69/29.86 apply zenon_H3fb. apply refl_equal.
% 29.69/29.86 apply zenon_H3fb. apply refl_equal.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.69/29.86 apply (zenon_L94_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.69/29.86 apply (zenon_L23_); trivial.
% 29.69/29.86 apply (zenon_L24_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 29.69/29.86 apply (zenon_L96_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H10a | zenon_intro zenon_H10d ].
% 29.69/29.86 apply (zenon_L57_); trivial.
% 29.69/29.86 apply (zenon_L58_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H3f3); [ zenon_intro zenon_H19c | zenon_intro zenon_H3ff ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hbc ].
% 29.69/29.86 apply (zenon_L97_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbd ].
% 29.69/29.86 exact (zenon_H88 zenon_H82).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_Hae | zenon_intro zenon_Hb5 ].
% 29.69/29.86 apply (zenon_L41_); trivial.
% 29.69/29.86 apply (zenon_L42_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H3ff); [ zenon_intro zenon_H401 | zenon_intro zenon_H400 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 cut (((h3 (e11)) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22)))) = ((h3 (op1 (e11) (e10))) = (op2 (h3 (e11)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H401.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H15f.
% 29.69/29.86 cut (((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e11)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H402].
% 29.69/29.86 cut (((h3 (e11)) = (h3 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H403].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e11) (e10))) = (h3 (op1 (e11) (e10))))); [ zenon_intro zenon_H404 | zenon_intro zenon_H405 ].
% 29.69/29.86 cut (((h3 (op1 (e11) (e10))) = (h3 (op1 (e11) (e10)))) = ((h3 (e11)) = (h3 (op1 (e11) (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H403.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H404.
% 29.69/29.86 cut (((h3 (op1 (e11) (e10))) = (h3 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H405].
% 29.69/29.86 cut (((h3 (op1 (e11) (e10))) = (h3 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H406].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H6d zenon_H14f).
% 29.69/29.86 apply zenon_H405. apply refl_equal.
% 29.69/29.86 apply zenon_H405. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10))))); [ zenon_intro zenon_H407 | zenon_intro zenon_H408 ].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10)))) = ((op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))) = (op2 (h3 (e11)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H402.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H407.
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H408].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H409].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (h3 (e11)) (h3 (e10))) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H409.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Heb.
% 29.69/29.86 cut (((e21) = (op2 (op2 (op2 (e22) (e22)) (op2 (e22) (e22))) (op2 (e22) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H258].
% 29.69/29.86 cut (((op2 (e21) (e20)) = (op2 (h3 (e11)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H40a].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10))))); [ zenon_intro zenon_H407 | zenon_intro zenon_H408 ].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10)))) = ((op2 (e21) (e20)) = (op2 (h3 (e11)) (h3 (e10))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H40a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H407.
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (h3 (e11)) (h3 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H408].
% 29.69/29.86 cut (((op2 (h3 (e11)) (h3 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H40b].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H99].
% 29.69/29.86 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L79_); trivial.
% 29.69/29.86 apply (zenon_L37_); trivial.
% 29.69/29.86 apply zenon_H408. apply refl_equal.
% 29.69/29.86 apply zenon_H408. apply refl_equal.
% 29.69/29.86 exact (zenon_H258 zenon_H2a).
% 29.69/29.86 apply zenon_H408. apply refl_equal.
% 29.69/29.86 apply zenon_H408. apply refl_equal.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H400); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H40c ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11d | zenon_intro zenon_H11c ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_Hf9. zenon_intro zenon_H11e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.69/29.86 apply (zenon_L6_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.69/29.86 apply (zenon_L98_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_Hbf | zenon_intro zenon_H3eb ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_H18 | zenon_intro zenon_H40d ].
% 29.69/29.86 exact (zenon_H16 zenon_H18).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40d); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H40e ].
% 29.69/29.86 apply (zenon_L106_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40e); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1dd ].
% 29.69/29.86 apply (zenon_L113_); trivial.
% 29.69/29.86 apply (zenon_L108_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3eb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H3ec ].
% 29.69/29.86 apply (zenon_L45_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ec); [ zenon_intro zenon_Hd9 | zenon_intro zenon_He5 ].
% 29.69/29.86 apply (zenon_L46_); trivial.
% 29.69/29.86 apply (zenon_L62_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.69/29.86 apply (zenon_L94_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.69/29.86 apply (zenon_L23_); trivial.
% 29.69/29.86 apply (zenon_L24_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_L12_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 29.69/29.86 apply (zenon_L96_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H10a | zenon_intro zenon_H10d ].
% 29.69/29.86 apply (zenon_L57_); trivial.
% 29.69/29.86 apply (zenon_L58_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H40c); [ zenon_intro zenon_H1fc | zenon_intro zenon_H40f ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11d | zenon_intro zenon_H11c ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_Hf9. zenon_intro zenon_H11e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_Hfe | zenon_intro zenon_H410 ].
% 29.69/29.86 apply (zenon_L114_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H410); [ zenon_intro zenon_Hfd | zenon_intro zenon_H411 ].
% 29.69/29.86 apply (zenon_L95_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H411); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ].
% 29.69/29.86 apply (zenon_L118_); trivial.
% 29.69/29.86 apply (zenon_L119_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.69/29.86 apply (zenon_L94_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.69/29.86 apply (zenon_L23_); trivial.
% 29.69/29.86 apply (zenon_L24_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 29.69/29.86 apply (zenon_L96_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H10a | zenon_intro zenon_H10d ].
% 29.69/29.86 apply (zenon_L57_); trivial.
% 29.69/29.86 apply (zenon_L58_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H40f); [ zenon_intro zenon_H22b | zenon_intro zenon_H412 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.69/29.86 apply (zenon_L6_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.69/29.86 apply (zenon_L98_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H21b | zenon_intro zenon_H413 ].
% 29.69/29.86 apply (zenon_L120_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H413); [ zenon_intro zenon_H2b | zenon_intro zenon_H414 ].
% 29.69/29.86 exact (zenon_H31 zenon_H2b).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H414); [ zenon_intro zenon_H21e | zenon_intro zenon_H22c ].
% 29.69/29.86 apply (zenon_L121_); trivial.
% 29.69/29.86 apply (zenon_L125_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_L12_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H412); [ zenon_intro zenon_H23b | zenon_intro zenon_H415 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H11d | zenon_intro zenon_H11c ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_Hf9. zenon_intro zenon_H11e.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.69/29.86 apply (zenon_L6_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.69/29.86 apply (zenon_L98_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6c); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H45. zenon_intro zenon_H70.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_Hbf | zenon_intro zenon_H3eb ].
% 29.69/29.86 apply (zenon_L130_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3eb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H3ec ].
% 29.69/29.86 apply (zenon_L45_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ec); [ zenon_intro zenon_Hd9 | zenon_intro zenon_He5 ].
% 29.69/29.86 apply (zenon_L46_); trivial.
% 29.69/29.86 apply (zenon_L62_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ].
% 29.69/29.86 apply (zenon_L94_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H60 | zenon_intro zenon_H63 ].
% 29.69/29.86 apply (zenon_L23_); trivial.
% 29.69/29.86 apply (zenon_L24_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_L12_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H120 | zenon_intro zenon_H11f ].
% 29.69/29.86 apply (zenon_L96_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H10a | zenon_intro zenon_H10d ].
% 29.69/29.86 apply (zenon_L57_); trivial.
% 29.69/29.86 apply (zenon_L58_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H415); [ zenon_intro zenon_H24e | zenon_intro zenon_H416 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H32d); [ zenon_intro zenon_H136 | zenon_intro zenon_H3f1 ].
% 29.69/29.86 apply (zenon_L73_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f1); [ zenon_intro zenon_H14c | zenon_intro zenon_H3f2 ].
% 29.69/29.86 apply (zenon_L132_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f2); [ zenon_intro zenon_H188 | zenon_intro zenon_H13b ].
% 29.69/29.86 apply (zenon_L88_); trivial.
% 29.69/29.86 apply (zenon_L71_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H416); [ zenon_intro zenon_H418 | zenon_intro zenon_H417 ].
% 29.69/29.86 cut (((h3 (e13)) = (op2 (e22) (e22))) = ((h3 (op1 (e12) (e12))) = (op2 (h3 (e12)) (h3 (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H418.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hc0.
% 29.69/29.86 cut (((op2 (e22) (e22)) = (op2 (h3 (e12)) (h3 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H419].
% 29.69/29.86 cut (((h3 (e13)) = (h3 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H41a].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e12) (e12))) = (h3 (op1 (e12) (e12))))); [ zenon_intro zenon_H41b | zenon_intro zenon_H41c ].
% 29.69/29.86 cut (((h3 (op1 (e12) (e12))) = (h3 (op1 (e12) (e12)))) = ((h3 (e13)) = (h3 (op1 (e12) (e12))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H41a.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H41b.
% 29.69/29.86 cut (((h3 (op1 (e12) (e12))) = (h3 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H41c].
% 29.69/29.86 cut (((h3 (op1 (e12) (e12))) = (h3 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H41d].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H55].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H55. apply sym_equal. exact zenon_H4e.
% 29.69/29.86 apply zenon_H41c. apply refl_equal.
% 29.69/29.86 apply zenon_H41c. apply refl_equal.
% 29.69/29.86 cut (((e22) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H41e].
% 29.69/29.86 cut (((e22) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H41e].
% 29.69/29.86 congruence.
% 29.69/29.86 apply zenon_H41e. apply sym_equal. exact zenon_H164.
% 29.69/29.86 apply zenon_H41e. apply sym_equal. exact zenon_H164.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H417); [ zenon_intro zenon_H420 | zenon_intro zenon_H41f ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H26 | zenon_intro zenon_H3f ].
% 29.69/29.86 apply (zenon_L6_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H32 | zenon_intro zenon_H40 ].
% 29.69/29.86 apply (zenon_L98_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H3b ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H36. zenon_intro zenon_H3a.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H7d | zenon_intro zenon_H95 ].
% 29.69/29.86 apply (zenon_L28_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H89 | zenon_intro zenon_H96 ].
% 29.69/29.86 apply (zenon_L133_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H90 | zenon_intro zenon_H91 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H8d. zenon_intro zenon_H6a.
% 29.69/29.86 cut (((h3 (e12)) = (e22)) = ((h3 (op1 (e12) (e13))) = (op2 (h3 (e12)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H420.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H164.
% 29.69/29.86 cut (((e22) = (op2 (h3 (e12)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H421].
% 29.69/29.86 cut (((h3 (e12)) = (h3 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H422].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((h3 (op1 (e12) (e13))) = (h3 (op1 (e12) (e13))))); [ zenon_intro zenon_H423 | zenon_intro zenon_H424 ].
% 29.69/29.86 cut (((h3 (op1 (e12) (e13))) = (h3 (op1 (e12) (e13)))) = ((h3 (e12)) = (h3 (op1 (e12) (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H422.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H423.
% 29.69/29.86 cut (((h3 (op1 (e12) (e13))) = (h3 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H424].
% 29.69/29.86 cut (((h3 (op1 (e12) (e13))) = (h3 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H425].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H65 zenon_H8d).
% 29.69/29.86 apply zenon_H424. apply refl_equal.
% 29.69/29.86 apply zenon_H424. apply refl_equal.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13))))); [ zenon_intro zenon_H426 | zenon_intro zenon_H427 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13)))) = ((e22) = (op2 (h3 (e12)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H421.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H426.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H428].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e22) (e23)) = (e22)) = ((op2 (h3 (e12)) (h3 (e13))) = (e22))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H428.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H36.
% 29.69/29.86 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H162].
% 29.69/29.86 cut (((op2 (e22) (e23)) = (op2 (h3 (e12)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H429].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13))))); [ zenon_intro zenon_H426 | zenon_intro zenon_H427 ].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13)))) = ((op2 (e22) (e23)) = (op2 (h3 (e12)) (h3 (e13))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H429.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H426.
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (op2 (h3 (e12)) (h3 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H427].
% 29.69/29.86 cut (((op2 (h3 (e12)) (h3 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H42a].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H228].
% 29.69/29.86 cut (((h3 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H20a].
% 29.69/29.86 congruence.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 apply zenon_H427. apply refl_equal.
% 29.69/29.86 apply zenon_H427. apply refl_equal.
% 29.69/29.86 apply zenon_H162. apply refl_equal.
% 29.69/29.86 apply zenon_H427. apply refl_equal.
% 29.69/29.86 apply zenon_H427. apply refl_equal.
% 29.69/29.86 apply (zenon_L34_); trivial.
% 29.69/29.86 apply (zenon_L12_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H41f); [ zenon_intro zenon_H26e | zenon_intro zenon_H42b ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H131 | zenon_intro zenon_H149 ].
% 29.69/29.86 apply (zenon_L141_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H2b | zenon_intro zenon_H14a ].
% 29.69/29.86 exact (zenon_H31 zenon_H2b).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13b | zenon_intro zenon_H142 ].
% 29.69/29.86 apply (zenon_L71_); trivial.
% 29.69/29.86 apply (zenon_L72_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H42b); [ zenon_intro zenon_H42d | zenon_intro zenon_H42c ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11))))); [ zenon_intro zenon_H42e | zenon_intro zenon_H42f ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11)))) = ((h3 (op1 (e13) (e11))) = (op2 (h3 (e13)) (h3 (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H42d.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H42e.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H42f].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (h3 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H430].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((op2 (e23) (e21)) = (e23)) = ((op2 (h3 (e13)) (h3 (e11))) = (h3 (op1 (e13) (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H430.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_Hd1.
% 29.69/29.86 cut (((e23) = (h3 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H27d].
% 29.69/29.86 cut (((op2 (e23) (e21)) = (op2 (h3 (e13)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H431].
% 29.69/29.86 congruence.
% 29.69/29.86 elim (classic ((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11))))); [ zenon_intro zenon_H42e | zenon_intro zenon_H42f ].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11)))) = ((op2 (e23) (e21)) = (op2 (h3 (e13)) (h3 (e11))))).
% 29.69/29.86 intro zenon_D_pnotp.
% 29.69/29.86 apply zenon_H431.
% 29.69/29.86 rewrite <- zenon_D_pnotp.
% 29.69/29.86 exact zenon_H42e.
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (op2 (h3 (e13)) (h3 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H42f].
% 29.69/29.86 cut (((op2 (h3 (e13)) (h3 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H432].
% 29.69/29.86 congruence.
% 29.69/29.86 cut (((h3 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H15e].
% 29.69/29.86 cut (((h3 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H228].
% 29.69/29.86 congruence.
% 29.69/29.86 apply (zenon_L124_); trivial.
% 29.69/29.86 apply (zenon_L79_); trivial.
% 29.69/29.86 apply zenon_H42f. apply refl_equal.
% 29.69/29.86 apply zenon_H42f. apply refl_equal.
% 29.69/29.86 apply (zenon_L142_); trivial.
% 29.69/29.86 apply zenon_H42f. apply refl_equal.
% 29.69/29.86 apply zenon_H42f. apply refl_equal.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H42c); [ zenon_intro zenon_H287 | zenon_intro zenon_H433 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H12 | zenon_intro zenon_H3e8 ].
% 29.69/29.86 apply (zenon_L1_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e8); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3e9 ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_Heb. zenon_intro zenon_H16.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H15 | zenon_intro zenon_H11b ].
% 29.69/29.86 apply (zenon_L2_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H19 | zenon_intro zenon_H124 ].
% 29.69/29.86 apply (zenon_L3_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H41 | zenon_intro zenon_H117 ].
% 29.69/29.86 apply (zenon_L14_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_Hd1. zenon_intro zenon_H31.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H12d | zenon_intro zenon_H3ee ].
% 29.69/29.86 apply (zenon_L68_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f0 | zenon_intro zenon_H3ef ].
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H14f. zenon_intro zenon_H173.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6b | zenon_intro zenon_H193 ].
% 29.69/29.86 apply (zenon_L25_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H74 | zenon_intro zenon_H194 ].
% 29.69/29.86 apply (zenon_L26_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H97 | zenon_intro zenon_H195 ].
% 29.69/29.86 apply (zenon_L36_); trivial.
% 29.69/29.86 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H9c. zenon_intro zenon_H88.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H25b | zenon_intro zenon_H434 ].
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H131 | zenon_intro zenon_H149 ].
% 29.69/29.86 apply (zenon_L134_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H2b | zenon_intro zenon_H14a ].
% 29.69/29.86 exact (zenon_H31 zenon_H2b).
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H13b | zenon_intro zenon_H142 ].
% 29.69/29.86 apply (zenon_L71_); trivial.
% 29.69/29.86 apply (zenon_L72_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H434); [ zenon_intro zenon_H283 | zenon_intro zenon_H435 ].
% 29.69/29.86 apply (zenon_L143_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H435); [ zenon_intro zenon_H289 | zenon_intro zenon_H142 ].
% 29.69/29.86 apply (zenon_L146_); trivial.
% 29.69/29.86 apply (zenon_L72_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3ef); [ zenon_intro zenon_H18a | zenon_intro zenon_H191 ].
% 29.69/29.86 apply (zenon_L89_); trivial.
% 29.69/29.86 apply (zenon_L92_); trivial.
% 29.69/29.86 apply (zenon_or_s _ _ zenon_H3e9); [ zenon_intro zenon_H12a | zenon_intro zenon_H12c ].
% 29.69/29.86 apply (zenon_L66_); trivial.
% 29.69/29.86 apply (zenon_L67_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H433); [ zenon_intro zenon_H2a0 | zenon_intro zenon_H436 ].
% 29.69/29.86 apply (zenon_L150_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H436); [ zenon_intro zenon_H438 | zenon_intro zenon_H437 ].
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H438). zenon_intro zenon_H99. zenon_intro zenon_H439.
% 29.69/29.86 apply (zenon_L37_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H437); [ zenon_intro zenon_H43b | zenon_intro zenon_H43a ].
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H43b). zenon_intro zenon_H43d. zenon_intro zenon_H43c.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H43c). zenon_intro zenon_H15e. zenon_intro zenon_H43e.
% 29.69/29.86 apply (zenon_L79_); trivial.
% 29.69/29.86 apply (zenon_notand_s _ _ zenon_H43a); [ zenon_intro zenon_H43f | zenon_intro zenon_H2aa ].
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H43f). zenon_intro zenon_H441. zenon_intro zenon_H440.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H440). zenon_intro zenon_H443. zenon_intro zenon_H442.
% 29.69/29.86 apply (zenon_notor_s _ _ zenon_H442). zenon_intro zenon_H20a. zenon_intro zenon_H444.
% 29.69/29.86 exact (zenon_H20a zenon_H164).
% 29.69/29.86 apply (zenon_L151_); trivial.
% 29.69/29.86 Qed.
% 29.69/29.86 % SZS output end Proof
% 29.69/29.86 (* END-PROOF *)
% 29.69/29.86 nodes searched: 1389613
% 29.69/29.86 max branch formulas: 1889
% 29.69/29.86 proof nodes created: 14201
% 29.69/29.86 formulas created: 673976
% 29.69/29.86
%------------------------------------------------------------------------------