TSTP Solution File: ALG138+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 18:30:13 EDT 2022
% Result : Unsatisfiable 0.92s 1.14s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 11:41:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.14 (* PROOF-FOUND *)
% 0.92/1.14 % SZS status Unsatisfiable
% 0.92/1.14 (* BEGIN-PROOF *)
% 0.92/1.14 % SZS output start Proof
% 0.92/1.14 Theorem zenon_thm : False.
% 0.92/1.14 Proof.
% 0.92/1.14 assert (zenon_L1_ : (~((e0) = (e0))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H1d.
% 0.92/1.14 apply zenon_H1d. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L1_ *)
% 0.92/1.14 assert (zenon_L2_ : (~((e2) = (e2))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H1e.
% 0.92/1.14 apply zenon_H1e. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L2_ *)
% 0.92/1.14 assert (zenon_L3_ : (~((e1) = (e1))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H1f.
% 0.92/1.14 apply zenon_H1f. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L3_ *)
% 0.92/1.14 assert (zenon_L4_ : ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H20 zenon_H21.
% 0.92/1.14 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.92/1.14 apply zenon_H23. apply sym_equal. exact zenon_H21.
% 0.92/1.14 elim (classic ((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ].
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2))) = ((e1) = (op (op (e3) (e2)) (e2)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H22.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H24.
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H26].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e0) (e2)) = (e1)) = ((op (op (e3) (e2)) (e2)) = (e1))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H26.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H20.
% 0.92/1.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 0.92/1.14 cut (((op (e0) (e2)) = (op (op (e3) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27].
% 0.92/1.14 congruence.
% 0.92/1.14 elim (classic ((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ].
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e3) (e2)) (e2)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H27.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H24.
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (op (op (e3) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 0.92/1.14 cut (((op (op (e3) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 0.92/1.14 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 0.92/1.14 congruence.
% 0.92/1.14 exact (zenon_H29 zenon_H21).
% 0.92/1.14 apply zenon_H1e. apply refl_equal.
% 0.92/1.14 apply zenon_H25. apply refl_equal.
% 0.92/1.14 apply zenon_H25. apply refl_equal.
% 0.92/1.14 apply zenon_H1f. apply refl_equal.
% 0.92/1.14 apply zenon_H25. apply refl_equal.
% 0.92/1.14 apply zenon_H25. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L4_ *)
% 0.92/1.14 assert (zenon_L5_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H2a zenon_H20 zenon_H2b.
% 0.92/1.14 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H2a.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H20.
% 0.92/1.14 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 0.92/1.14 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H2d. apply refl_equal.
% 0.92/1.14 apply zenon_H2c. apply sym_equal. exact zenon_H2b.
% 0.92/1.14 (* end of lemma zenon_L5_ *)
% 0.92/1.14 assert (zenon_L6_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H2e zenon_H2f zenon_H30.
% 0.92/1.14 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H2e.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H2f.
% 0.92/1.14 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 0.92/1.14 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H32. apply refl_equal.
% 0.92/1.14 apply zenon_H31. apply sym_equal. exact zenon_H30.
% 0.92/1.14 (* end of lemma zenon_L6_ *)
% 0.92/1.14 assert (zenon_L7_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H33 zenon_H34 zenon_H35.
% 0.92/1.14 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H35.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H36.
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H38].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H38.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H33.
% 0.92/1.14 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 apply zenon_H39. apply sym_equal. exact zenon_H34.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L7_ *)
% 0.92/1.14 assert (zenon_L8_ : (~((e3) = (e3))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H3a.
% 0.92/1.14 apply zenon_H3a. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L8_ *)
% 0.92/1.14 assert (zenon_L9_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H3b zenon_H3c.
% 0.92/1.14 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 0.92/1.14 apply zenon_H3e. apply sym_equal. exact zenon_H3c.
% 0.92/1.14 elim (classic ((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ].
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3))) = ((e1) = (op (op (e2) (e3)) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H3d.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H3f.
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H41].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e0) (e3)) = (e1)) = ((op (op (e2) (e3)) (e3)) = (e1))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H41.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H3b.
% 0.92/1.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 0.92/1.14 cut (((op (e0) (e3)) = (op (op (e2) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H42].
% 0.92/1.14 congruence.
% 0.92/1.14 elim (classic ((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ].
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e2) (e3)) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H42.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H3f.
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (op (op (e2) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.92/1.14 cut (((op (op (e2) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H43].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H3a].
% 0.92/1.14 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H44].
% 0.92/1.14 congruence.
% 0.92/1.14 exact (zenon_H44 zenon_H3c).
% 0.92/1.14 apply zenon_H3a. apply refl_equal.
% 0.92/1.14 apply zenon_H40. apply refl_equal.
% 0.92/1.14 apply zenon_H40. apply refl_equal.
% 0.92/1.14 apply zenon_H1f. apply refl_equal.
% 0.92/1.14 apply zenon_H40. apply refl_equal.
% 0.92/1.14 apply zenon_H40. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L9_ *)
% 0.92/1.14 assert (zenon_L10_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H45 zenon_H3b zenon_H46.
% 0.92/1.14 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H45.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H3b.
% 0.92/1.14 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 0.92/1.14 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H48. apply refl_equal.
% 0.92/1.14 apply zenon_H47. apply sym_equal. exact zenon_H46.
% 0.92/1.14 (* end of lemma zenon_L10_ *)
% 0.92/1.14 assert (zenon_L11_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H49 zenon_H2f zenon_H4a.
% 0.92/1.14 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H49.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H2f.
% 0.92/1.14 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b].
% 0.92/1.14 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H32. apply refl_equal.
% 0.92/1.14 apply zenon_H4b. apply sym_equal. exact zenon_H4a.
% 0.92/1.14 (* end of lemma zenon_L11_ *)
% 0.92/1.14 assert (zenon_L12_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False).
% 0.92/1.14 do 0 intro. intros zenon_H33 zenon_H4c zenon_H4d.
% 0.92/1.14 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H4d.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H36.
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4e].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H4e.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_H33.
% 0.92/1.14 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 0.92/1.14 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 apply zenon_H4f. apply sym_equal. exact zenon_H4c.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 apply zenon_H37. apply refl_equal.
% 0.92/1.14 (* end of lemma zenon_L12_ *)
% 0.92/1.14 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H51. zenon_intro zenon_H50.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H53. zenon_intro zenon_H52.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H59. zenon_intro zenon_H58.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c.
% 0.92/1.14 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 0.92/1.14 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H79. zenon_intro zenon_H78.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7d. zenon_intro zenon_H7c.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8d. zenon_intro zenon_H8c.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H2a. zenon_intro zenon_H90.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H2e. zenon_intro zenon_H95.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H45. zenon_intro zenon_H98.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9e. zenon_intro zenon_H9d.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H4d. zenon_intro zenon_H9f.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_H9f). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Ha8). zenon_intro zenon_Hab. zenon_intro zenon_Haa.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Had. zenon_intro zenon_Hac.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hac). zenon_intro zenon_Haf. zenon_intro zenon_Hae.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Hb1. zenon_intro zenon_Hb0.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hb0). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_Hb9. zenon_intro zenon_Hb8.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hb8). zenon_intro zenon_Hbb. zenon_intro zenon_Hba.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbd. zenon_intro zenon_Hbc.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbf. zenon_intro zenon_Hbe.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hbe). zenon_intro zenon_Hc1. zenon_intro zenon_Hc0.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_H49. zenon_intro zenon_Hc2.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hc4. zenon_intro zenon_Hc3.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc5.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_Hca. zenon_intro zenon_Hc9.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hcb. zenon_intro zenon_H35.
% 0.92/1.14 apply (zenon_and_s _ _ ax4). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 0.92/1.14 apply (zenon_and_s _ _ ax5). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 0.92/1.14 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_H2f. zenon_intro zenon_H33.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd2 ].
% 0.92/1.14 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_H1f ].
% 0.92/1.14 cut (((e1) = (e1)) = ((e0) = (e1))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_Hcd.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_Hd4.
% 0.92/1.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 0.92/1.14 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e0) (e0)) = (e0)) = ((e1) = (e0))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_Hd5.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_Hcf.
% 0.92/1.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 0.92/1.14 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hd6].
% 0.92/1.14 congruence.
% 0.92/1.14 exact (zenon_Hd6 zenon_Hd3).
% 0.92/1.14 apply zenon_H1d. apply refl_equal.
% 0.92/1.14 apply zenon_H1f. apply refl_equal.
% 0.92/1.14 apply zenon_H1f. apply refl_equal.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd7 ].
% 0.92/1.14 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ].
% 0.92/1.14 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_H81.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_Hd9.
% 0.92/1.14 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 0.92/1.14 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 0.92/1.14 congruence.
% 0.92/1.14 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))).
% 0.92/1.14 intro zenon_D_pnotp.
% 0.92/1.14 apply zenon_Hdb.
% 0.92/1.14 rewrite <- zenon_D_pnotp.
% 0.92/1.14 exact zenon_Hd1.
% 0.92/1.14 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdc].
% 0.92/1.14 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 0.92/1.14 congruence.
% 0.92/1.14 apply zenon_Hda. apply refl_equal.
% 0.92/1.14 apply zenon_Hdc. apply sym_equal. exact zenon_Hd8.
% 0.92/1.14 apply zenon_Hda. apply refl_equal.
% 0.92/1.14 apply zenon_Hda. apply refl_equal.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_H20 | zenon_intro zenon_H3b ].
% 0.92/1.14 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H21 | zenon_intro zenon_Hdd ].
% 0.92/1.14 apply (zenon_L4_); trivial.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H2b | zenon_intro zenon_Hde ].
% 0.92/1.14 apply (zenon_L5_); trivial.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H30 | zenon_intro zenon_H34 ].
% 0.92/1.14 apply (zenon_L6_); trivial.
% 0.92/1.14 apply (zenon_L7_); trivial.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H3c | zenon_intro zenon_Hdf ].
% 0.92/1.14 apply (zenon_L9_); trivial.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H46 | zenon_intro zenon_He0 ].
% 0.92/1.14 apply (zenon_L10_); trivial.
% 0.92/1.14 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H4a | zenon_intro zenon_H4c ].
% 0.92/1.14 apply (zenon_L11_); trivial.
% 0.92/1.14 apply (zenon_L12_); trivial.
% 0.92/1.14 Qed.
% 0.92/1.14 % SZS output end Proof
% 0.92/1.14 (* END-PROOF *)
% 0.92/1.14 nodes searched: 18402
% 0.92/1.14 max branch formulas: 275
% 0.92/1.14 proof nodes created: 916
% 0.92/1.14 formulas created: 9399
% 0.92/1.14
%------------------------------------------------------------------------------