TSTP Solution File: LCL893+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 : Sun Jul 17 16:25:37 EDT 2022
% Result : Theorem 13.88s 14.07s
% Output : Proof 13.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 02:32:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 13.88/14.07 (* PROOF-FOUND *)
% 13.88/14.07 % SZS status Theorem
% 13.88/14.07 (* BEGIN-PROOF *)
% 13.88/14.07 % SZS output start Proof
% 13.88/14.07 Theorem goals_15 : (forall X17 : zenon_U, (((h X17) = X17)->(X17 = (0)))).
% 13.88/14.07 Proof.
% 13.88/14.07 assert (zenon_L1_ : forall (zenon_TX17_s : zenon_U), ((>= (+ zenon_TX17_s (0)) zenon_TX17_s)<->(>= (0) (==> zenon_TX17_s zenon_TX17_s))) -> (~(>= (0) (==> zenon_TX17_s zenon_TX17_s))) -> ((+ zenon_TX17_s (0)) = zenon_TX17_s) -> False).
% 13.88/14.07 do 1 intro. intros zenon_Hf zenon_H10 zenon_H11.
% 13.88/14.07 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H15; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 13.88/14.07 generalize (sos_05 (+ zenon_TX17_s (0))). zenon_intro zenon_H16.
% 13.88/14.07 cut ((>= (+ zenon_TX17_s (0)) (+ zenon_TX17_s (0))) = (>= (+ zenon_TX17_s (0)) zenon_TX17_s)).
% 13.88/14.07 intro zenon_D_pnotp.
% 13.88/14.07 apply zenon_H15.
% 13.88/14.07 rewrite <- zenon_D_pnotp.
% 13.88/14.07 exact zenon_H16.
% 13.88/14.07 cut (((+ zenon_TX17_s (0)) = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H17].
% 13.88/14.07 cut (((+ zenon_TX17_s (0)) = (+ zenon_TX17_s (0)))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 13.88/14.07 congruence.
% 13.88/14.07 apply zenon_H18. apply refl_equal.
% 13.88/14.07 exact (zenon_H17 zenon_H11).
% 13.88/14.07 exact (zenon_H10 zenon_H13).
% 13.88/14.07 (* end of lemma zenon_L1_ *)
% 13.88/14.07 assert (zenon_L2_ : (~((0) = (0))) -> False).
% 13.88/14.07 do 0 intro. intros zenon_H19.
% 13.88/14.07 apply zenon_H19. apply refl_equal.
% 13.88/14.07 (* end of lemma zenon_L2_ *)
% 13.88/14.07 assert (zenon_L3_ : forall (zenon_TX17_s : zenon_U), (~((==> zenon_TX17_s zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))) -> ((h zenon_TX17_s) = zenon_TX17_s) -> False).
% 13.88/14.07 do 1 intro. intros zenon_H1a zenon_H1b.
% 13.88/14.07 cut ((zenon_TX17_s = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 13.88/14.07 cut ((zenon_TX17_s = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 13.88/14.07 congruence.
% 13.88/14.07 apply zenon_H1d. apply sym_equal. exact zenon_H1b.
% 13.88/14.07 apply zenon_H1c. apply refl_equal.
% 13.88/14.07 (* end of lemma zenon_L3_ *)
% 13.88/14.07 assert (zenon_L4_ : forall (zenon_TX17_s : zenon_U), ((+ zenon_TX17_s (0)) = zenon_TX17_s) -> (~(>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))) -> ((h zenon_TX17_s) = zenon_TX17_s) -> False).
% 13.88/14.07 do 1 intro. intros zenon_H11 zenon_H1e zenon_H1b.
% 13.88/14.07 generalize (sos_08 zenon_TX17_s). zenon_intro zenon_H1f.
% 13.88/14.07 generalize (zenon_H1f (0)). zenon_intro zenon_H20.
% 13.88/14.07 generalize (zenon_H20 zenon_TX17_s). zenon_intro zenon_Hf.
% 13.88/14.07 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H15; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 13.88/14.07 apply (zenon_L1_ zenon_TX17_s); trivial.
% 13.88/14.07 cut ((>= (0) (==> zenon_TX17_s zenon_TX17_s)) = (>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))).
% 13.88/14.07 intro zenon_D_pnotp.
% 13.88/14.07 apply zenon_H1e.
% 13.88/14.07 rewrite <- zenon_D_pnotp.
% 13.88/14.07 exact zenon_H13.
% 13.88/14.07 cut (((==> zenon_TX17_s zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 13.88/14.07 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 13.88/14.07 congruence.
% 13.88/14.07 apply zenon_H19. apply refl_equal.
% 13.88/14.07 apply (zenon_L3_ zenon_TX17_s); trivial.
% 13.88/14.07 (* end of lemma zenon_L4_ *)
% 13.88/14.07 apply NNPP. intro zenon_G.
% 13.88/14.07 apply (zenon_notallex_s (fun X17 : zenon_U => (((h X17) = X17)->(X17 = (0)))) zenon_G); [ zenon_intro zenon_H21; idtac ].
% 13.88/14.07 elim zenon_H21. zenon_intro zenon_TX17_s. zenon_intro zenon_H22.
% 13.88/14.07 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H1b. zenon_intro zenon_H23.
% 13.88/14.07 generalize (sos_07 (0)). zenon_intro zenon_H24.
% 13.88/14.07 generalize (sos_09 zenon_TX17_s). zenon_intro zenon_H25.
% 13.88/14.07 generalize (zenon_H24 zenon_TX17_s). zenon_intro zenon_H26.
% 13.88/14.07 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 13.88/14.07 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 13.88/14.07 elim (classic (>= (0) (h zenon_TX17_s))); [ zenon_intro zenon_H2b | zenon_intro zenon_H2c ].
% 13.88/14.07 cut ((>= (0) (h zenon_TX17_s)) = (>= (0) zenon_TX17_s)).
% 13.88/14.07 intro zenon_D_pnotp.
% 13.88/14.07 apply zenon_H2a.
% 13.88/14.07 rewrite <- zenon_D_pnotp.
% 13.88/14.07 exact zenon_H2b.
% 13.88/14.07 cut (((h zenon_TX17_s) = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 13.88/14.07 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 13.88/14.07 congruence.
% 13.88/14.07 apply zenon_H19. apply refl_equal.
% 13.88/14.07 exact (zenon_H2d zenon_H1b).
% 13.88/14.07 generalize (sos_14 zenon_TX17_s). zenon_intro zenon_H2e.
% 13.88/14.07 elim (classic ((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ].
% 13.88/14.08 elim (classic (>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))); [ zenon_intro zenon_H31 | zenon_intro zenon_H1e ].
% 13.88/14.08 cut ((>= (0) (==> (h zenon_TX17_s) zenon_TX17_s)) = (>= (0) (h zenon_TX17_s))).
% 13.88/14.08 intro zenon_D_pnotp.
% 13.88/14.08 apply zenon_H2c.
% 13.88/14.08 rewrite <- zenon_D_pnotp.
% 13.88/14.08 exact zenon_H31.
% 13.88/14.08 cut (((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 13.88/14.08 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 13.88/14.08 congruence.
% 13.88/14.08 apply zenon_H19. apply refl_equal.
% 13.88/14.08 exact (zenon_H30 zenon_H2f).
% 13.88/14.08 generalize (sos_03 zenon_TX17_s). zenon_intro zenon_H11.
% 13.88/14.08 apply (zenon_L4_ zenon_TX17_s); trivial.
% 13.88/14.08 elim (classic ((h zenon_TX17_s) = (h zenon_TX17_s))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ].
% 13.88/14.08 cut (((h zenon_TX17_s) = (h zenon_TX17_s)) = ((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))).
% 13.88/14.08 intro zenon_D_pnotp.
% 13.88/14.08 apply zenon_H30.
% 13.88/14.08 rewrite <- zenon_D_pnotp.
% 13.88/14.08 exact zenon_H32.
% 13.88/14.08 cut (((h zenon_TX17_s) = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H33].
% 13.88/14.08 cut (((h zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 13.88/14.08 congruence.
% 13.88/14.08 exact (zenon_H34 zenon_H2e).
% 13.88/14.08 apply zenon_H33. apply refl_equal.
% 13.88/14.08 apply zenon_H33. apply refl_equal.
% 13.88/14.08 exact (zenon_H29 zenon_H25).
% 13.88/14.08 apply zenon_H23. apply sym_equal. exact zenon_H27.
% 13.88/14.08 Qed.
% 13.88/14.08 % SZS output end Proof
% 13.88/14.08 (* END-PROOF *)
% 13.88/14.08 nodes searched: 1173125
% 13.88/14.08 max branch formulas: 8785
% 13.88/14.08 proof nodes created: 3299
% 13.88/14.08 formulas created: 221950
% 13.88/14.08
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